Patch bigint.js so that it doesn't throw an error when a CSPRNG is not present

Instead, we'll check for it in converse.js and just disable OTR if it's not
there.

build.js

@@ -27,7 +27,7 @@
         "strophe.vcard": "components/strophe.vcard/index",
         "strophe.disco": "components/strophe.disco/index",
         "salsa20": "components/otr/build/dep/salsa20",
-        "bigint": "components/otr/build/dep/bigint",
+        "bigint": "src/bigint",
         "crypto.core": "components/otr/vendor/cryptojs/core",
         "crypto.enc-base64": "components/otr/vendor/cryptojs/enc-base64",
         "crypto.md5": "components/crypto-js/src/md5",

main.js

@@ -12,7 +12,7 @@ require.config({
         "strophe.vcard": "components/strophe.vcard/index",
         "strophe.disco": "components/strophe.disco/index",
         "salsa20": "components/otr/build/dep/salsa20",
-        "bigint": "components/otr/build/dep/bigint",
+        "bigint": "src/bigint",
         "crypto.core": "components/otr/vendor/cryptojs/core",
         "crypto.enc-base64": "components/otr/vendor/cryptojs/enc-base64",
         "crypto.md5": "components/crypto-js/src/md5",

src/bigint.js

+;(function (root, factory) {
+
+  var Salsa20, crypto
+  if (typeof define === 'function' && define.amd) {
+    define(['salsa20'], factory.bind(root, root.crypto))
+  } else if (typeof module !== 'undefined' && module.exports) {
+    Salsa20 = require('./salsa20.js')
+    crypto = require('crypto')
+    module.exports = factory(crypto, Salsa20)
+  } else {
+    root.BigInt = factory(root.crypto, root.Salsa20)
+  }
+
+}(this, function (crypto, Salsa20) {
+
+  ////////////////////////////////////////////////////////////////////////////////////////
+  // Big Integer Library v. 5.5
+  // Created 2000, last modified 2013
+  // Leemon Baird
+  // www.leemon.com
+  //
+  // Version history:
+  // v 5.5  17 Mar 2013
+  //   - two lines of a form like "if (x<0) x+=n" had the "if" changed to "while" to
+  //     handle the case when x<-n. (Thanks to James Ansell for finding that bug)
+  // v 5.4  3 Oct 2009
+  //   - added "var i" to greaterShift() so i is not global. (Thanks to Péter Szabó for finding that bug)
+  //
+  // v 5.3  21 Sep 2009
+  //   - added randProbPrime(k) for probable primes
+  //   - unrolled loop in mont_ (slightly faster)
+  //   - millerRabin now takes a bigInt parameter rather than an int
+  //
+  // v 5.2  15 Sep 2009
+  //   - fixed capitalization in call to int2bigInt in randBigInt
+  //     (thanks to Emili Evripidou, Reinhold Behringer, and Samuel Macaleese for finding that bug)
+  //
+  // v 5.1  8 Oct 2007 
+  //   - renamed inverseModInt_ to inverseModInt since it doesn't change its parameters
+  //   - added functions GCD and randBigInt, which call GCD_ and randBigInt_
+  //   - fixed a bug found by Rob Visser (see comment with his name below)
+  //   - improved comments
+  //
+  // This file is public domain.   You can use it for any purpose without restriction.
+  // I do not guarantee that it is correct, so use it at your own risk.  If you use 
+  // it for something interesting, I'd appreciate hearing about it.  If you find 
+  // any bugs or make any improvements, I'd appreciate hearing about those too.
+  // It would also be nice if my name and URL were left in the comments.  But none 
+  // of that is required.
+  //
+  // This code defines a bigInt library for arbitrary-precision integers.
+  // A bigInt is an array of integers storing the value in chunks of bpe bits, 
+  // little endian (buff[0] is the least significant word).
+  // Negative bigInts are stored two's complement.  Almost all the functions treat
+  // bigInts as nonnegative.  The few that view them as two's complement say so
+  // in their comments.  Some functions assume their parameters have at least one 
+  // leading zero element. Functions with an underscore at the end of the name put
+  // their answer into one of the arrays passed in, and have unpredictable behavior 
+  // in case of overflow, so the caller must make sure the arrays are big enough to 
+  // hold the answer.  But the average user should never have to call any of the 
+  // underscored functions.  Each important underscored function has a wrapper function 
+  // of the same name without the underscore that takes care of the details for you.  
+  // For each underscored function where a parameter is modified, that same variable 
+  // must not be used as another argument too.  So, you cannot square x by doing 
+  // multMod_(x,x,n).  You must use squareMod_(x,n) instead, or do y=dup(x); multMod_(x,y,n).
+  // Or simply use the multMod(x,x,n) function without the underscore, where
+  // such issues never arise, because non-underscored functions never change
+  // their parameters; they always allocate new memory for the answer that is returned.
+  //
+  // These functions are designed to avoid frequent dynamic memory allocation in the inner loop.
+  // For most functions, if it needs a BigInt as a local variable it will actually use
+  // a global, and will only allocate to it only when it's not the right size.  This ensures
+  // that when a function is called repeatedly with same-sized parameters, it only allocates
+  // memory on the first call.
+  //
+  // Note that for cryptographic purposes, the calls to Math.random() must 
+  // be replaced with calls to a better pseudorandom number generator.
+  //
+  // In the following, "bigInt" means a bigInt with at least one leading zero element,
+  // and "integer" means a nonnegative integer less than radix.  In some cases, integer 
+  // can be negative.  Negative bigInts are 2s complement.
+  // 
+  // The following functions do not modify their inputs.
+  // Those returning a bigInt, string, or Array will dynamically allocate memory for that value.
+  // Those returning a boolean will return the integer 0 (false) or 1 (true).
+  // Those returning boolean or int will not allocate memory except possibly on the first 
+  // time they're called with a given parameter size.
+  // 
+  // bigInt  add(x,y)               //return (x+y) for bigInts x and y.  
+  // bigInt  addInt(x,n)            //return (x+n) where x is a bigInt and n is an integer.
+  // string  bigInt2str(x,base)     //return a string form of bigInt x in a given base, with 2 <= base <= 95
+  // int     bitSize(x)             //return how many bits long the bigInt x is, not counting leading zeros
+  // bigInt  dup(x)                 //return a copy of bigInt x
+  // boolean equals(x,y)            //is the bigInt x equal to the bigint y?
+  // boolean equalsInt(x,y)         //is bigint x equal to integer y?
+  // bigInt  expand(x,n)            //return a copy of x with at least n elements, adding leading zeros if needed
+  // Array   findPrimes(n)          //return array of all primes less than integer n
+  // bigInt  GCD(x,y)               //return greatest common divisor of bigInts x and y (each with same number of elements).
+  // boolean greater(x,y)           //is x>y?  (x and y are nonnegative bigInts)
+  // boolean greaterShift(x,y,shift)//is (x <<(shift*bpe)) > y?
+  // bigInt  int2bigInt(t,n,m)      //return a bigInt equal to integer t, with at least n bits and m array elements
+  // bigInt  inverseMod(x,n)        //return (x**(-1) mod n) for bigInts x and n.  If no inverse exists, it returns null
+  // int     inverseModInt(x,n)     //return x**(-1) mod n, for integers x and n.  Return 0 if there is no inverse
+  // boolean isZero(x)              //is the bigInt x equal to zero?
+  // boolean millerRabin(x,b)       //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime? (b is bigInt, 1<b<x)
+  // boolean millerRabinInt(x,b)    //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime? (b is int,    1<b<x)
+  // bigInt  mod(x,n)               //return a new bigInt equal to (x mod n) for bigInts x and n.
+  // int     modInt(x,n)            //return x mod n for bigInt x and integer n.
+  // bigInt  mult(x,y)              //return x*y for bigInts x and y. This is faster when y<x.
+  // bigInt  multMod(x,y,n)         //return (x*y mod n) for bigInts x,y,n.  For greater speed, let y<x.
+  // boolean negative(x)            //is bigInt x negative?
+  // 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.
+  // 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.
+  // bigInt  randTruePrime(k)       //return a new, random, k-bit, true prime bigInt using Maurer's algorithm.
+  // bigInt  randProbPrime(k)       //return a new, random, k-bit, probable prime bigInt (probability it's composite less than 2^-80).
+  // 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
+  // bigInt  sub(x,y)               //return (x-y) for bigInts x and y.  Negative answers will be 2s complement
+  // bigInt  trim(x,k)              //return a copy of x with exactly k leading zero elements
+  //
+  //
+  // The following functions each have a non-underscored version, which most users should call instead.
+  // These functions each write to a single parameter, and the caller is responsible for ensuring the array 
+  // passed in is large enough to hold the result. 
+  //
+  // void    addInt_(x,n)          //do x=x+n where x is a bigInt and n is an integer
+  // void    add_(x,y)             //do x=x+y for bigInts x and y
+  // void    copy_(x,y)            //do x=y on bigInts x and y
+  // void    copyInt_(x,n)         //do x=n on bigInt x and integer n
+  // void    GCD_(x,y)             //set x to the greatest common divisor of bigInts x and y, (y is destroyed).  (This never overflows its array).
+  // boolean inverseMod_(x,n)      //do x=x**(-1) mod n, for bigInts x and n. Returns 1 (0) if inverse does (doesn't) exist
+  // void    mod_(x,n)             //do x=x mod n for bigInts x and n. (This never overflows its array).
+  // void    mult_(x,y)            //do x=x*y for bigInts x and y.
+  // void    multMod_(x,y,n)       //do x=x*y  mod n for bigInts x,y,n.
+  // 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.
+  // 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.
+  // void    randTruePrime_(ans,k) //do ans = a random k-bit true random prime (not just probable prime) with 1 in the msb.
+  // void    sub_(x,y)             //do x=x-y for bigInts x and y. Negative answers will be 2s complement.
+  //
+  // The following functions do NOT have a non-underscored version. 
+  // They each write a bigInt result to one or more parameters.  The caller is responsible for
+  // ensuring the arrays passed in are large enough to hold the results. 
+  //
+  // void addShift_(x,y,ys)       //do x=x+(y<<(ys*bpe))
+  // void carry_(x)               //do carries and borrows so each element of the bigInt x fits in bpe bits.
+  // void divide_(x,y,q,r)        //divide x by y giving quotient q and remainder r
+  // int  divInt_(x,n)            //do x=floor(x/n) for bigInt x and integer n, and return the remainder. (This never overflows its array).
+  // int  eGCD_(x,y,d,a,b)        //sets a,b,d to positive bigInts such that d = GCD_(x,y) = a*x-b*y
+  // void halve_(x)               //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement.  (This never overflows its array).
+  // void leftShift_(x,n)         //left shift bigInt x by n bits.  n<bpe.
+  // void linComb_(x,y,a,b)       //do x=a*x+b*y for bigInts x and y and integers a and b
+  // void linCombShift_(x,y,b,ys) //do x=x+b*(y<<(ys*bpe)) for bigInts x and y, and integers b and ys
+  // void mont_(x,y,n,np)         //Montgomery multiplication (see comments where the function is defined)
+  // void multInt_(x,n)           //do x=x*n where x is a bigInt and n is an integer.
+  // void rightShift_(x,n)        //right shift bigInt x by n bits.  0 <= n < bpe. (This never overflows its array).
+  // void squareMod_(x,n)         //do x=x*x  mod n for bigInts x,n
+  // void subShift_(x,y,ys)       //do x=x-(y<<(ys*bpe)). Negative answers will be 2s complement.
+  //
+  // The following functions are based on algorithms from the _Handbook of Applied Cryptography_
+  //    powMod_()           = algorithm 14.94, Montgomery exponentiation
+  //    eGCD_,inverseMod_() = algorithm 14.61, Binary extended GCD_
+  //    GCD_()              = algorothm 14.57, Lehmer's algorithm
+  //    mont_()             = algorithm 14.36, Montgomery multiplication
+  //    divide_()           = algorithm 14.20  Multiple-precision division
+  //    squareMod_()        = algorithm 14.16  Multiple-precision squaring
+  //    randTruePrime_()    = algorithm  4.62, Maurer's algorithm
+  //    millerRabin()       = algorithm  4.24, Miller-Rabin algorithm
+  //
+  // Profiling shows:
+  //     randTruePrime_() spends:
+  //         10% of its time in calls to powMod_()
+  //         85% of its time in calls to millerRabin()
+  //     millerRabin() spends:
+  //         99% of its time in calls to powMod_()   (always with a base of 2)
+  //     powMod_() spends:
+  //         94% of its time in calls to mont_()  (almost always with x==y)
+  //
+  // This suggests there are several ways to speed up this library slightly:
+  //     - convert powMod_ to use a Montgomery form of k-ary window (or maybe a Montgomery form of sliding window)
+  //         -- this should especially focus on being fast when raising 2 to a power mod n
+  //     - convert randTruePrime_() to use a minimum r of 1/3 instead of 1/2 with the appropriate change to the test
+  //     - tune the parameters in randTruePrime_(), including c, m, and recLimit
+  //     - speed up the single loop in mont_() that takes 95% of the runtime, perhaps by reducing checking
+  //       within the loop when all the parameters are the same length.
+  //
+  // There are several ideas that look like they wouldn't help much at all:
+  //     - replacing trial division in randTruePrime_() with a sieve (that speeds up something taking almost no time anyway)
+  //     - 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)
+  //     - speeding up mont_(x,y,n,np) when x==y by doing a non-modular, non-Montgomery square
+  //       followed by a Montgomery reduction.  The intermediate answer will be twice as long as x, so that
+  //       method would be slower.  This is unfortunate because the code currently spends almost all of its time
+  //       doing mont_(x,x,...), both for randTruePrime_() and powMod_().  A faster method for Montgomery squaring
+  //       would have a large impact on the speed of randTruePrime_() and powMod_().  HAC has a couple of poorly-worded
+  //       sentences that seem to imply it's faster to do a non-modular square followed by a single
+  //       Montgomery reduction, but that's obviously wrong.
+  ////////////////////////////////////////////////////////////////////////////////////////
+
+  //globals
+  var bpe = 0        // bits stored per array element
+  var mask=0;        //AND this with an array element to chop it down to bpe bits
+  var radix=mask+1;  //equals 2^bpe.  A single 1 bit to the left of the last bit of mask.
+
+  //the digits for converting to different bases
+  var digitsStr='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-';
+
+  //initialize the global variables
+  for (bpe = 0; (1<<(bpe+1)) > (1<<bpe); bpe++);  // bpe = number of bits in the mantissa on this platform
+  bpe>>=1;                   // bpe = number of bits in one element of the array representing the bigInt
+  mask=(1<<bpe)-1;           //AND the mask with an integer to get its bpe least significant bits
+  radix=mask+1;              //2^bpe.  a single 1 bit to the left of the first bit of mask
+  var one=int2bigInt(1,1,1);     //constant used in powMod_()
+
+  //the following global variables are scratchpad memory to 
+  //reduce dynamic memory allocation in the inner loop
+  var t=new Array(0);
+  var ss=t;       //used in mult_()
+  var s0=t;       //used in multMod_(), squareMod_()
+  var s1=t;       //used in powMod_(), multMod_(), squareMod_()
+  var s2=t;       //used in powMod_(), multMod_()
+  var s3=t;       //used in powMod_()
+  var s4=t, s5=t; //used in mod_()
+  var s6=t;       //used in bigInt2str()
+  var s7=t;       //used in powMod_()
+  var T=t;        //used in GCD_()
+  var sa=t;       //used in mont_()
+  var mr_x1=t, mr_r=t, mr_a=t;                                      //used in millerRabin()
+  var eg_v=t, eg_u=t, eg_A=t, eg_B=t, eg_C=t, eg_D=t;               //used in eGCD_(), inverseMod_()
+  var md_q1=t, md_q2=t, md_q3=t, md_r=t, md_r1=t, md_r2=t, md_tt=t; //used in mod_()
+
+  var primes=t, pows=t, s_i=t, s_i2=t, s_R=t, s_rm=t, s_q=t, s_n1=t;
+  var 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_()
+    
+  var rpprb=t; //used in randProbPrimeRounds() (which also uses "primes")
+
+  ////////////////////////////////////////////////////////////////////////////////////////
+
+
+  //return array of all primes less than integer n
+  function findPrimes(n) {
+    var i,s,p,ans;
+    s=new Array(n);
+    for (i=0;i<n;i++)
+      s[i]=0;
+    s[0]=2;
+    p=0;    //first p elements of s are primes, the rest are a sieve
+    for(;s[p]<n;) {                  //s[p] is the pth prime
+      for(i=s[p]*s[p]; i<n; i+=s[p]) //mark multiples of s[p]
+        s[i]=1;
+      p++;
+      s[p]=s[p-1]+1;
+      for(; s[p]<n && s[s[p]]; s[p]++); //find next prime (where s[p]==0)
+    }
+    ans=new Array(p);
+    for(i=0;i<p;i++)
+      ans[i]=s[i];
+    return ans;
+  }
+
+
+  //does a single round of Miller-Rabin base b consider x to be a possible prime?
+  //x is a bigInt, and b is an integer, with b<x
+  function millerRabinInt(x,b) {
+    if (mr_x1.length!=x.length) {
+      mr_x1=dup(x);
+      mr_r=dup(x);
+      mr_a=dup(x);
+    }
+
+    copyInt_(mr_a,b);
+    return millerRabin(x,mr_a);
+  }
+
+  //does a single round of Miller-Rabin base b consider x to be a possible prime?
+  //x and b are bigInts with b<x
+  function millerRabin(x,b) {
+    var i,j,k,s;
+
+    if (mr_x1.length!=x.length) {
+      mr_x1=dup(x);
+      mr_r=dup(x);
+      mr_a=dup(x);
+    }
+
+    copy_(mr_a,b);
+    copy_(mr_r,x);
+    copy_(mr_x1,x);
+
+    addInt_(mr_r,-1);
+    addInt_(mr_x1,-1);
+
+    //s=the highest power of two that divides mr_r
+
+    /*
+    k=0;
+    for (i=0;i<mr_r.length;i++)
+      for (j=1;j<mask;j<<=1)
+        if (x[i] & j) {
+          s=(k<mr_r.length+bpe ? k : 0); 
+           i=mr_r.length;
+           j=mask;
+        } else
+          k++;
+    */
+
+    /* http://www.javascripter.net/math/primes/millerrabinbug-bigint54.htm */
+    if (isZero(mr_r)) return 0;
+    for (k=0; mr_r[k]==0; k++);
+    for (i=1,j=2; mr_r[k]%j==0; j*=2,i++ );
+    s = k*bpe + i - 1;
+    /* end */
+
+    if (s)                
+      rightShift_(mr_r,s);
+
+    powMod_(mr_a,mr_r,x);
+
+    if (!equalsInt(mr_a,1) && !equals(mr_a,mr_x1)) {
+      j=1;
+      while (j<=s-1 && !equals(mr_a,mr_x1)) {
+        squareMod_(mr_a,x);
+        if (equalsInt(mr_a,1)) {
+          return 0;
+        }
+        j++;
+      }
+      if (!equals(mr_a,mr_x1)) {
+        return 0;
+      }
+    }
+    return 1;  
+  }
+
+  //returns how many bits long the bigInt is, not counting leading zeros.
+  function bitSize(x) {
+    var j,z,w;
+    for (j=x.length-1; (x[j]==0) && (j>0); j--);
+    for (z=0,w=x[j]; w; (w>>=1),z++);
+    z+=bpe*j;
+    return z;
+  }
+
+  //return a copy of x with at least n elements, adding leading zeros if needed
+  function expand(x,n) {
+    var ans=int2bigInt(0,(x.length>n ? x.length : n)*bpe,0);
+    copy_(ans,x);
+    return ans;
+  }
+
+  //return a k-bit true random prime using Maurer's algorithm.
+  function randTruePrime(k) {
+    var ans=int2bigInt(0,k,0);
+    randTruePrime_(ans,k);
+    return trim(ans,1);
+  }
+
+  //return a k-bit random probable prime with probability of error < 2^-80
+  function randProbPrime(k) {
+    if (k>=600) return randProbPrimeRounds(k,2); //numbers from HAC table 4.3
+    if (k>=550) return randProbPrimeRounds(k,4);
+    if (k>=500) return randProbPrimeRounds(k,5);
+    if (k>=400) return randProbPrimeRounds(k,6);
+    if (k>=350) return randProbPrimeRounds(k,7);
+    if (k>=300) return randProbPrimeRounds(k,9);
+    if (k>=250) return randProbPrimeRounds(k,12); //numbers from HAC table 4.4
+    if (k>=200) return randProbPrimeRounds(k,15);
+    if (k>=150) return randProbPrimeRounds(k,18);
+    if (k>=100) return randProbPrimeRounds(k,27);
+                return randProbPrimeRounds(k,40); //number from HAC remark 4.26 (only an estimate)
+  }
+
+  //return a k-bit probable random prime using n rounds of Miller Rabin (after trial division with small primes)
+  function randProbPrimeRounds(k,n) {
+    var ans, i, divisible, B; 
+    B=30000;  //B is largest prime to use in trial division
+    ans=int2bigInt(0,k,0);
+    
+    //optimization: try larger and smaller B to find the best limit.
+    
+    if (primes.length==0)
+      primes=findPrimes(30000);  //check for divisibility by primes <=30000
+
+    if (rpprb.length!=ans.length)
+      rpprb=dup(ans);
+
+    for (;;) { //keep trying random values for ans until one appears to be prime
+      //optimization: pick a random number times L=2*3*5*...*p, plus a 
+      //   random element of the list of all numbers in [0,L) not divisible by any prime up to p.
+      //   This can reduce the amount of random number generation.
+      
+      randBigInt_(ans,k,0); //ans = a random odd number to check
+      ans[0] |= 1; 
+      divisible=0;
+    
+      //check ans for divisibility by small primes up to B
+      for (i=0; (i<primes.length) && (primes[i]<=B); i++)
+        if (modInt(ans,primes[i])==0 && !equalsInt(ans,primes[i])) {
+          divisible=1;
+          break;
+        }      
+      
+      //optimization: change millerRabin so the base can be bigger than the number being checked, then eliminate the while here.
+      
+      //do n rounds of Miller Rabin, with random bases less than ans
+      for (i=0; i<n && !divisible; i++) {
+        randBigInt_(rpprb,k,0);
+        while(!greater(ans,rpprb)) //pick a random rpprb that's < ans
+          randBigInt_(rpprb,k,0);
+        if (!millerRabin(ans,rpprb))
+          divisible=1;
+      }
+      
+      if(!divisible)
+        return ans;
+    }  
+  }
+
+  //return a new bigInt equal to (x mod n) for bigInts x and n.
+  function mod(x,n) {
+    var ans=dup(x);
+    mod_(ans,n);
+    return trim(ans,1);
+  }
+
+  //return (x+n) where x is a bigInt and n is an integer.
+  function addInt(x,n) {
+    var ans=expand(x,x.length+1);
+    addInt_(ans,n);
+    return trim(ans,1);
+  }
+
+  //return x*y for bigInts x and y. This is faster when y<x.
+  function mult(x,y) {
+    var ans=expand(x,x.length+y.length);
+    mult_(ans,y);
+    return trim(ans,1);
+  }
+
+  //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation.  0**0=1. Faster for odd n.
+  function powMod(x,y,n) {
+    var ans=expand(x,n.length);  
+    powMod_(ans,trim(y,2),trim(n,2),0);  //this should work without the trim, but doesn't
+    return trim(ans,1);
+  }
+
+  //return (x-y) for bigInts x and y.  Negative answers will be 2s complement
+  function sub(x,y) {
+    var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); 
+    sub_(ans,y);
+    return trim(ans,1);
+  }
+
+  //return (x+y) for bigInts x and y.  
+  function add(x,y) {
+    var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); 
+    add_(ans,y);
+    return trim(ans,1);
+  }
+
+  //return (x**(-1) mod n) for bigInts x and n.  If no inverse exists, it returns null
+  function inverseMod(x,n) {
+    var ans=expand(x,n.length); 
+    var s;
+    s=inverseMod_(ans,n);
+    return s ? trim(ans,1) : null;
+  }
+
+  //return (x*y mod n) for bigInts x,y,n.  For greater speed, let y<x.
+  function multMod(x,y,n) {
+    var ans=expand(x,n.length);
+    multMod_(ans,y,n);
+    return trim(ans,1);
+  }
+
+  //generate a k-bit true random prime using Maurer's algorithm,
+  //and put it into ans.  The bigInt ans must be large enough to hold it.
+  function randTruePrime_(ans,k) {
+    var c,w,m,pm,dd,j,r,B,divisible,z,zz,recSize,recLimit;
+
+    if (primes.length==0)
+      primes=findPrimes(30000);  //check for divisibility by primes <=30000
+
+    if (pows.length==0) {
+      pows=new Array(512);
+      for (j=0;j<512;j++) {
+        pows[j]=Math.pow(2,j/511.0-1.0);
+      }
+    }
+
+    //c and m should be tuned for a particular machine and value of k, to maximize speed
+    c=0.1;  //c=0.1 in HAC
+    m=20;   //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits
+    recLimit=20; //stop recursion when k <=recLimit.  Must have recLimit >= 2
+
+    if (s_i2.length!=ans.length) {
+      s_i2=dup(ans);
+      s_R =dup(ans);
+      s_n1=dup(ans);
+      s_r2=dup(ans);
+      s_d =dup(ans);
+      s_x1=dup(ans);
+      s_x2=dup(ans);
+      s_b =dup(ans);
+      s_n =dup(ans);
+      s_i =dup(ans);
+      s_rm=dup(ans);
+      s_q =dup(ans);
+      s_a =dup(ans);
+      s_aa=dup(ans);
+    }
+
+    if (k <= recLimit) {  //generate small random primes by trial division up to its square root
+      pm=(1<<((k+2)>>1))-1; //pm is binary number with all ones, just over sqrt(2^k)
+      copyInt_(ans,0);
+      for (dd=1;dd;) {
+        dd=0;
+        ans[0]= 1 | (1<<(k-1)) | randomBitInt(k);  //random, k-bit, odd integer, with msb 1
+        for (j=1;(j<primes.length) && ((primes[j]&pm)==primes[j]);j++) { //trial division by all primes 3...sqrt(2^k)
+          if (0==(ans[0]%primes[j])) {
+            dd=1;
+            break;
+          }
+        }
+      }
+      carry_(ans);
+      return;
+    }
+
+    B=c*k*k;    //try small primes up to B (or all the primes[] array if the largest is less than B).
+    if (k>2*m)  //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits
+      for (r=1; k-k*r<=m; )
+        r=pows[randomBitInt(9)];   //r=Math.pow(2,Math.random()-1);
+    else
+      r=0.5;
+
+    //simulation suggests the more complex algorithm using r=.333 is only slightly faster.
+
+    recSize=Math.floor(r*k)+1;
+
+    randTruePrime_(s_q,recSize);
+    copyInt_(s_i2,0);
+    s_i2[Math.floor((k-2)/bpe)] |= (1<<((k-2)%bpe));   //s_i2=2^(k-2)
+    divide_(s_i2,s_q,s_i,s_rm);                        //s_i=floor((2^(k-1))/(2q))
+
+    z=bitSize(s_i);
+
+    for (;;) {
+      for (;;) {  //generate z-bit numbers until one falls in the range [0,s_i-1]
+        randBigInt_(s_R,z,0);
+        if (greater(s_i,s_R))
+          break;
+      }                //now s_R is in the range [0,s_i-1]
+      addInt_(s_R,1);  //now s_R is in the range [1,s_i]
+      add_(s_R,s_i);   //now s_R is in the range [s_i+1,2*s_i]
+
+      copy_(s_n,s_q);
+      mult_(s_n,s_R); 
+      multInt_(s_n,2);
+      addInt_(s_n,1);    //s_n=2*s_R*s_q+1
+      
+      copy_(s_r2,s_R);
+      multInt_(s_r2,2);  //s_r2=2*s_R
+
+      //check s_n for divisibility by small primes up to B
+      for (divisible=0,j=0; (j<primes.length) && (primes[j]<B); j++)
+        if (modInt(s_n,primes[j])==0 && !equalsInt(s_n,primes[j])) {
+          divisible=1;
+          break;
+        }      
+
+      if (!divisible)    //if it passes small primes check, then try a single Miller-Rabin base 2
+        if (!millerRabinInt(s_n,2)) //this line represents 75% of the total runtime for randTruePrime_ 
+          divisible=1;
+
+      if (!divisible) {  //if it passes that test, continue checking s_n
+        addInt_(s_n,-3);
+        for (j=s_n.length-1;(s_n[j]==0) && (j>0); j--);  //strip leading zeros
+        for (zz=0,w=s_n[j]; w; (w>>=1),zz++);
+        zz+=bpe*j;                             //zz=number of bits in s_n, ignoring leading zeros
+        for (;;) {  //generate z-bit numbers until one falls in the range [0,s_n-1]
+          randBigInt_(s_a,zz,0);
+          if (greater(s_n,s_a))
+            break;
+        }                //now s_a is in the range [0,s_n-1]
+        addInt_(s_n,3);  //now s_a is in the range [0,s_n-4]
+        addInt_(s_a,2);  //now s_a is in the range [2,s_n-2]
+        copy_(s_b,s_a);
+        copy_(s_n1,s_n);
+        addInt_(s_n1,-1);
+        powMod_(s_b,s_n1,s_n);   //s_b=s_a^(s_n-1) modulo s_n
+        addInt_(s_b,-1);
+        if (isZero(s_b)) {
+          copy_(s_b,s_a);
+          powMod_(s_b,s_r2,s_n);
+          addInt_(s_b,-1);
+          copy_(s_aa,s_n);
+          copy_(s_d,s_b);
+          GCD_(s_d,s_n);  //if s_b and s_n are relatively prime, then s_n is a prime
+          if (equalsInt(s_d,1)) {
+            copy_(ans,s_aa);
+            return;     //if we've made it this far, then s_n is absolutely guaranteed to be prime
+          }
+        }
+      }
+    }
+  }
+
+  //Return an n-bit random BigInt (n>=1).  If s=1, then the most significant of those n bits is set to 1.
+  function randBigInt(n,s) {
+    var a,b;
+    a=Math.floor((n-1)/bpe)+2; //# array elements to hold the BigInt with a leading 0 element
+    b=int2bigInt(0,0,a);
+    randBigInt_(b,n,s);
+    return b;
+  }
+
+  //Set b to an n-bit random BigInt.  If s=1, then the most significant of those n bits is set to 1.
+  //Array b must be big enough to hold the result. Must have n>=1
+  function randBigInt_(b,n,s) {
+    var i,a;
+    for (i=0;i<b.length;i++)
+      b[i]=0;
+    a=Math.floor((n-1)/bpe)+1; //# array elements to hold the BigInt
+    for (i=0;i<a;i++) {
+      b[i]=randomBitInt(bpe);
+    }
+    b[a-1] &= (2<<((n-1)%bpe))-1;
+    if (s==1)
+      b[a-1] |= (1<<((n-1)%bpe));
+  }
+
+  //Return the greatest common divisor of bigInts x and y (each with same number of elements).
+  function GCD(x,y) {
+    var xc,yc;
+    xc=dup(x);
+    yc=dup(y);
+    GCD_(xc,yc);
+    return xc;
+  }
+
+  //set x to the greatest common divisor of bigInts x and y (each with same number of elements).
+  //y is destroyed.
+  function GCD_(x,y) {
+    var i,xp,yp,A,B,C,D,q,sing,qp;
+    if (T.length!=x.length)
+      T=dup(x);
+
+    sing=1;
+    while (sing) { //while y has nonzero elements other than y[0]
+      sing=0;
+      for (i=1;i<y.length;i++) //check if y has nonzero elements other than 0
+        if (y[i]) {
+          sing=1;
+          break;
+        }
+      if (!sing) break; //quit when y all zero elements except possibly y[0]
+
+      for (i=x.length;!x[i] && i>=0;i--);  //find most significant element of x
+      xp=x[i];
+      yp=y[i];
+      A=1; B=0; C=0; D=1;
+      while ((yp+C) && (yp+D)) {
+        q =Math.floor((xp+A)/(yp+C));
+        qp=Math.floor((xp+B)/(yp+D));
+        if (q!=qp)
+          break;
+        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)      
+        t= B-q*D;   B=D;   D=t;
+        t=xp-q*yp; xp=yp; yp=t;
+      }
+      if (B) {
+        copy_(T,x);
+        linComb_(x,y,A,B); //x=A*x+B*y
+        linComb_(y,T,D,C); //y=D*y+C*T
+      } else {
+        mod_(x,y);
+        copy_(T,x);
+        copy_(x,y);
+        copy_(y,T);
+      } 
+    }
+    if (y[0]==0)
+      return;
+    t=modInt(x,y[0]);
+    copyInt_(x,y[0]);
+    y[0]=t;
+    while (y[0]) {
+      x[0]%=y[0];
+      t=x[0]; x[0]=y[0]; y[0]=t;
+    }
+  }
+
+  //do x=x**(-1) mod n, for bigInts x and n.
+  //If no inverse exists, it sets x to zero and returns 0, else it returns 1.
+  //The x array must be at least as large as the n array.
+  function inverseMod_(x,n) {
+    var k=1+2*Math.max(x.length,n.length);
+
+    if(!(x[0]&1)  && !(n[0]&1)) {  //if both inputs are even, then inverse doesn't exist
+      copyInt_(x,0);
+      return 0;
+    }
+
+    if (eg_u.length!=k) {
+      eg_u=new Array(k);
+      eg_v=new Array(k);
+      eg_A=new Array(k);
+      eg_B=new Array(k);
+      eg_C=new Array(k);
+      eg_D=new Array(k);
+    }
+
+    copy_(eg_u,x);
+    copy_(eg_v,n);
+    copyInt_(eg_A,1);
+    copyInt_(eg_B,0);
+    copyInt_(eg_C,0);
+    copyInt_(eg_D,1);
+    for (;;) {
+      while(!(eg_u[0]&1)) {  //while eg_u is even
+        halve_(eg_u);
+        if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if eg_A==eg_B==0 mod 2
+          halve_(eg_A);
+          halve_(eg_B);      
+        } else {
+          add_(eg_A,n);  halve_(eg_A);
+          sub_(eg_B,x);  halve_(eg_B);
+        }
+      }
+
+      while (!(eg_v[0]&1)) {  //while eg_v is even
+        halve_(eg_v);
+        if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if eg_C==eg_D==0 mod 2
+          halve_(eg_C);
+          halve_(eg_D);      
+        } else {
+          add_(eg_C,n);  halve_(eg_C);
+          sub_(eg_D,x);  halve_(eg_D);
+        }
+      }
+
+      if (!greater(eg_v,eg_u)) { //eg_v <= eg_u
+        sub_(eg_u,eg_v);
+        sub_(eg_A,eg_C);
+        sub_(eg_B,eg_D);
+      } else {                   //eg_v > eg_u
+        sub_(eg_v,eg_u);
+        sub_(eg_C,eg_A);
+        sub_(eg_D,eg_B);
+      }
+
+      if (equalsInt(eg_u,0)) {
+        while (negative(eg_C)) //make sure answer is nonnegative
+          add_(eg_C,n);
+        copy_(x,eg_C);
+
+        if (!equalsInt(eg_v,1)) { //if GCD_(x,n)!=1, then there is no inverse
+          copyInt_(x,0);
+          return 0;
+        }
+        return 1;
+      }
+    }
+  }
+
+  //return x**(-1) mod n, for integers x and n.  Return 0 if there is no inverse
+  function inverseModInt(x,n) {
+    var a=1,b=0,t;
+    for (;;) {
+      if (x==1) return a;
+      if (x==0) return 0;
+      b-=a*Math.floor(n/x);
+      n%=x;
+
+      if (n==1) return b; //to avoid negatives, change this b to n-b, and each -= to +=
+      if (n==0) return 0;
+      a-=b*Math.floor(x/n);
+      x%=n;
+    }
+  }
+
+  //this deprecated function is for backward compatibility only. 
+  function inverseModInt_(x,n) {
+     return inverseModInt(x,n);
+  }
+
+
+  //Given positive bigInts x and y, change the bigints v, a, and b to positive bigInts such that:
+  //     v = GCD_(x,y) = a*x-b*y
+  //The bigInts v, a, b, must have exactly as many elements as the larger of x and y.
+  function eGCD_(x,y,v,a,b) {
+    var g=0;
+    var k=Math.max(x.length,y.length);
+    if (eg_u.length!=k) {
+      eg_u=new Array(k);
+      eg_A=new Array(k);
+      eg_B=new Array(k);
+      eg_C=new Array(k);
+      eg_D=new Array(k);
+    }
+    while(!(x[0]&1)  && !(y[0]&1)) {  //while x and y both even
+      halve_(x);
+      halve_(y);
+      g++;
+    }
+    copy_(eg_u,x);
+    copy_(v,y);
+    copyInt_(eg_A,1);
+    copyInt_(eg_B,0);
+    copyInt_(eg_C,0);
+    copyInt_(eg_D,1);
+    for (;;) {
+      while(!(eg_u[0]&1)) {  //while u is even
+        halve_(eg_u);
+        if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if A==B==0 mod 2
+          halve_(eg_A);
+          halve_(eg_B);      
+        } else {
+          add_(eg_A,y);  halve_(eg_A);
+          sub_(eg_B,x);  halve_(eg_B);
+        }
+      }
+
+      while (!(v[0]&1)) {  //while v is even
+        halve_(v);
+        if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if C==D==0 mod 2
+          halve_(eg_C);
+          halve_(eg_D);      
+        } else {
+          add_(eg_C,y);  halve_(eg_C);
+          sub_(eg_D,x);  halve_(eg_D);
+        }
+      }
+
+      if (!greater(v,eg_u)) { //v<=u
+        sub_(eg_u,v);
+        sub_(eg_A,eg_C);
+        sub_(eg_B,eg_D);
+      } else {                //v>u
+        sub_(v,eg_u);
+        sub_(eg_C,eg_A);
+        sub_(eg_D,eg_B);
+      }
+      if (equalsInt(eg_u,0)) {
+        while (negative(eg_C)) {   //make sure a (C) is nonnegative
+          add_(eg_C,y);
+          sub_(eg_D,x);
+        }
+        multInt_(eg_D,-1);  ///make sure b (D) is nonnegative
+        copy_(a,eg_C);
+        copy_(b,eg_D);
+        leftShift_(v,g);
+        return;
+      }
+    }
+  }
+
+
+  //is bigInt x negative?
+  function negative(x) {
+    return ((x[x.length-1]>>(bpe-1))&1);
+  }
+
+
+  //is (x << (shift*bpe)) > y?
+  //x and y are nonnegative bigInts
+  //shift is a nonnegative integer
+  function greaterShift(x,y,shift) {
+    var i, kx=x.length, ky=y.length;
+    var k=((kx+shift)<ky) ? (kx+shift) : ky;
+    for (i=ky-1-shift; i<kx && i>=0; i++) 
+      if (x[i]>0)
+        return 1; //if there are nonzeros in x to the left of the first column of y, then x is bigger
+    for (i=kx-1+shift; i<ky; i++)
+      if (y[i]>0)
+        return 0; //if there are nonzeros in y to the left of the first column of x, then x is not bigger
+    for (i=k-1; i>=shift; i--)
+      if      (x[i-shift]>y[i]) return 1;
+      else if (x[i-shift]<y[i]) return 0;
+    return 0;
+  }
+
+  //is x > y? (x and y both nonnegative)
+  function greater(x,y) {
+    var i;
+    var k=(x.length<y.length) ? x.length : y.length;
+
+    for (i=x.length;i<y.length;i++)
+      if (y[i])
+        return 0;  //y has more digits
+
+    for (i=y.length;i<x.length;i++)
+      if (x[i])
+        return 1;  //x has more digits
+
+    for (i=k-1;i>=0;i--)
+      if (x[i]>y[i])
+        return 1;
+      else if (x[i]<y[i])
+        return 0;
+    return 0;
+  }
+
+  //divide x by y giving quotient q and remainder r.  (q=floor(x/y),  r=x mod y).  All 4 are bigints.
+  //x must have at least one leading zero element.
+  //y must be nonzero.
+  //q and r must be arrays that are exactly the same length as x. (Or q can have more).
+  //Must have x.length >= y.length >= 2.
+  function divide_(x,y,q,r) {
+    var kx, ky;
+    var i,j,y1,y2,c,a,b;
+    copy_(r,x);
+    for (ky=y.length;y[ky-1]==0;ky--); //ky is number of elements in y, not including leading zeros
+
+    //normalize: ensure the most significant element of y has its highest bit set  
+    b=y[ky-1];
+    for (a=0; b; a++)
+      b>>=1;  
+    a=bpe-a;  //a is how many bits to shift so that the high order bit of y is leftmost in its array element
+    leftShift_(y,a);  //multiply both by 1<<a now, then divide both by that at the end
+    leftShift_(r,a);
+
+    //Rob Visser discovered a bug: the following line was originally just before the normalization.
+    for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); //kx is number of elements in normalized x, not including leading zeros
+
+    copyInt_(q,0);                      // q=0
+    while (!greaterShift(y,r,kx-ky)) {  // while (leftShift_(y,kx-ky) <= r) {
+      subShift_(r,y,kx-ky);             //   r=r-leftShift_(y,kx-ky)
+      q[kx-ky]++;                       //   q[kx-ky]++;
+    }                                   // }
+
+    for (i=kx-1; i>=ky; i--) {
+      if (r[i]==y[ky-1])
+        q[i-ky]=mask;
+      else
+        q[i-ky]=Math.floor((r[i]*radix+r[i-1])/y[ky-1]);
+
+      //The following for(;;) loop is equivalent to the commented while loop, 
+      //except that the uncommented version avoids overflow.
+      //The commented loop comes from HAC, which assumes r[-1]==y[-1]==0
+      //  while (q[i-ky]*(y[ky-1]*radix+y[ky-2]) > r[i]*radix*radix+r[i-1]*radix+r[i-2])
+      //    q[i-ky]--;    
+      for (;;) {
+        y2=(ky>1 ? y[ky-2] : 0)*q[i-ky];
+        c=y2>>bpe;
+        y2=y2 & mask;
+        y1=c+q[i-ky]*y[ky-1];
+        c=y1>>bpe;
+        y1=y1 & mask;
+
+        if (c==r[i] ? y1==r[i-1] ? y2>(i>1 ? r[i-2] : 0) : y1>r[i-1] : c>r[i]) 
+          q[i-ky]--;
+        else
+          break;
+      }
+
+      linCombShift_(r,y,-q[i-ky],i-ky);    //r=r-q[i-ky]*leftShift_(y,i-ky)
+      if (negative(r)) {
+        addShift_(r,y,i-ky);         //r=r+leftShift_(y,i-ky)
+        q[i-ky]--;
+      }
+    }
+
+    rightShift_(y,a);  //undo the normalization step
+    rightShift_(r,a);  //undo the normalization step
+  }
+
+  //do carries and borrows so each element of the bigInt x fits in bpe bits.
+  function carry_(x) {
+    var i,k,c,b;
+    k=x.length;
+    c=0;
+    for (i=0;i<k;i++) {
+      c+=x[i];
+      b=0;
+      if (c<0) {
+        b=-(c>>bpe);
+        c+=b*radix;
+      }
+      x[i]=c & mask;
+      c=(c>>bpe)-b;
+    }
+  }
+
+  //return x mod n for bigInt x and integer n.
+  function modInt(x,n) {
+    var i,c=0;
+    for (i=x.length-1; i>=0; i--)
+      c=(c*radix+x[i])%n;
+    return c;
+  }
+
+  //convert the integer t into a bigInt with at least the given number of bits.
+  //the returned array stores the bigInt in bpe-bit chunks, little endian (buff[0] is least significant word)
+  //Pad the array with leading zeros so that it has at least minSize elements.
+  //There will always be at least one leading 0 element.
+  function int2bigInt(t,bits,minSize) {   
+    var i,k, buff;
+    k=Math.ceil(bits/bpe)+1;
+    k=minSize>k ? minSize : k;
+    buff=new Array(k);
+    copyInt_(buff,t);
+    return buff;
+  }
+
+  //return the bigInt given a string representation in a given base.  
+  //Pad the array with leading zeros so that it has at least minSize elements.
+  //If base=-1, then it reads in a space-separated list of array elements in decimal.
+  //The array will always have at least one leading zero, unless base=-1.
+  function str2bigInt(s,base,minSize) {
+    var d, i, j, x, y, kk;
+    var k=s.length;
+    if (base==-1) { //comma-separated list of array elements in decimal
+      x=new Array(0);
+      for (;;) {
+        y=new Array(x.length+1);
+        for (i=0;i<x.length;i++)
+          y[i+1]=x[i];
+        y[0]=parseInt(s,10);
+        x=y;
+        d=s.indexOf(',',0);
+        if (d<1) 
+          break;
+        s=s.substring(d+1);
+        if (s.length==0)
+          break;
+      }
+      if (x.length<minSize) {
+        y=new Array(minSize);
+        copy_(y,x);
+        return y;
+      }
+      return x;
+    }
+
+    // log2(base)*k
+    var bb = base, p = 0;
+    var b = base == 1 ? k : 0;
+    while (bb > 1) {
+      if (bb & 1) p = 1;
+      b += k;
+      bb >>= 1;
+    }
+    b += p*k;
+
+    x=int2bigInt(0,b,0);
+    for (i=0;i<k;i++) {
+      d=digitsStr.indexOf(s.substring(i,i+1),0);
+      if (base<=36 && d>=36)  //convert lowercase to uppercase if base<=36
+        d-=26;
+      if (d>=base || d<0) {   //stop at first illegal character
+        break;
+      }
+      multInt_(x,base);
+      addInt_(x,d);
+    }
+
+    for (k=x.length;k>0 && !x[k-1];k--); //strip off leading zeros
+    k=minSize>k+1 ? minSize : k+1;
+    y=new Array(k);
+    kk=k<x.length ? k : x.length;
+    for (i=0;i<kk;i++)
+      y[i]=x[i];
+    for (;i<k;i++)
+      y[i]=0;
+    return y;
+  }
+
+  //is bigint x equal to integer y?
+  //y must have less than bpe bits
+  function equalsInt(x,y) {
+    var i;
+    if (x[0]!=y)
+      return 0;
+    for (i=1;i<x.length;i++)
+      if (x[i])
+        return 0;
+    return 1;
+  }
+
+  //are bigints x and y equal?
+  //this works even if x and y are different lengths and have arbitrarily many leading zeros
+  function equals(x,y) {
+    var i;
+    var k=x.length<y.length ? x.length : y.length;
+    for (i=0;i<k;i++)
+      if (x[i]!=y[i])
+        return 0;
+    if (x.length>y.length) {
+      for (;i<x.length;i++)
+        if (x[i])
+          return 0;
+    } else {
+      for (;i<y.length;i++)
+        if (y[i])
+          return 0;
+    }
+    return 1;
+  }
+
+  //is the bigInt x equal to zero?
+  function isZero(x) {
+    var i;
+    for (i=0;i<x.length;i++)
+      if (x[i])
+        return 0;
+    return 1;
+  }
+
+  //convert a bigInt into a string in a given base, from base 2 up to base 95.
+  //Base -1 prints the contents of the array representing the number.
+  function bigInt2str(x,base) {
+    var i,t,s="";
+
+    if (s6.length!=x.length) 
+      s6=dup(x);
+    else
+      copy_(s6,x);
+
+    if (base==-1) { //return the list of array contents
+      for (i=x.length-1;i>0;i--)
+        s+=x[i]+',';
+      s+=x[0];
+    }
+    else { //return it in the given base
+      while (!isZero(s6)) {
+        t=divInt_(s6,base);  //t=s6 % base; s6=floor(s6/base);
+        s=digitsStr.substring(t,t+1)+s;
+      }
+    }
+    if (s.length==0)
+      s="0";
+    return s;
+  }
+
+  //returns a duplicate of bigInt x
+  function dup(x) {
+    var i, buff;
+    buff=new Array(x.length);
+    copy_(buff,x);
+    return buff;
+  }
+
+  //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).
+  function copy_(x,y) {
+    var i;
+    var k=x.length<y.length ? x.length : y.length;
+    for (i=0;i<k;i++)
+      x[i]=y[i];
+    for (i=k;i<x.length;i++)
+      x[i]=0;
+  }
+
+  //do x=y on bigInt x and integer y.  
+  function copyInt_(x,n) {
+    var i,c;
+    for (c=n,i=0;i<x.length;i++) {
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+  }
+
+  //do x=x+n where x is a bigInt and n is an integer.
+  //x must be large enough to hold the result.
+  function addInt_(x,n) {
+    var i,k,c,b;
+    x[0]+=n;
+    k=x.length;
+    c=0;
+    for (i=0;i<k;i++) {
+      c+=x[i];
+      b=0;
+      if (c<0) {
+        b=-(c>>bpe);
+        c+=b*radix;
+      }
+      x[i]=c & mask;
+      c=(c>>bpe)-b;
+      if (!c) return; //stop carrying as soon as the carry is zero
+    }
+  }
+
+  //right shift bigInt x by n bits.  0 <= n < bpe.
+  function rightShift_(x,n) {
+    var i;
+    var k=Math.floor(n/bpe);
+    if (k) {
+      for (i=0;i<x.length-k;i++) //right shift x by k elements
+        x[i]=x[i+k];
+      for (;i<x.length;i++)
+        x[i]=0;
+      n%=bpe;
+    }
+    for (i=0;i<x.length-1;i++) {
+      x[i]=mask & ((x[i+1]<<(bpe-n)) | (x[i]>>n));
+    }
+    x[i]>>=n;
+  }
+
+  //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement
+  function halve_(x) {
+    var i;
+    for (i=0;i<x.length-1;i++) {
+      x[i]=mask & ((x[i+1]<<(bpe-1)) | (x[i]>>1));
+    }
+    x[i]=(x[i]>>1) | (x[i] & (radix>>1));  //most significant bit stays the same
+  }
+
+  //left shift bigInt x by n bits.
+  function leftShift_(x,n) {
+    var i;
+    var k=Math.floor(n/bpe);
+    if (k) {
+      for (i=x.length; i>=k; i--) //left shift x by k elements
+        x[i]=x[i-k];
+      for (;i>=0;i--)
+        x[i]=0;  
+      n%=bpe;
+    }
+    if (!n)
+      return;
+    for (i=x.length-1;i>0;i--) {
+      x[i]=mask & ((x[i]<<n) | (x[i-1]>>(bpe-n)));
+    }
+    x[i]=mask & (x[i]<<n);
+  }
+
+  //do x=x*n where x is a bigInt and n is an integer.
+  //x must be large enough to hold the result.
+  function multInt_(x,n) {
+    var i,k,c,b;
+    if (!n)
+      return;
+    k=x.length;
+    c=0;
+    for (i=0;i<k;i++) {
+      c+=x[i]*n;
+      b=0;
+      if (c<0) {
+        b=-(c>>bpe);
+        c+=b*radix;
+      }
+      x[i]=c & mask;
+      c=(c>>bpe)-b;
+    }
+  }
+
+  //do x=floor(x/n) for bigInt x and integer n, and return the remainder
+  function divInt_(x,n) {
+    var i,r=0,s;
+    for (i=x.length-1;i>=0;i--) {
+      s=r*radix+x[i];
+      x[i]=Math.floor(s/n);
+      r=s%n;
+    }
+    return r;
+  }
+
+  //do the linear combination x=a*x+b*y for bigInts x and y, and integers a and b.
+  //x must be large enough to hold the answer.
+  function linComb_(x,y,a,b) {
+    var i,c,k,kk;
+    k=x.length<y.length ? x.length : y.length;
+    kk=x.length;
+    for (c=0,i=0;i<k;i++) {
+      c+=a*x[i]+b*y[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+    for (i=k;i<kk;i++) {
+      c+=a*x[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+  }
+
+  //do the linear combination x=a*x+b*(y<<(ys*bpe)) for bigInts x and y, and integers a, b and ys.
+  //x must be large enough to hold the answer.
+  function linCombShift_(x,y,b,ys) {
+    var i,c,k,kk;
+    k=x.length<ys+y.length ? x.length : ys+y.length;
+    kk=x.length;
+    for (c=0,i=ys;i<k;i++) {
+      c+=x[i]+b*y[i-ys];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+    for (i=k;c && i<kk;i++) {
+      c+=x[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+  }
+
+  //do x=x+(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys.
+  //x must be large enough to hold the answer.
+  function addShift_(x,y,ys) {
+    var i,c,k,kk;
+    k=x.length<ys+y.length ? x.length : ys+y.length;
+    kk=x.length;
+    for (c=0,i=ys;i<k;i++) {
+      c+=x[i]+y[i-ys];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+    for (i=k;c && i<kk;i++) {
+      c+=x[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+  }
+
+  //do x=x-(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys.
+  //x must be large enough to hold the answer.
+  function subShift_(x,y,ys) {
+    var i,c,k,kk;
+    k=x.length<ys+y.length ? x.length : ys+y.length;
+    kk=x.length;
+    for (c=0,i=ys;i<k;i++) {
+      c+=x[i]-y[i-ys];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+    for (i=k;c && i<kk;i++) {
+      c+=x[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+  }
+
+  //do x=x-y for bigInts x and y.
+  //x must be large enough to hold the answer.
+  //negative answers will be 2s complement
+  function sub_(x,y) {
+    var i,c,k,kk;
+    k=x.length<y.length ? x.length : y.length;
+    for (c=0,i=0;i<k;i++) {
+      c+=x[i]-y[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+    for (i=k;c && i<x.length;i++) {
+      c+=x[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+  }
+
+  //do x=x+y for bigInts x and y.
+  //x must be large enough to hold the answer.
+  function add_(x,y) {
+    var i,c,k,kk;
+    k=x.length<y.length ? x.length : y.length;
+    for (c=0,i=0;i<k;i++) {
+      c+=x[i]+y[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+    for (i=k;c && i<x.length;i++) {
+      c+=x[i];
+      x[i]=c & mask;
+      c>>=bpe;
+    }
+  }
+
+  //do x=x*y for bigInts x and y.  This is faster when y<x.
+  function mult_(x,y) {
+    var i;
+    if (ss.length!=2*x.length)
+      ss=new Array(2*x.length);
+    copyInt_(ss,0);
+    for (i=0;i<y.length;i++)
+      if (y[i])
+        linCombShift_(ss,x,y[i],i);   //ss=1*ss+y[i]*(x<<(i*bpe))
+    copy_(x,ss);
+  }
+
+  //do x=x mod n for bigInts x and n.
+  function mod_(x,n) {
+    if (s4.length!=x.length)
+      s4=dup(x);
+    else
+      copy_(s4,x);
+    if (s5.length!=x.length)
+      s5=dup(x);  
+    divide_(s4,n,s5,x);  //x = remainder of s4 / n
+  }
+
+  //do x=x*y mod n for bigInts x,y,n.
+  //for greater speed, let y<x.
+  function multMod_(x,y,n) {
+    var i;
+    if (s0.length!=2*x.length)
+      s0=new Array(2*x.length);
+    copyInt_(s0,0);
+    for (i=0;i<y.length;i++)
+      if (y[i])
+        linCombShift_(s0,x,y[i],i);   //s0=1*s0+y[i]*(x<<(i*bpe))
+    mod_(s0,n);
+    copy_(x,s0);
+  }
+
+  //do x=x*x mod n for bigInts x,n.
+  function squareMod_(x,n) {
+    var i,j,d,c,kx,kn,k;
+    for (kx=x.length; kx>0 && !x[kx-1]; kx--);  //ignore leading zeros in x
+    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
+    if (s0.length!=k) 
+      s0=new Array(k);
+    copyInt_(s0,0);
+    for (i=0;i<kx;i++) {
+      c=s0[2*i]+x[i]*x[i];
+      s0[2*i]=c & mask;
+      c>>=bpe;
+      for (j=i+1;j<kx;j++) {
+        c=s0[i+j]+2*x[i]*x[j]+c;
+        s0[i+j]=(c & mask);
+        c>>=bpe;
+      }
+      s0[i+kx]=c;
+    }
+    mod_(s0,n);
+    copy_(x,s0);
+  }
+
+  //return x with exactly k leading zero elements
+  function trim(x,k) {
+    var i,y;
+    for (i=x.length; i>0 && !x[i-1]; i--);
+    y=new Array(i+k);
+    copy_(y,x);
+    return y;
+  }
+
+  //do x=x**y mod n, where x,y,n are bigInts and ** is exponentiation.  0**0=1.
+  //this is faster when n is odd.  x usually needs to have as many elements as n.
+  function powMod_(x,y,n) {
+    var k1,k2,kn,np;
+    if(s7.length!=n.length)
+      s7=dup(n);
+
+    //for even modulus, use a simple square-and-multiply algorithm,
+    //rather than using the more complex Montgomery algorithm.
+    if ((n[0]&1)==0) {
+      copy_(s7,x);
+      copyInt_(x,1);
+      while(!equalsInt(y,0)) {
+        if (y[0]&1)
+          multMod_(x,s7,n);
+        divInt_(y,2);
+        squareMod_(s7,n); 
+      }
+      return;
+    }
+
+    //calculate np from n for the Montgomery multiplications
+    copyInt_(s7,0);
+    for (kn=n.length;kn>0 && !n[kn-1];kn--);
+    np=radix-inverseModInt(modInt(n,radix),radix);
+    s7[kn]=1;
+    multMod_(x ,s7,n);   // x = x * 2**(kn*bp) mod n
+
+    if (s3.length!=x.length)
+      s3=dup(x);
+    else
+      copy_(s3,x);
+
+    for (k1=y.length-1;k1>0 & !y[k1]; k1--);  //k1=first nonzero element of y
+    if (y[k1]==0) {  //anything to the 0th power is 1
+      copyInt_(x,1);
+      return;
+    }
+    for (k2=1<<(bpe-1);k2 && !(y[k1] & k2); k2>>=1);  //k2=position of first 1 bit in y[k1]
+    for (;;) {
+      if (!(k2>>=1)) {  //look at next bit of y
+        k1--;
+        if (k1<0) {
+          mont_(x,one,n,np);
+          return;
+        }
+        k2=1<<(bpe-1);
+      }    
+      mont_(x,x,n,np);
+
+      if (k2 & y[k1]) //if next bit is a 1
+        mont_(x,s3,n,np);
+    }
+  }
+
+
+  //do x=x*y*Ri mod n for bigInts x,y,n, 
+  //  where Ri = 2**(-kn*bpe) mod n, and kn is the 
+  //  number of elements in the n array, not 
+  //  counting leading zeros.  
+  //x array must have at least as many elemnts as the n array
+  //It's OK if x and y are the same variable.
+  //must have:
+  //  x,y < n
+  //  n is odd
+  //  np = -(n^(-1)) mod radix
+  function mont_(x,y,n,np) {
+    var i,j,c,ui,t,ks;
+    var kn=n.length;
+    var ky=y.length;
+
+    if (sa.length!=kn)
+      sa=new Array(kn);
+      
+    copyInt_(sa,0);
+
+    for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n
+    for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y
+    ks=sa.length-1; //sa will never have more than this many nonzero elements.  
+
+    //the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large numbers
+    for (i=0; i<kn; i++) {
+      t=sa[0]+x[i]*y[0];
+      ui=((t & mask) * np) & mask;  //the inner "& mask" was needed on Safari (but not MSIE) at one time
+      c=(t+ui*n[0]) >> bpe;
+      t=x[i];
+      
+      //do sa=(sa+x[i]*y+ui*n)/b   where b=2**bpe.  Loop is unrolled 5-fold for speed
+      j=1;
+      for (;j<ky-4;) { c+=sa[j]+ui*n[j]+t*y[j];   sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j]+t*y[j];   sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j]+t*y[j];   sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j]+t*y[j];   sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j]+t*y[j];   sa[j-1]=c & mask;   c>>=bpe;   j++; }    
+      for (;j<ky;)   { c+=sa[j]+ui*n[j]+t*y[j];   sa[j-1]=c & mask;   c>>=bpe;   j++; }
+      for (;j<kn-4;) { c+=sa[j]+ui*n[j];          sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j];          sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j];          sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j];          sa[j-1]=c & mask;   c>>=bpe;   j++;
+                       c+=sa[j]+ui*n[j];          sa[j-1]=c & mask;   c>>=bpe;   j++; }  
+      for (;j<kn;)   { c+=sa[j]+ui*n[j];          sa[j-1]=c & mask;   c>>=bpe;   j++; }   
+      for (;j<ks;)   { c+=sa[j];                  sa[j-1]=c & mask;   c>>=bpe;   j++; }  
+      sa[j-1]=c & mask;
+    }
+
+    if (!greater(n,sa))
+      sub_(sa,n);
+    copy_(x,sa);
+  }
+
+
+  // otr.js stuff
+
+  var BigInt = {
+      str2bigInt    : str2bigInt
+    , bigInt2str    : bigInt2str
+    , int2bigInt    : int2bigInt
+    , multMod       : multMod
+    , powMod        : powMod
+    , inverseMod    : inverseMod
+    , randBigInt    : randBigInt
+    , randBigInt_   : randBigInt_
+    , equals        : equals
+    , equalsInt     : equalsInt
+    , sub           : sub
+    , mod           : mod
+    , mod_          : mod_
+    , modInt        : modInt
+    , mult          : mult
+    , divInt_       : divInt_
+    , rightShift_   : rightShift_
+    , leftShift_    : leftShift_
+    , dup           : dup
+    , greater       : greater
+    , add           : add
+    , addInt        : addInt
+    , addInt_       : addInt_
+    , isZero        : isZero
+    , bitSize       : bitSize
+    , randTruePrime : randTruePrime
+    , millerRabin   : millerRabin
+    , divide_       : divide_
+    , trim          : trim
+    , expand        : expand
+    , bpe           : bpe
+    , primes        : primes
+    , findPrimes    : findPrimes
+    , getSeed       : getSeed
+  }
+
+  // from http://davidbau.com/encode/seedrandom.js
+
+  var randomBitInt
+
+  function seedRand(buf) {
+
+    var state = new Salsa20([
+      buf[ 0], buf[ 1], buf[ 2], buf[ 3], buf[ 4], buf[ 5], buf[ 6], buf[ 7],
+      buf[ 8], buf[ 9], buf[10], buf[11], buf[12], buf[13], buf[14], buf[15],
+      buf[16], buf[17], buf[18], buf[19], buf[20], buf[21], buf[22], buf[23],
+      buf[24], buf[25], buf[26], buf[27], buf[28], buf[29], buf[30], buf[31]
+    ],[
+      buf[32], buf[33], buf[34], buf[35], buf[36], buf[37], buf[38], buf[39]
+    ])
+
+    var width = 256
+      , chunks = 6
+      , significance = Math.pow(2, 52)
+      , overflow = significance * 2
+
+    function numerator() {
+      var bytes = state.getBytes(chunks)
+      var i = 0, r = 0
+      for (; i < chunks; i++) {
+        r = r * width + bytes[i]
+      }
+      return r
+    }
+
+    function randomByte() {
+      return state.getBytes(1)[0]
+    }
+
+    randomBitInt = function (k) {
+      if (k > 31) throw new Error("Too many bits.")
+      var i = 0, r = 0
+      var b = Math.floor(k / 8)
+      var mask = (1 << (k % 8)) - 1
+      if (mask) r = randomByte() & mask
+      for (; i < b; i++)
+        r = (256 * r) + randomByte()
+      return r
+    }
+
+    // This function returns a random double in [0, 1) that contains
+    // randomness in every bit of the mantissa of the IEEE 754 value.
+
+    return function () {               // Closure to return a random double:
+      var n = numerator()              // Start with a numerator n < 2 ^ 48
+        , d = Math.pow(width, chunks)  //   and denominator d = 2 ^ 48.
+        , x = 0                        //   and no 'extra last byte'.
+      while (n < significance) {       // Fill up all significant digits by
+        n = (n + x) * width            //   shifting numerator and
+        d *= width                     //   denominator and generating a
+        x = randomByte()               //   new least-significant-byte.
+      }
+      while (n >= overflow) {          // To avoid rounding up, before adding
+        n /= 2                         //   last byte, shift everything
+        d /= 2                         //   right using integer math until
+        x >>>= 1                       //   we have exactly the desired bits.
+      }
+      return (n + x) / d               // Form the number within [0, 1).
+    }
+
+  }
+
+  function getSeed() {
+    var buf
+    if ( (typeof crypto !== 'undefined') &&
+         (typeof crypto.randomBytes === 'function')
+    ) {
+      try {
+        buf = crypto.randomBytes(40)
+      } catch (e) { throw e }
+    } else if ( (typeof crypto !== 'undefined') &&
+                (typeof crypto.getRandomValues === 'function')
+    ) {
+      buf = new Uint8Array(40)
+      crypto.getRandomValues(buf)
+    } else {
+      throw new Error('Keys should not be generated without CSPRNG.')
+    }
+    return Array.prototype.slice.call(buf, 0)
+  }
+
+  ;(function seed() {
+    var HAS_CSPRNG = ((typeof crypto === 'undefined') || 
+        ((typeof crypto.randomBytes !== 'function') &&
+            (typeof crypto.getRandomValues !== 'function')
+    ));
+    if (!HAS_CSPRNG) {
+        return;
+    }
+    Math.random = seedRand(getSeed())
+
+    // reseed every 5 mins (not in ww)
+    if ( typeof setTimeout === 'function' && typeof document !== 'undefined' )
+      setTimeout(seed, 5 * 60 * 1000)
+
+  }())
+
+  return BigInt
+}))

tests_main.js

@@ -12,7 +12,7 @@ require.config({
         "strophe.vcard": "components/strophe.vcard/index",
         "strophe.disco": "components/strophe.disco/index",
         "salsa20": "components/otr/build/dep/salsa20",
-        "bigint": "components/otr/build/dep/bigint",
+        "bigint": "src/bigint",
         "crypto.core": "components/otr/vendor/cryptojs/core",
         "crypto.enc-base64": "components/otr/vendor/cryptojs/enc-base64",
         "crypto.md5": "components/crypto-js/src/md5",