includes/clientside/static/libbigint.js
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////////////////////////////////////////////////////////////////////////////////////////
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// Big Integer Library v. 5.1
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// Created 2000, last modified 2007
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// Leemon Baird
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// www.leemon.com
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//
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// Version history:
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//
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// v 5.1  8 Oct 2007 
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//   - renamed inverseModInt_ to inverseModInt since it doesn't change its parameters
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//   - added functions GCD and randBigInt, which call GCD_ and randBigInt_
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//   - fixed a bug found by Rob Visser (see comment with his name below)
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//   - improved comments
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//
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// This file is public domain.   You can use it for any purpose without restriction.
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// I do not guarantee that it is correct, so use it at your own risk.  If you use 
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// it for something interesting, I'd appreciate hearing about it.  If you find 
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// any bugs or make any improvements, I'd appreciate hearing about those too.
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// It would also be nice if my name and address were left in the comments.
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// But none of that is required.
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//
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// This code defines a bigInt library for arbitrary-precision integers.
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// A bigInt is an array of integers storing the value in chunks of bpe bits, 
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// little endian (buff[0] is the least significant word).
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// Negative bigInts are stored two's complement.
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// Some functions assume their parameters have at least one leading zero element.
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// Functions with an underscore at the end of the name have unpredictable behavior in case of overflow, 
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// so the caller must make sure the arrays must be big enough to hold the answer.
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// For each function where a parameter is modified, that same 
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// variable must not be used as another argument too.
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// So, you cannot square x by doing multMod_(x,x,n).  
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// You must use squareMod_(x,n) instead, or do y=dup(x); multMod_(x,y,n).
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//
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// These functions are designed to avoid frequent dynamic memory allocation in the inner loop.
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// For most functions, if it needs a BigInt as a local variable it will actually use
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// a global, and will only allocate to it only when it's not the right size.  This ensures
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// that when a function is called repeatedly with same-sized parameters, it only allocates
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// memory on the first call.
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//
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// Note that for cryptographic purposes, the calls to Math.random() must 
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// be replaced with calls to a better pseudorandom number generator.
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//
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// In the following, "bigInt" means a bigInt with at least one leading zero element,
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// and "integer" means a nonnegative integer less than radix.  In some cases, integer 
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// can be negative.  Negative bigInts are 2s complement.
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// 
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// The following functions do not modify their inputs.
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// Those returning a bigInt, string, or Array will dynamically allocate memory for that value.
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// Those returning a boolean will return the integer 0 (false) or 1 (true).
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// Those returning boolean or int will not allocate memory except possibly on the first time they're called with a given parameter size.
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// 
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// bigInt  add(x,y)               //return (x+y) for bigInts x and y.  
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// bigInt  addInt(x,n)            //return (x+n) where x is a bigInt and n is an integer.
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// string  bigInt2str(x,base)     //return a string form of bigInt x in a given base, with 2 <= base <= 95
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// int     bitSize(x)             //return how many bits long the bigInt x is, not counting leading zeros
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// bigInt  dup(x)                 //return a copy of bigInt x
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// boolean equals(x,y)            //is the bigInt x equal to the bigint y?
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// boolean equalsInt(x,y)         //is bigint x equal to integer y?
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// bigInt  expand(x,n)            //return a copy of x with at least n elements, adding leading zeros if needed
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// Array   findPrimes(n)          //return array of all primes less than integer n
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// bigInt  GCD(x,y)               //return greatest common divisor of bigInts x and y (each with same number of elements).
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// boolean greater(x,y)           //is x>y?  (x and y are nonnegative bigInts)
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// boolean greaterShift(x,y,shift)//is (x <<(shift*bpe)) > y?
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// bigInt  int2bigInt(t,n,m)      //return a bigInt equal to integer t, with at least n bits and m array elements
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// bigInt  inverseMod(x,n)        //return (x**(-1) mod n) for bigInts x and n.  If no inverse exists, it returns null
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// int     inverseModInt(x,n)     //return x**(-1) mod n, for integers x and n.  Return 0 if there is no inverse
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// boolean isZero(x)              //is the bigInt x equal to zero?
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// boolean millerRabin(x,b)       //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime (as opposed to definitely composite)?
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// bigInt  mod(x,n)               //return a new bigInt equal to (x mod n) for bigInts x and n.
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// int     modInt(x,n)            //return x mod n for bigInt x and integer n.
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// bigInt  mult(x,y)              //return x*y for bigInts x and y. This is faster when y<x.
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// bigInt  multMod(x,y,n)         //return (x*y mod n) for bigInts x,y,n.  For greater speed, let y<x.
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// boolean negative(x)            //is bigInt x negative?
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// bigInt  powMod(x,y,n)          //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation.  0**0=1. Faster for odd n.
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// bigInt  randBigInt(n,s)        //return an n-bit random BigInt (n>=1).  If s=1, then the most significant of those n bits is set to 1.
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// bigInt  randTruePrime(k)       //return a new, random, k-bit, true prime bigInt using Maurer's algorithm.
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// bigInt  str2bigInt(s,b,n,m)    //return a bigInt for number represented in string s in base b with at least n bits and m array elements
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// bigInt  sub(x,y)               //return (x-y) for bigInts x and y.  Negative answers will be 2s complement
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// bigInt  bigint_trim(x,k)              //return a copy of x with exactly k leading zero elements
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//
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//
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// The following functions each have a non-underscored version, which most users should call instead.
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// These functions each write to a single parameter, and the caller is responsible for ensuring the array 
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// passed in is large enough to hold the result. 
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//
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// void    addInt_(x,n)          //do x=x+n where x is a bigInt and n is an integer
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// void    add_(x,y)             //do x=x+y for bigInts x and y
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// void    copy_(x,y)            //do x=y on bigInts x and y
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// void    copyInt_(x,n)         //do x=n on bigInt x and integer n
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// void    GCD_(x,y)             //set x to the greatest common divisor of bigInts x and y, (y is destroyed).  (This never overflows its array).
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// boolean inverseMod_(x,n)      //do x=x**(-1) mod n, for bigInts x and n. Returns 1 (0) if inverse does (doesn't) exist
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// void    mod_(x,n)             //do x=x mod n for bigInts x and n. (This never overflows its array).
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// void    mult_(x,y)            //do x=x*y for bigInts x and y.
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// void    multMod_(x,y,n)       //do x=x*y  mod n for bigInts x,y,n.
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// void    powMod_(x,y,n)        //do x=x**y mod n, where x,y,n are bigInts (n is odd) and ** is exponentiation.  0**0=1.
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// void    randBigInt_(b,n,s)    //do b = an n-bit random BigInt. if s=1, then nth bit (most significant bit) is set to 1. n>=1.
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// void    randTruePrime_(ans,k) //do ans = a random k-bit true random prime (not just probable prime) with 1 in the msb.
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// void    sub_(x,y)             //do x=x-y for bigInts x and y. Negative answers will be 2s complement.
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//
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// The following functions do NOT have a non-underscored version. 
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// They each write a bigInt result to one or more parameters.  The caller is responsible for
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// ensuring the arrays passed in are large enough to hold the results. 
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//
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// void addShift_(x,y,ys)       //do x=x+(y<<(ys*bpe))
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// void carry_(x)               //do carries and borrows so each element of the bigInt x fits in bpe bits.
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// void divide_(x,y,q,r)        //divide x by y giving quotient q and remainder r
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// int  divInt_(x,n)            //do x=floor(x/n) for bigInt x and integer n, and return the remainder. (This never overflows its array).
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// int  eGCD_(x,y,d,a,b)        //sets a,b,d to positive bigInts such that d = GCD_(x,y) = a*x-b*y
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// void halve_(x)               //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement.  (This never overflows its array).
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// void leftShift_(x,n)         //left shift bigInt x by n bits.  n<bpe.
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// void linComb_(x,y,a,b)       //do x=a*x+b*y for bigInts x and y and integers a and b
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// void linCombShift_(x,y,b,ys) //do x=x+b*(y<<(ys*bpe)) for bigInts x and y, and integers b and ys
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// void mont_(x,y,n,np)         //Montgomery multiplication (see comments where the function is defined)
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// void multInt_(x,n)           //do x=x*n where x is a bigInt and n is an integer.
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// void rightShift_(x,n)        //right shift bigInt x by n bits.  0 <= n < bpe. (This never overflows its array).
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// void squareMod_(x,n)         //do x=x*x  mod n for bigInts x,n
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// void subShift_(x,y,ys)       //do x=x-(y<<(ys*bpe)). Negative answers will be 2s complement.
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//
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// The following functions are based on algorithms from the _Handbook of Applied Cryptography_
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//    powMod_()           = algorithm 14.94, Montgomery exponentiation
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//    eGCD_,inverseMod_() = algorithm 14.61, Binary extended GCD_
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//    GCD_()              = algorothm 14.57, Lehmer's algorithm
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//    mont_()             = algorithm 14.36, Montgomery multiplication
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//    divide_()           = algorithm 14.20  Multiple-precision division
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//    squareMod_()        = algorithm 14.16  Multiple-precision squaring
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//    randTruePrime_()    = algorithm  4.62, Maurer's algorithm
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//    millerRabin()       = algorithm  4.24, Miller-Rabin algorithm
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//
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// Profiling shows:
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//     randTruePrime_() spends:
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//         10% of its time in calls to powMod_()
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//         85% of its time in calls to millerRabin()
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//     millerRabin() spends:
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//         99% of its time in calls to powMod_()   (always with a base of 2)
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//     powMod_() spends:
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//         94% of its time in calls to mont_()  (almost always with x==y)
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//
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// This suggests there are several ways to speed up this library slightly:
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//     - convert powMod_ to use a Montgomery form of k-ary window (or maybe a Montgomery form of sliding window)
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//         -- this should especially focus on being fast when raising 2 to a power mod n
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//     - convert randTruePrime_() to use a minimum r of 1/3 instead of 1/2 with the appropriate change to the test
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//     - tune the parameters in randTruePrime_(), including c, m, and recLimit
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//     - speed up the single loop in mont_() that takes 95% of the runtime, perhaps by reducing checking
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//       within the loop when all the parameters are the same length.
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//
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// There are several ideas that look like they wouldn't help much at all:
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//     - replacing trial division in randTruePrime_() with a sieve (that speeds up something taking almost no time anyway)
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//     - increase bpe from 15 to 30 (that would help if we had a 32*32->64 multiplier, but not with JavaScript's 32*32->32)
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//     - speeding up mont_(x,y,n,np) when x==y by doing a non-modular, non-Montgomery square
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//       followed by a Montgomery reduction.  The intermediate answer will be twice as long as x, so that
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//       method would be slower.  This is unfortunate because the code currently spends almost all of its time
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//       doing mont_(x,x,...), both for randTruePrime_() and powMod_().  A faster method for Montgomery squaring
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//       would have a large impact on the speed of randTruePrime_() and powMod_().  HAC has a couple of poorly-worded
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//       sentences that seem to imply it's faster to do a non-modular square followed by a single
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//       Montgomery reduction, but that's obviously wrong.
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////////////////////////////////////////////////////////////////////////////////////////
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//globals
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bpe=0;         //bits stored per array element
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mask=0;        //AND this with an array element to chop it down to bpe bits
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radix=mask+1;  //equals 2^bpe.  A single 1 bit to the left of the last bit of mask.
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//the digits for converting to different bases
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digitsStr='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-';
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//initialize the global variables
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for (bpe=0; (1<<(bpe+1)) > (1<<bpe); bpe++);  //bpe=number of bits in the mantissa on this platform
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bpe>>=1;                   //bpe=number of bits in one element of the array representing the bigInt
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mask=(1<<bpe)-1;           //AND the mask with an integer to get its bpe least significant bits
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radix=mask+1;              //2^bpe.  a single 1 bit to the left of the first bit of mask
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one=int2bigInt(1,1,1);     //constant used in powMod_()
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//the following global variables are scratchpad memory to 
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//reduce dynamic memory allocation in the inner loop
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t=new Array(0);
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ss=t;       //used in mult_()
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s0=t;       //used in multMod_(), squareMod_() 
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s1=t;       //used in powMod_(), multMod_(), squareMod_() 
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s2=t;       //used in powMod_(), multMod_()
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s3=t;       //used in powMod_()
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s4=t; s5=t; //used in mod_()
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s6=t;       //used in bigInt2str()
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s7=t;       //used in powMod_()
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T=t;        //used in GCD_()
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sa=t;       //used in mont_()
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mr_x1=t; mr_r=t; mr_a=t;                                      //used in millerRabin()
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eg_v=t; eg_u=t; eg_A=t; eg_B=t; eg_C=t; eg_D=t;               //used in eGCD_(), inverseMod_()
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md_q1=t; md_q2=t; md_q3=t; md_r=t; md_r1=t; md_r2=t; md_tt=t; //used in mod_()
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primes=t; pows=t; s_i=t; s_i2=t; s_R=t; s_rm=t; s_q=t; s_n1=t; 
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  s_a=t; s_r2=t; s_n=t; s_b=t; s_d=t; s_x1=t; s_x2=t, s_aa=t; //used in randTruePrime_()
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////////////////////////////////////////////////////////////////////////////////////////
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//return array of all primes less than integer n
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function findPrimes(n) {
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  var i,s,p,ans;
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  s=new Array(n);
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  for (i=0;i<n;i++)
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    s[i]=0;
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  s[0]=2;
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  p=0;    //first p elements of s are primes, the rest are a sieve
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  for(;s[p]<n;) {                  //s[p] is the pth prime
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    for(i=s[p]*s[p]; i<n; i+=s[p]) //mark multiples of s[p]
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      s[i]=1;
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    p++;
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    s[p]=s[p-1]+1;
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    for(; s[p]<n && s[s[p]]; s[p]++); //find next prime (where s[p]==0)
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  }
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  ans=new Array(p);
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  for(i=0;i<p;i++)
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    ans[i]=s[i];
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  return ans;
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}
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//does a single round of Miller-Rabin base b consider x to be a possible prime?
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//x is a bigInt, and b is an integer
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function millerRabin(x,b) {
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  var i,j,k,s;
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  if (mr_x1.length!=x.length) {
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    mr_x1=dup(x);
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    mr_r=dup(x);
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    mr_a=dup(x);
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  }
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  copyInt_(mr_a,b);
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  copy_(mr_r,x);
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  copy_(mr_x1,x);
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  addInt_(mr_r,-1);
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  addInt_(mr_x1,-1);
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  //s=the highest power of two that divides mr_r
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  k=0;
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  for (i=0;i<mr_r.length;i++)
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    for (j=1;j<mask;j<<=1)
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      if (x[i] & j) {
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        s=(k<mr_r.length+bpe ? k : 0); 
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         i=mr_r.length;
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         j=mask;
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      } else
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        k++;
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  if (s)                
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    rightShift_(mr_r,s);
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  powMod_(mr_a,mr_r,x);
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  if (!equalsInt(mr_a,1) && !equals(mr_a,mr_x1)) {
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    j=1;
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    while (j<=s-1 && !equals(mr_a,mr_x1)) {
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      squareMod_(mr_a,x);
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      if (equalsInt(mr_a,1)) {
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        return 0;
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      }
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      j++;
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    }
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    if (!equals(mr_a,mr_x1)) {
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      return 0;
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    }
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  }
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  return 1;  
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}
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//returns how many bits long the bigInt is, not counting leading zeros.
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function bitSize(x) {
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  var j,z,w;
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  for (j=x.length-1; (x[j]==0) && (j>0); j--);
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  for (z=0,w=x[j]; w; (w>>=1),z++);
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  z+=bpe*j;
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parents:
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   272
  return z;
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   273
}
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   274
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   275
//return a copy of x with at least n elements, adding leading zeros if needed
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parents:
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   276
function expand(x,n) {
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parents:
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   277
  var ans=int2bigInt(0,(x.length>n ? x.length : n)*bpe,0);
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parents:
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   278
  copy_(ans,x);
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parents:
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   279
  return ans;
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parents:
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   280
}
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   281
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parents:
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   282
//return a k-bit true random prime using Maurer's algorithm.
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parents:
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   283
function randTruePrime(k) {
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parents:
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   284
  var ans=int2bigInt(0,k,0);
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parents:
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   285
  randTruePrime_(ans,k);
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Dan
parents:
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   286
  return bigint_trim(ans,1);
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parents:
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   287
}
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   288
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parents:
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   289
//return a new bigInt equal to (x mod n) for bigInts x and n.
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parents:
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   290
function mod(x,n) {
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Dan
parents:
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   291
  var ans=dup(x);
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Dan
parents:
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   292
  mod_(ans,n);
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Dan
parents:
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   293
  return bigint_trim(ans,1);
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Dan
parents:
diff changeset
   294
}
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parents:
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   295
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Dan
parents:
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   296
//return (x+n) where x is a bigInt and n is an integer.
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parents:
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   297
function addInt(x,n) {
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Dan
parents:
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   298
  var ans=expand(x,x.length+1);
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parents:
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   299
  addInt_(ans,n);
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   300
  return bigint_trim(ans,1);
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parents:
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   301
}
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parents:
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   302
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Dan
parents:
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   303
//return x*y for bigInts x and y. This is faster when y<x.
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Dan
parents:
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   304
function mult(x,y) {
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Dan
parents:
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   305
  var ans=expand(x,x.length+y.length);
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Dan
parents:
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   306
  mult_(ans,y);
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Dan
parents:
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   307
  return bigint_trim(ans,1);
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Dan
parents:
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   308
}
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parents:
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   309
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parents:
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   310
//return (x**y mod n) where x,y,n are bigInts and ** is exponentiation.  0**0=1. Faster for odd n.
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parents:
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   311
function powMod(x,y,n) {
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Dan
parents:
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   312
  var ans=expand(x,n.length);  
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Dan
parents:
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   313
  powMod_(ans,bigint_trim(y,2),bigint_trim(n,2),0);  //this should work without the trim, but doesn't
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Dan
parents:
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   314
  return bigint_trim(ans,1);
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Dan
parents:
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   315
}
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Dan
parents:
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   316
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Dan
parents:
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   317
//return (x-y) for bigInts x and y.  Negative answers will be 2s complement
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Dan
parents:
diff changeset
   318
function sub(x,y) {
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Dan
parents:
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   319
  var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); 
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Dan
parents:
diff changeset
   320
  sub_(ans,y);
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Dan
parents:
diff changeset
   321
  return bigint_trim(ans,1);
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Dan
parents:
diff changeset
   322
}
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Dan
parents:
diff changeset
   323
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Dan
parents:
diff changeset
   324
//return (x+y) for bigInts x and y.  
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Dan
parents:
diff changeset
   325
function add(x,y) {
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Dan
parents:
diff changeset
   326
  var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); 
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Dan
parents:
diff changeset
   327
  add_(ans,y);
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Dan
parents:
diff changeset
   328
  return bigint_trim(ans,1);
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Dan
parents:
diff changeset
   329
}
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Dan
parents:
diff changeset
   330
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   331
//return (x**(-1) mod n) for bigInts x and n.  If no inverse exists, it returns null
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Dan
parents:
diff changeset
   332
function inverseMod(x,n) {
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Dan
parents:
diff changeset
   333
  var ans=expand(x,n.length); 
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Dan
parents:
diff changeset
   334
  var s;
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Dan
parents:
diff changeset
   335
  s=inverseMod_(ans,n);
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Dan
parents:
diff changeset
   336
  return s ? bigint_trim(ans,1) : null;
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Dan
parents:
diff changeset
   337
}
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Dan
parents:
diff changeset
   338
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   339
//return (x*y mod n) for bigInts x,y,n.  For greater speed, let y<x.
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Dan
parents:
diff changeset
   340
function multMod(x,y,n) {
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Dan
parents:
diff changeset
   341
  var ans=expand(x,n.length);
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Dan
parents:
diff changeset
   342
  multMod_(ans,y,n);
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Dan
parents:
diff changeset
   343
  return bigint_trim(ans,1);
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Dan
parents:
diff changeset
   344
}
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Dan
parents:
diff changeset
   345
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   346
//generate a k-bit true random prime using Maurer's algorithm,
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Dan
parents:
diff changeset
   347
//and put it into ans.  The bigInt ans must be large enough to hold it.
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Dan
parents:
diff changeset
   348
function randTruePrime_(ans,k) {
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Dan
parents:
diff changeset
   349
  var c,m,pm,dd,j,r,B,divisible,z,zz,recSize;
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Dan
parents:
diff changeset
   350
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Dan
parents:
diff changeset
   351
  if (primes.length==0)
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Dan
parents:
diff changeset
   352
    primes=findPrimes(30000);  //check for divisibility by primes <=30000
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Dan
parents:
diff changeset
   353
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Dan
parents:
diff changeset
   354
  if (pows.length==0) {
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Dan
parents:
diff changeset
   355
    pows=new Array(512);
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Dan
parents:
diff changeset
   356
    for (j=0;j<512;j++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   357
      pows[j]=Math.pow(2,j/511.-1.);
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Dan
parents:
diff changeset
   358
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   359
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   360
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   361
  //c and m should be tuned for a particular machine and value of k, to maximize speed
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Dan
parents:
diff changeset
   362
  c=0.1;  //c=0.1 in HAC
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Dan
parents:
diff changeset
   363
  m=20;   //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   364
  recLimit=20; //stop recursion when k <=recLimit.  Must have recLimit >= 2
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   365
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   366
  if (s_i2.length!=ans.length) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   367
    s_i2=dup(ans);
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Dan
parents:
diff changeset
   368
    s_R =dup(ans);
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Dan
parents:
diff changeset
   369
    s_n1=dup(ans);
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Dan
parents:
diff changeset
   370
    s_r2=dup(ans);
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Dan
parents:
diff changeset
   371
    s_d =dup(ans);
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Dan
parents:
diff changeset
   372
    s_x1=dup(ans);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   373
    s_x2=dup(ans);
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Dan
parents:
diff changeset
   374
    s_b =dup(ans);
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Dan
parents:
diff changeset
   375
    s_n =dup(ans);
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Dan
parents:
diff changeset
   376
    s_i =dup(ans);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   377
    s_rm=dup(ans);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   378
    s_q =dup(ans);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   379
    s_a =dup(ans);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   380
    s_aa=dup(ans);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   381
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   382
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   383
  if (k <= recLimit) {  //generate small random primes by trial division up to its square root
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   384
    pm=(1<<((k+2)>>1))-1; //pm is binary number with all ones, just over sqrt(2^k)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   385
    copyInt_(ans,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   386
    for (dd=1;dd;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   387
      dd=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   388
      ans[0]= 1 | (1<<(k-1)) | Math.floor(Math.random()*(1<<k));  //random, k-bit, odd integer, with msb 1
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   389
      for (j=1;(j<primes.length) && ((primes[j]&pm)==primes[j]);j++) { //trial division by all primes 3...sqrt(2^k)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   390
        if (0==(ans[0]%primes[j])) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   391
          dd=1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   392
          break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   393
        }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   394
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   395
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   396
    carry_(ans);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   397
    return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   398
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   399
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   400
  B=c*k*k;    //try small primes up to B (or all the primes[] array if the largest is less than B).
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   401
  if (k>2*m)  //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   402
    for (r=1; k-k*r<=m; )
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   403
      r=pows[Math.floor(Math.random()*512)];   //r=Math.pow(2,Math.random()-1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   404
  else
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   405
    r=.5;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   406
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   407
  //simulation suggests the more complex algorithm using r=.333 is only slightly faster.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   408
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   409
  recSize=Math.floor(r*k)+1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   410
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   411
  randTruePrime_(s_q,recSize);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   412
  copyInt_(s_i2,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   413
  s_i2[Math.floor((k-2)/bpe)] |= (1<<((k-2)%bpe));   //s_i2=2^(k-2)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   414
  divide_(s_i2,s_q,s_i,s_rm);                        //s_i=floor((2^(k-1))/(2q))
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   415
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   416
  z=bitSize(s_i);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   417
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   418
  for (;;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   419
    for (;;) {  //generate z-bit numbers until one falls in the range [0,s_i-1]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   420
      randBigInt_(s_R,z,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   421
      if (greater(s_i,s_R))
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   422
        break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   423
    }                //now s_R is in the range [0,s_i-1]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   424
    addInt_(s_R,1);  //now s_R is in the range [1,s_i]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   425
    add_(s_R,s_i);   //now s_R is in the range [s_i+1,2*s_i]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   426
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   427
    copy_(s_n,s_q);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   428
    mult_(s_n,s_R); 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   429
    multInt_(s_n,2);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   430
    addInt_(s_n,1);    //s_n=2*s_R*s_q+1
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   431
    
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   432
    copy_(s_r2,s_R);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   433
    multInt_(s_r2,2);  //s_r2=2*s_R
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   434
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   435
    //check s_n for divisibility by small primes up to B
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   436
    for (divisible=0,j=0; (j<primes.length) && (primes[j]<B); j++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   437
      if (modInt(s_n,primes[j])==0) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   438
        divisible=1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   439
        break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   440
      }      
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   441
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   442
    if (!divisible)    //if it passes small primes check, then try a single Miller-Rabin base 2
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   443
      if (!millerRabin(s_n,2)) //this line represents 75% of the total runtime for randTruePrime_ 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   444
        divisible=1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   445
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   446
    if (!divisible) {  //if it passes that test, continue checking s_n
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   447
      addInt_(s_n,-3);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   448
      for (j=s_n.length-1;(s_n[j]==0) && (j>0); j--);  //strip leading zeros
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   449
      for (zz=0,w=s_n[j]; w; (w>>=1),zz++);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   450
      zz+=bpe*j;                             //zz=number of bits in s_n, ignoring leading zeros
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   451
      for (;;) {  //generate z-bit numbers until one falls in the range [0,s_n-1]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   452
        randBigInt_(s_a,zz,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   453
        if (greater(s_n,s_a))
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   454
          break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   455
      }                //now s_a is in the range [0,s_n-1]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   456
      addInt_(s_n,3);  //now s_a is in the range [0,s_n-4]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   457
      addInt_(s_a,2);  //now s_a is in the range [2,s_n-2]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   458
      copy_(s_b,s_a);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   459
      copy_(s_n1,s_n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   460
      addInt_(s_n1,-1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   461
      powMod_(s_b,s_n1,s_n);   //s_b=s_a^(s_n-1) modulo s_n
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   462
      addInt_(s_b,-1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   463
      if (isZero(s_b)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   464
        copy_(s_b,s_a);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   465
        powMod_(s_b,s_r2,s_n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   466
        addInt_(s_b,-1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   467
        copy_(s_aa,s_n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   468
        copy_(s_d,s_b);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   469
        GCD_(s_d,s_n);  //if s_b and s_n are relatively prime, then s_n is a prime
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   470
        if (equalsInt(s_d,1)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   471
          copy_(ans,s_aa);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   472
          return;     //if we've made it this far, then s_n is absolutely guaranteed to be prime
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   473
        }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   474
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   475
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   476
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   477
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   478
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   479
//Return an n-bit random BigInt (n>=1).  If s=1, then the most significant of those n bits is set to 1.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   480
function randBigInt(n,s) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   481
  var a,b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   482
  a=Math.floor((n-1)/bpe)+2; //# array elements to hold the BigInt with a leading 0 element
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   483
  b=int2bigInt(0,0,a);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   484
  randBigInt_(b,n,s);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   485
  return b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   486
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   487
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   488
//Set b to an n-bit random BigInt.  If s=1, then the most significant of those n bits is set to 1.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   489
//Array b must be big enough to hold the result. Must have n>=1
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   490
function randBigInt_(b,n,s) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   491
  var i,a;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   492
  for (i=0;i<b.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   493
    b[i]=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   494
  a=Math.floor((n-1)/bpe)+1; //# array elements to hold the BigInt
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   495
  for (i=0;i<a;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   496
    b[i]=Math.floor(Math.random()*(1<<(bpe-1)));
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   497
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   498
  b[a-1] &= (2<<((n-1)%bpe))-1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   499
  if (s==1)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   500
    b[a-1] |= (1<<((n-1)%bpe));
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   501
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   502
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   503
//Return the greatest common divisor of bigInts x and y (each with same number of elements).
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   504
function GCD(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   505
  var xc,yc;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   506
  xc=dup(x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   507
  yc=dup(y);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   508
  GCD_(xc,yc);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   509
  return xc;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   510
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   511
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   512
//set x to the greatest common divisor of bigInts x and y (each with same number of elements).
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   513
//y is destroyed.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   514
function GCD_(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   515
  var i,xp,yp,A,B,C,D,q,sing;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   516
  if (T.length!=x.length)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   517
    T=dup(x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   518
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   519
  sing=1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   520
  while (sing) { //while y has nonzero elements other than y[0]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   521
    sing=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   522
    for (i=1;i<y.length;i++) //check if y has nonzero elements other than 0
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   523
      if (y[i]) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   524
        sing=1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   525
        break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   526
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   527
    if (!sing) break; //quit when y all zero elements except possibly y[0]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   528
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   529
    for (i=x.length;!x[i] && i>=0;i--);  //find most significant element of x
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   530
    xp=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   531
    yp=y[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   532
    A=1; B=0; C=0; D=1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   533
    while ((yp+C) && (yp+D)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   534
      q =Math.floor((xp+A)/(yp+C));
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   535
      qp=Math.floor((xp+B)/(yp+D));
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   536
      if (q!=qp)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   537
        break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   538
      t= A-q*C;   A=C;   C=t;    //  do (A,B,xp, C,D,yp) = (C,D,yp, A,B,xp) - q*(0,0,0, C,D,yp)      
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   539
      t= B-q*D;   B=D;   D=t;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   540
      t=xp-q*yp; xp=yp; yp=t;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   541
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   542
    if (B) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   543
      copy_(T,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   544
      linComb_(x,y,A,B); //x=A*x+B*y
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   545
      linComb_(y,T,D,C); //y=D*y+C*T
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   546
    } else {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   547
      mod_(x,y);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   548
      copy_(T,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   549
      copy_(x,y);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   550
      copy_(y,T);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   551
    } 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   552
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   553
  if (y[0]==0)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   554
    return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   555
  t=modInt(x,y[0]);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   556
  copyInt_(x,y[0]);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   557
  y[0]=t;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   558
  while (y[0]) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   559
    x[0]%=y[0];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   560
    t=x[0]; x[0]=y[0]; y[0]=t;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   561
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   562
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   563
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   564
//do x=x**(-1) mod n, for bigInts x and n.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   565
//If no inverse exists, it sets x to zero and returns 0, else it returns 1.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   566
//The x array must be at least as large as the n array.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   567
function inverseMod_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   568
  var k=1+2*Math.max(x.length,n.length);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   569
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   570
  if(!(x[0]&1)  && !(n[0]&1)) {  //if both inputs are even, then inverse doesn't exist
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   571
    copyInt_(x,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   572
    return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   573
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   574
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   575
  if (eg_u.length!=k) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   576
    eg_u=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   577
    eg_v=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   578
    eg_A=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   579
    eg_B=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   580
    eg_C=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   581
    eg_D=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   582
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   583
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   584
  copy_(eg_u,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   585
  copy_(eg_v,n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   586
  copyInt_(eg_A,1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   587
  copyInt_(eg_B,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   588
  copyInt_(eg_C,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   589
  copyInt_(eg_D,1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   590
  for (;;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   591
    while(!(eg_u[0]&1)) {  //while eg_u is even
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   592
      halve_(eg_u);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   593
      if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if eg_A==eg_B==0 mod 2
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   594
        halve_(eg_A);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   595
        halve_(eg_B);      
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   596
      } else {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   597
        add_(eg_A,n);  halve_(eg_A);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   598
        sub_(eg_B,x);  halve_(eg_B);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   599
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   600
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   601
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   602
    while (!(eg_v[0]&1)) {  //while eg_v is even
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   603
      halve_(eg_v);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   604
      if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if eg_C==eg_D==0 mod 2
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   605
        halve_(eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   606
        halve_(eg_D);      
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   607
      } else {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   608
        add_(eg_C,n);  halve_(eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   609
        sub_(eg_D,x);  halve_(eg_D);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   610
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   611
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   612
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   613
    if (!greater(eg_v,eg_u)) { //eg_v <= eg_u
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   614
      sub_(eg_u,eg_v);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   615
      sub_(eg_A,eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   616
      sub_(eg_B,eg_D);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   617
    } else {                   //eg_v > eg_u
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   618
      sub_(eg_v,eg_u);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   619
      sub_(eg_C,eg_A);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   620
      sub_(eg_D,eg_B);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   621
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   622
  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   623
    if (equalsInt(eg_u,0)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   624
      if (negative(eg_C)) //make sure answer is nonnegative
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   625
        add_(eg_C,n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   626
      copy_(x,eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   627
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   628
      if (!equalsInt(eg_v,1)) { //if GCD_(x,n)!=1, then there is no inverse
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   629
        copyInt_(x,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   630
        return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   631
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   632
      return 1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   633
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   634
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   635
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   636
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   637
//return x**(-1) mod n, for integers x and n.  Return 0 if there is no inverse
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   638
function inverseModInt(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   639
  var a=1,b=0,t;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   640
  for (;;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   641
    if (x==1) return a;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   642
    if (x==0) return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   643
    b-=a*Math.floor(n/x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   644
    n%=x;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   645
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   646
    if (n==1) return b; //to avoid negatives, change this b to n-b, and each -= to +=
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   647
    if (n==0) return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   648
    a-=b*Math.floor(x/n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   649
    x%=n;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   650
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   651
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   652
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   653
//this deprecated function is for backward compatibility only. 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   654
function inverseModInt_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   655
   return inverseModInt(x,n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   656
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   657
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   658
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   659
//Given positive bigInts x and y, change the bigints v, a, and b to positive bigInts such that:
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   660
//     v = GCD_(x,y) = a*x-b*y
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   661
//The bigInts v, a, b, must have exactly as many elements as the larger of x and y.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   662
function eGCD_(x,y,v,a,b) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   663
  var g=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   664
  var k=Math.max(x.length,y.length);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   665
  if (eg_u.length!=k) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   666
    eg_u=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   667
    eg_A=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   668
    eg_B=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   669
    eg_C=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   670
    eg_D=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   671
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   672
  while(!(x[0]&1)  && !(y[0]&1)) {  //while x and y both even
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   673
    halve_(x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   674
    halve_(y);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   675
    g++;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   676
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   677
  copy_(eg_u,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   678
  copy_(v,y);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   679
  copyInt_(eg_A,1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   680
  copyInt_(eg_B,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   681
  copyInt_(eg_C,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   682
  copyInt_(eg_D,1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   683
  for (;;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   684
    while(!(eg_u[0]&1)) {  //while u is even
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   685
      halve_(eg_u);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   686
      if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if A==B==0 mod 2
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   687
        halve_(eg_A);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   688
        halve_(eg_B);      
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   689
      } else {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   690
        add_(eg_A,y);  halve_(eg_A);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   691
        sub_(eg_B,x);  halve_(eg_B);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   692
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   693
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   694
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   695
    while (!(v[0]&1)) {  //while v is even
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   696
      halve_(v);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   697
      if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if C==D==0 mod 2
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   698
        halve_(eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   699
        halve_(eg_D);      
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   700
      } else {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   701
        add_(eg_C,y);  halve_(eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   702
        sub_(eg_D,x);  halve_(eg_D);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   703
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   704
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   705
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   706
    if (!greater(v,eg_u)) { //v<=u
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   707
      sub_(eg_u,v);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   708
      sub_(eg_A,eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   709
      sub_(eg_B,eg_D);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   710
    } else {                //v>u
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   711
      sub_(v,eg_u);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   712
      sub_(eg_C,eg_A);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   713
      sub_(eg_D,eg_B);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   714
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   715
    if (equalsInt(eg_u,0)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   716
      if (negative(eg_C)) {   //make sure a (C)is nonnegative
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   717
        add_(eg_C,y);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   718
        sub_(eg_D,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   719
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   720
      multInt_(eg_D,-1);  ///make sure b (D) is nonnegative
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   721
      copy_(a,eg_C);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   722
      copy_(b,eg_D);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   723
      leftShift_(v,g);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   724
      return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   725
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   726
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   727
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   728
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   729
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   730
//is bigInt x negative?
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   731
function negative(x) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   732
  return ((x[x.length-1]>>(bpe-1))&1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   733
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   734
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   735
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   736
//is (x << (shift*bpe)) > y?
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   737
//x and y are nonnegative bigInts
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   738
//shift is a nonnegative integer
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   739
function greaterShift(x,y,shift) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   740
  var kx=x.length, ky=y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   741
  k=((kx+shift)<ky) ? (kx+shift) : ky;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   742
  for (i=ky-1-shift; i<kx && i>=0; i++) 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   743
    if (x[i]>0)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   744
      return 1; //if there are nonzeros in x to the left of the first column of y, then x is bigger
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   745
  for (i=kx-1+shift; i<ky; i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   746
    if (y[i]>0)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   747
      return 0; //if there are nonzeros in y to the left of the first column of x, then x is not bigger
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   748
  for (i=k-1; i>=shift; i--)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   749
    if      (x[i-shift]>y[i]) return 1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   750
    else if (x[i-shift]<y[i]) return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   751
  return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   752
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   753
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   754
//is x > y? (x and y both nonnegative)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   755
function greater(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   756
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   757
  var k=(x.length<y.length) ? x.length : y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   758
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   759
  for (i=x.length;i<y.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   760
    if (y[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   761
      return 0;  //y has more digits
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   762
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   763
  for (i=y.length;i<x.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   764
    if (x[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   765
      return 1;  //x has more digits
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   766
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   767
  for (i=k-1;i>=0;i--)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   768
    if (x[i]>y[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   769
      return 1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   770
    else if (x[i]<y[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   771
      return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   772
  return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   773
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   774
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   775
//divide x by y giving quotient q and remainder r.  (q=floor(x/y),  r=x mod y).  All 4 are bigints.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   776
//x must have at least one leading zero element.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   777
//y must be nonzero.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   778
//q and r must be arrays that are exactly the same length as x. (Or q can have more).
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   779
//Must have x.length >= y.length >= 2.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   780
function divide_(x,y,q,r) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   781
  var kx, ky;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   782
  var i,j,y1,y2,c,a,b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   783
  copy_(r,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   784
  for (ky=y.length;y[ky-1]==0;ky--); //ky is number of elements in y, not including leading zeros
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   785
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   786
  //normalize: ensure the most significant element of y has its highest bit set  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   787
  b=y[ky-1];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   788
  for (a=0; b; a++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   789
    b>>=1;  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   790
  a=bpe-a;  //a is how many bits to shift so that the high order bit of y is leftmost in its array element
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   791
  leftShift_(y,a);  //multiply both by 1<<a now, then divide both by that at the end
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   792
  leftShift_(r,a);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   793
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   794
  //Rob Visser discovered a bug: the following line was originally just before the normalization.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   795
  for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); //kx is number of elements in normalized x, not including leading zeros
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   796
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   797
  copyInt_(q,0);                      // q=0
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   798
  while (!greaterShift(y,r,kx-ky)) {  // while (leftShift_(y,kx-ky) <= r) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   799
    subShift_(r,y,kx-ky);             //   r=r-leftShift_(y,kx-ky)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   800
    q[kx-ky]++;                       //   q[kx-ky]++;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   801
  }                                   // }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   802
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   803
  for (i=kx-1; i>=ky; i--) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   804
    if (r[i]==y[ky-1])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   805
      q[i-ky]=mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   806
    else
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   807
      q[i-ky]=Math.floor((r[i]*radix+r[i-1])/y[ky-1]);	
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   808
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   809
    //The following for(;;) loop is equivalent to the commented while loop, 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   810
    //except that the uncommented version avoids overflow.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   811
    //The commented loop comes from HAC, which assumes r[-1]==y[-1]==0
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   812
    //  while (q[i-ky]*(y[ky-1]*radix+y[ky-2]) > r[i]*radix*radix+r[i-1]*radix+r[i-2])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   813
    //    q[i-ky]--;    
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   814
    for (;;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   815
      y2=(ky>1 ? y[ky-2] : 0)*q[i-ky];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   816
      c=y2>>bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   817
      y2=y2 & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   818
      y1=c+q[i-ky]*y[ky-1];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   819
      c=y1>>bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   820
      y1=y1 & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   821
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   822
      if (c==r[i] ? y1==r[i-1] ? y2>(i>1 ? r[i-2] : 0) : y1>r[i-1] : c>r[i]) 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   823
        q[i-ky]--;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   824
      else
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   825
        break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   826
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   827
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   828
    linCombShift_(r,y,-q[i-ky],i-ky);    //r=r-q[i-ky]*leftShift_(y,i-ky)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   829
    if (negative(r)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   830
      addShift_(r,y,i-ky);         //r=r+leftShift_(y,i-ky)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   831
      q[i-ky]--;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   832
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   833
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   834
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   835
  rightShift_(y,a);  //undo the normalization step
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   836
  rightShift_(r,a);  //undo the normalization step
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   837
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   838
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   839
//do carries and borrows so each element of the bigInt x fits in bpe bits.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   840
function carry_(x) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   841
  var i,k,c,b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   842
  k=x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   843
  c=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   844
  for (i=0;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   845
    c+=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   846
    b=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   847
    if (c<0) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   848
      b=-(c>>bpe);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   849
      c+=b*radix;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   850
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   851
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   852
    c=(c>>bpe)-b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   853
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   854
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   855
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   856
//return x mod n for bigInt x and integer n.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   857
function modInt(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   858
  var i,c=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   859
  for (i=x.length-1; i>=0; i--)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   860
    c=(c*radix+x[i])%n;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   861
  return c;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   862
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   863
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   864
//convert the integer t into a bigInt with at least the given number of bits.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   865
//the returned array stores the bigInt in bpe-bit chunks, little endian (buff[0] is least significant word)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   866
//Pad the array with leading zeros so that it has at least minSize elements.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   867
//There will always be at least one leading 0 element.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   868
function int2bigInt(t,bits,minSize) {   
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   869
  var i,k;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   870
  k=Math.ceil(bits/bpe)+1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   871
  k=minSize>k ? minSize : k;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   872
  buff=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   873
  copyInt_(buff,t);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   874
  return buff;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   875
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   876
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   877
//return the bigInt given a string representation in a given base.  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   878
//Pad the array with leading zeros so that it has at least minSize elements.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   879
//If base=-1, then it reads in a space-separated list of array elements in decimal.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   880
//The array will always have at least one leading zero, unless base=-1.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   881
function str2bigInt(s,base,minSize) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   882
  var d, i, j, x, y, kk;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   883
  var k=s.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   884
  if (base==-1) { //comma-separated list of array elements in decimal
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   885
    x=new Array(0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   886
    for (;;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   887
      y=new Array(x.length+1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   888
      for (i=0;i<x.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   889
        y[i+1]=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   890
      y[0]=parseInt(s,10);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   891
      x=y;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   892
      d=s.indexOf(',',0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   893
      if (d<1) 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   894
        break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   895
      s=s.substring(d+1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   896
      if (s.length==0)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   897
        break;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   898
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   899
    if (x.length<minSize) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   900
      y=new Array(minSize);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   901
      copy_(y,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   902
      return y;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   903
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   904
    return x;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   905
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   906
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   907
  x=int2bigInt(0,base*k,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   908
  for (i=0;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   909
    d=digitsStr.indexOf(s.substring(i,i+1),0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   910
    if (base<=36 && d>=36)  //convert lowercase to uppercase if base<=36
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   911
      d-=26;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   912
    if (d<base && d>=0) {   //ignore illegal characters
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   913
      multInt_(x,base);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   914
      addInt_(x,d);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   915
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   916
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   917
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   918
  for (k=x.length;k>0 && !x[k-1];k--); //strip off leading zeros
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   919
  k=minSize>k+1 ? minSize : k+1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   920
  y=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   921
  kk=k<x.length ? k : x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   922
  for (i=0;i<kk;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   923
    y[i]=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   924
  for (;i<k;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   925
    y[i]=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   926
  return y;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   927
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   928
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   929
//is bigint x equal to integer y?
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   930
//y must have less than bpe bits
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   931
function equalsInt(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   932
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   933
  if (x[0]!=y)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   934
    return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   935
  for (i=1;i<x.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   936
    if (x[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   937
      return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   938
  return 1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   939
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   940
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   941
//are bigints x and y equal?
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   942
//this works even if x and y are different lengths and have arbitrarily many leading zeros
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   943
function equals(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   944
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   945
  var k=x.length<y.length ? x.length : y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   946
  for (i=0;i<k;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   947
    if (x[i]!=y[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   948
      return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   949
  if (x.length>y.length) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   950
    for (;i<x.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   951
      if (x[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   952
        return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   953
  } else {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   954
    for (;i<y.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   955
      if (y[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   956
        return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   957
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   958
  return 1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   959
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   960
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   961
//is the bigInt x equal to zero?
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   962
function isZero(x) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   963
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   964
  for (i=0;i<x.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   965
    if (x[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   966
      return 0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   967
  return 1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   968
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   969
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   970
//convert a bigInt into a string in a given base, from base 2 up to base 95.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   971
//Base -1 prints the contents of the array representing the number.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   972
function bigInt2str(x,base) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   973
  var i,t,s="";
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   974
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   975
  if (s6.length!=x.length) 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   976
    s6=dup(x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   977
  else
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   978
    copy_(s6,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   979
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   980
  if (base==-1) { //return the list of array contents
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   981
    for (i=x.length-1;i>0;i--)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   982
      s+=x[i]+',';
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   983
    s+=x[0];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   984
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   985
  else { //return it in the given base
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   986
    while (!isZero(s6)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   987
      t=divInt_(s6,base);  //t=s6 % base; s6=floor(s6/base);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   988
      s=digitsStr.substring(t,t+1)+s;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   989
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   990
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   991
  if (s.length==0)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   992
    s="0";
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   993
  return s;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   994
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   995
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   996
//returns a duplicate of bigInt x
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   997
function dup(x) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   998
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
   999
  buff=new Array(x.length);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1000
  copy_(buff,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1001
  return buff;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1002
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1003
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1004
//do x=y on bigInts x and y.  x must be an array at least as big as y (not counting the leading zeros in y).
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1005
function copy_(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1006
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1007
  var k=x.length<y.length ? x.length : y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1008
  for (i=0;i<k;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1009
    x[i]=y[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1010
  for (i=k;i<x.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1011
    x[i]=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1012
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1013
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1014
//do x=y on bigInt x and integer y.  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1015
function copyInt_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1016
  var i,c;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1017
  for (c=n,i=0;i<x.length;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1018
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1019
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1020
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1021
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1022
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1023
//do x=x+n where x is a bigInt and n is an integer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1024
//x must be large enough to hold the result.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1025
function addInt_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1026
  var i,k,c,b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1027
  x[0]+=n;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1028
  k=x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1029
  c=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1030
  for (i=0;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1031
    c+=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1032
    b=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1033
    if (c<0) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1034
      b=-(c>>bpe);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1035
      c+=b*radix;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1036
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1037
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1038
    c=(c>>bpe)-b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1039
    if (!c) return; //stop carrying as soon as the carry_ is zero
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1040
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1041
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1042
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1043
//right shift bigInt x by n bits.  0 <= n < bpe.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1044
function rightShift_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1045
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1046
  var k=Math.floor(n/bpe);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1047
  if (k) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1048
    for (i=0;i<x.length-k;i++) //right shift x by k elements
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1049
      x[i]=x[i+k];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1050
    for (;i<x.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1051
      x[i]=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1052
    n%=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1053
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1054
  for (i=0;i<x.length-1;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1055
    x[i]=mask & ((x[i+1]<<(bpe-n)) | (x[i]>>n));
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1056
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1057
  x[i]>>=n;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1058
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1059
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1060
//do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1061
function halve_(x) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1062
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1063
  for (i=0;i<x.length-1;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1064
    x[i]=mask & ((x[i+1]<<(bpe-1)) | (x[i]>>1));
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1065
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1066
  x[i]=(x[i]>>1) | (x[i] & (radix>>1));  //most significant bit stays the same
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1067
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1068
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1069
//left shift bigInt x by n bits.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1070
function leftShift_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1071
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1072
  var k=Math.floor(n/bpe);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1073
  if (k) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1074
    for (i=x.length; i>=k; i--) //left shift x by k elements
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1075
      x[i]=x[i-k];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1076
    for (;i>=0;i--)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1077
      x[i]=0;  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1078
    n%=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1079
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1080
  if (!n)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1081
    return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1082
  for (i=x.length-1;i>0;i--) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1083
    x[i]=mask & ((x[i]<<n) | (x[i-1]>>(bpe-n)));
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1084
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1085
  x[i]=mask & (x[i]<<n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1086
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1087
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1088
//do x=x*n where x is a bigInt and n is an integer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1089
//x must be large enough to hold the result.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1090
function multInt_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1091
  var i,k,c,b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1092
  if (!n)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1093
    return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1094
  k=x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1095
  c=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1096
  for (i=0;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1097
    c+=x[i]*n;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1098
    b=0;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1099
    if (c<0) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1100
      b=-(c>>bpe);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1101
      c+=b*radix;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1102
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1103
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1104
    c=(c>>bpe)-b;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1105
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1106
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1107
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1108
//do x=floor(x/n) for bigInt x and integer n, and return the remainder
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1109
function divInt_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1110
  var i,r=0,s;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1111
  for (i=x.length-1;i>=0;i--) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1112
    s=r*radix+x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1113
    x[i]=Math.floor(s/n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1114
    r=s%n;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1115
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1116
  return r;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1117
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1118
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1119
//do the linear combination x=a*x+b*y for bigInts x and y, and integers a and b.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1120
//x must be large enough to hold the answer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1121
function linComb_(x,y,a,b) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1122
  var i,c,k,kk;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1123
  k=x.length<y.length ? x.length : y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1124
  kk=x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1125
  for (c=0,i=0;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1126
    c+=a*x[i]+b*y[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1127
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1128
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1129
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1130
  for (i=k;i<kk;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1131
    c+=a*x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1132
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1133
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1134
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1135
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1136
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1137
//do the linear combination x=a*x+b*(y<<(ys*bpe)) for bigInts x and y, and integers a, b and ys.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1138
//x must be large enough to hold the answer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1139
function linCombShift_(x,y,b,ys) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1140
  var i,c,k,kk;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1141
  k=x.length<ys+y.length ? x.length : ys+y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1142
  kk=x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1143
  for (c=0,i=ys;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1144
    c+=x[i]+b*y[i-ys];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1145
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1146
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1147
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1148
  for (i=k;c && i<kk;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1149
    c+=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1150
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1151
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1152
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1153
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1154
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1155
//do x=x+(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1156
//x must be large enough to hold the answer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1157
function addShift_(x,y,ys) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1158
  var i,c,k,kk;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1159
  k=x.length<ys+y.length ? x.length : ys+y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1160
  kk=x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1161
  for (c=0,i=ys;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1162
    c+=x[i]+y[i-ys];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1163
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1164
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1165
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1166
  for (i=k;c && i<kk;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1167
    c+=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1168
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1169
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1170
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1171
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1172
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1173
//do x=x-(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1174
//x must be large enough to hold the answer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1175
function subShift_(x,y,ys) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1176
  var i,c,k,kk;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1177
  k=x.length<ys+y.length ? x.length : ys+y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1178
  kk=x.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1179
  for (c=0,i=ys;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1180
    c+=x[i]-y[i-ys];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1181
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1182
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1183
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1184
  for (i=k;c && i<kk;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1185
    c+=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1186
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1187
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1188
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1189
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1190
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1191
//do x=x-y for bigInts x and y.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1192
//x must be large enough to hold the answer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1193
//negative answers will be 2s complement
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1194
function sub_(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1195
  var i,c,k,kk;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1196
  k=x.length<y.length ? x.length : y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1197
  for (c=0,i=0;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1198
    c+=x[i]-y[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1199
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1200
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1201
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1202
  for (i=k;c && i<x.length;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1203
    c+=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1204
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1205
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1206
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1207
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1208
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1209
//do x=x+y for bigInts x and y.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1210
//x must be large enough to hold the answer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1211
function add_(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1212
  var i,c,k,kk;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1213
  k=x.length<y.length ? x.length : y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1214
  for (c=0,i=0;i<k;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1215
    c+=x[i]+y[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1216
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1217
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1218
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1219
  for (i=k;c && i<x.length;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1220
    c+=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1221
    x[i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1222
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1223
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1224
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1225
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1226
//do x=x*y for bigInts x and y.  This is faster when y<x.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1227
function mult_(x,y) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1228
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1229
  if (ss.length!=2*x.length)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1230
    ss=new Array(2*x.length);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1231
  copyInt_(ss,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1232
  for (i=0;i<y.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1233
    if (y[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1234
      linCombShift_(ss,x,y[i],i);   //ss=1*ss+y[i]*(x<<(i*bpe))
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1235
  copy_(x,ss);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1236
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1237
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1238
//do x=x mod n for bigInts x and n.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1239
function mod_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1240
  if (s4.length!=x.length)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1241
    s4=dup(x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1242
  else
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1243
    copy_(s4,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1244
  if (s5.length!=x.length)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1245
    s5=dup(x);  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1246
  divide_(s4,n,s5,x);  //x = remainder of s4 / n
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1247
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1248
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1249
//do x=x*y mod n for bigInts x,y,n.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1250
//for greater speed, let y<x.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1251
function multMod_(x,y,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1252
  var i;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1253
  if (s0.length!=2*x.length)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1254
    s0=new Array(2*x.length);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1255
  copyInt_(s0,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1256
  for (i=0;i<y.length;i++)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1257
    if (y[i])
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1258
      linCombShift_(s0,x,y[i],i);   //s0=1*s0+y[i]*(x<<(i*bpe))
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1259
  mod_(s0,n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1260
  copy_(x,s0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1261
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1262
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1263
//do x=x*x mod n for bigInts x,n.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1264
function squareMod_(x,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1265
  var i,j,d,c,kx,kn,k;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1266
  for (kx=x.length; kx>0 && !x[kx-1]; kx--);  //ignore leading zeros in x
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1267
  k=kx>n.length ? 2*kx : 2*n.length; //k=# elements in the product, which is twice the elements in the larger of x and n
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1268
  if (s0.length!=k) 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1269
    s0=new Array(k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1270
  copyInt_(s0,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1271
  for (i=0;i<kx;i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1272
    c=s0[2*i]+x[i]*x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1273
    s0[2*i]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1274
    c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1275
    for (j=i+1;j<kx;j++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1276
      c=s0[i+j]+2*x[i]*x[j]+c;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1277
      s0[i+j]=(c & mask);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1278
      c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1279
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1280
    s0[i+kx]=c;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1281
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1282
  mod_(s0,n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1283
  copy_(x,s0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1284
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1285
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1286
//return x with exactly k leading zero elements
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1287
function bigint_trim(x,k) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1288
  var i,y;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1289
  for (i=x.length; i>0 && !x[i-1]; i--);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1290
  y=new Array(i+k);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1291
  copy_(y,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1292
  return y;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1293
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1294
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1295
//do x=x**y mod n, where x,y,n are bigInts and ** is exponentiation.  0**0=1.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1296
//this is faster when n is odd.  x usually needs to have as many elements as n.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1297
function powMod_(x,y,n) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1298
  var k1,k2,kn,np;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1299
  if(s7.length!=n.length)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1300
    s7=dup(n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1301
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1302
  //for even modulus, use a simple square-and-multiply algorithm,
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1303
  //rather than using the more complex Montgomery algorithm.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1304
  if ((n[0]&1)==0) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1305
    copy_(s7,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1306
    copyInt_(x,1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1307
    while(!equalsInt(y,0)) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1308
      if (y[0]&1)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1309
        multMod_(x,s7,n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1310
      divInt_(y,2);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1311
      squareMod_(s7,n); 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1312
    }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1313
    return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1314
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1315
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1316
  //calculate np from n for the Montgomery multiplications
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1317
  copyInt_(s7,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1318
  for (kn=n.length;kn>0 && !n[kn-1];kn--);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1319
  np=radix-inverseModInt(modInt(n,radix),radix);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1320
  s7[kn]=1;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1321
  multMod_(x ,s7,n);   // x = x * 2**(kn*bp) mod n
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1322
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1323
  if (s3.length!=x.length)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1324
    s3=dup(x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1325
  else
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1326
    copy_(s3,x);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1327
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1328
  for (k1=y.length-1;k1>0 & !y[k1]; k1--);  //k1=first nonzero element of y
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1329
  if (y[k1]==0) {  //anything to the 0th power is 1
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1330
    copyInt_(x,1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1331
    return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1332
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1333
  for (k2=1<<(bpe-1);k2 && !(y[k1] & k2); k2>>=1);  //k2=position of first 1 bit in y[k1]
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1334
  for (;;) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1335
    if (!(k2>>=1)) {  //look at next bit of y
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1336
      k1--;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1337
      if (k1<0) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1338
        mont_(x,one,n,np);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1339
        return;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1340
      }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1341
      k2=1<<(bpe-1);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1342
    }    
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1343
    mont_(x,x,n,np);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1344
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1345
    if (k2 & y[k1]) //if next bit is a 1
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1346
      mont_(x,s3,n,np);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1347
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1348
}    
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1349
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1350
//do x=x*y*Ri mod n for bigInts x,y,n, 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1351
//  where Ri = 2**(-kn*bpe) mod n, and kn is the 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1352
//  number of elements in the n array, not 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1353
//  counting leading zeros.  
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1354
//x must be large enough to hold the answer.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1355
//It's OK if x and y are the same variable.
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1356
//must have:
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1357
//  x,y < n
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1358
//  n is odd
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1359
//  np = -(n^(-1)) mod radix
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1360
function mont_(x,y,n,np) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1361
  var i,j,c,ui,t;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1362
  var kn=n.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1363
  var ky=y.length;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1364
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1365
  if (sa.length!=kn)
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1366
    sa=new Array(kn);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1367
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1368
  for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1369
  //this function sometimes gives wrong answers when the next line is uncommented
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1370
  //for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1371
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1372
  copyInt_(sa,0);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1373
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1374
  //the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large keys
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1375
  for (i=0; i<kn; i++) {
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1376
    t=sa[0]+x[i]*y[0];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1377
    ui=((t & mask) * np) & mask;  //the inner "& mask" is needed on Macintosh MSIE, but not windows MSIE
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1378
    c=(t+ui*n[0]) >> bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1379
    t=x[i];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1380
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1381
    //do sa=(sa+x[i]*y+ui*n)/b   where b=2**bpe
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1382
    for (j=1;j<ky;j++) { 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1383
      c+=sa[j]+t*y[j]+ui*n[j];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1384
      sa[j-1]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1385
      c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1386
    }    
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1387
    for (;j<kn;j++) { 
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1388
      c+=sa[j]+ui*n[j];
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1389
      sa[j-1]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1390
      c>>=bpe;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1391
    }    
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1392
    sa[j-1]=c & mask;
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1393
  }
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1394
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1395
  if (!greater(n,sa))
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1396
    sub_(sa,n);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1397
  copy_(x,sa);
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1398
}
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1399
242353360e37 Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff changeset
  1400