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authorausiv4 <ausiv4@eb105b4a-77de-11de-a249-6bf219df57d5>2009-07-24 14:01:04 +0000
committerausiv4 <ausiv4@eb105b4a-77de-11de-a249-6bf219df57d5>2009-07-24 14:01:04 +0000
commit67f64e7564d5eea4cb71afd719786fd7977f4b98 (patch)
tree3be51d7f78d37ab3560d4982b595842d1643ae0d
parent8d359f4d8e27bf5992508bc11486a482d270d6f8 (diff)
Merge proper-random with trunk.
Diffstat
-rw-r--r--django/srpproject/srp/views.py22
-rw-r--r--javascript/BigInt.js1400
-rw-r--r--javascript/jsbn.js559
-rw-r--r--javascript/jsbn2.js645
-rw-r--r--javascript/prng4.js45
-rw-r--r--javascript/rng.js68
-rw-r--r--javascript/srp.js44
7 files changed, 1354 insertions, 1429 deletions
diff --git a/django/srpproject/srp/views.py b/django/srpproject/srp/views.py
index d0feef8..9d2563b 100644
--- a/django/srpproject/srp/views.py
+++ b/django/srpproject/srp/views.py
@@ -29,9 +29,12 @@ def generate_fake_salt(I):
def login_page(request):
return HttpResponse("""<html>
<head>
- <script src="http://%s/srp-test/BigInt.js"></script>
- <script src="http://%s/srp-test/SHA256.js"></script>
- <script src="http://%s/srp-test/srp.js"></script>
+ <script src="http://%s/srp-test/javascript/SHA256.js"></script>
+ <script src="http://%s/srp-test/javascript/prng4.js"></script>
+ <script src="http://%s/srp-test/javascript/rng.js"></script>
+ <script src="http://%s/srp-test/javascript/jsbn.js"></script>
+ <script src="http://%s/srp-test/javascript/jsbn2.js"></script>
+ <script src="http://%s/srp-test/javascript/srp.js"></script>
<script type="text/javascript">
function srp_success()
{
@@ -46,14 +49,17 @@ def login_page(request):
<input type="submit"/>
</form>
</body>
-</html>""" % (request.get_host(), request.get_host(), request.get_host()))
+</html>""" % (request.get_host(), request.get_host(), request.get_host(),request.get_host(), request.get_host(), request.get_host()))
def register_page(request):
return HttpResponse("""<html>
<head>
- <script src="http://localhost/srp-test/BigInt.js"></script>
- <script src="http://localhost/srp-test/SHA256.js"></script>
- <script src="http://localhost/srp-test/srp.js"></script>
+ <script src="http://%s/srp-test/javascript/SHA256.js"></script>
+ <script src="http://%s/srp-test/javascript/prng4.js"></script>
+ <script src="http://%s/srp-test/javascript/rng.js"></script>
+ <script src="http://%s/srp-test/javascript/jsbn.js"></script>
+ <script src="http://%s/srp-test/javascript/jsbn2.js"></script>
+ <script src="http://%s/srp-test/javascript/srp.js"></script>
<script type="text/javascript">
function register()
{
@@ -79,7 +85,7 @@ function srp_success()
<input type="submit"/>
</form>
</body>
-</html>""")
+</html>""" % (request.get_host(), request.get_host(), request.get_host(),request.get_host(), request.get_host(), request.get_host()))
###
### User Registration
diff --git a/javascript/BigInt.js b/javascript/BigInt.js
deleted file mode 100644
index c96ab73..0000000
--- a/javascript/BigInt.js
+++ /dev/null
@@ -1,1400 +0,0 @@
-////////////////////////////////////////////////////////////////////////////////////////
-// Big Integer Library v. 5.1
-// Created 2000, last modified 2007
-// Leemon Baird
-// www.leemon.com
-//
-// Version history:
-//
-// 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 address 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.
-// Some functions assume their parameters have at least one leading zero element.
-// Functions with an underscore at the end of the name have unpredictable behavior in case of overflow,
-// so the caller must make sure the arrays must be big enough to hold the answer.
-// For each 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).
-//
-// 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 (as opposed to definitely composite)?
-// 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 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
-bpe=0; //bits stored per array element
-mask=0; //AND this with an array element to chop it down to bpe bits
-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
-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
-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
-t=new Array(0);
-ss=t; //used in mult_()
-s0=t; //used in multMod_(), squareMod_()
-s1=t; //used in powMod_(), multMod_(), squareMod_()
-s2=t; //used in powMod_(), multMod_()
-s3=t; //used in powMod_()
-s4=t; s5=t; //used in mod_()
-s6=t; //used in bigInt2str()
-s7=t; //used in powMod_()
-T=t; //used in GCD_()
-sa=t; //used in mont_()
-mr_x1=t; mr_r=t; mr_a=t; //used in millerRabin()
-eg_v=t; eg_u=t; eg_A=t; eg_B=t; eg_C=t; eg_D=t; //used in eGCD_(), inverseMod_()
-md_q1=t; md_q2=t; md_q3=t; md_r=t; md_r1=t; md_r2=t; md_tt=t; //used in mod_()
-
-primes=t; pows=t; s_i=t; s_i2=t; s_R=t; s_rm=t; s_q=t; s_n1=t;
- 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_()
-
-////////////////////////////////////////////////////////////////////////////////////////
-
-//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
-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);
- }
-
- copyInt_(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++;
-
- 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 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,m,pm,dd,j,r,B,divisible,z,zz,recSize;
-
- 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.-1.);
- }
- }
-
- //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)) | Math.floor(Math.random()*(1<<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[Math.floor(Math.random()*512)]; //r=Math.pow(2,Math.random()-1);
- else
- r=.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) {
- divisible=1;
- break;
- }
-
- if (!divisible) //if it passes small primes check, then try a single Miller-Rabin base 2
- if (!millerRabin(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]=Math.floor(Math.random()*(1<<(bpe-1)));
- }
- 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;
- 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)) {
- if (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)) {
- if (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 kx=x.length, ky=y.length;
- 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;
- 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;
- }
-
- x=int2bigInt(0,base*k,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) { //ignore illegal characters
- 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.toLowerCase();
-};
-
-//returns a duplicate of bigInt x
-function dup(x) {
- var i;
- 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 must be large enough to hold the answer.
-//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;
- var kn=n.length;
- var ky=y.length;
-
- if (sa.length!=kn)
- sa=new Array(kn);
-
- for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n
- //this function sometimes gives wrong answers when the next line is uncommented
- //for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y
-
- copyInt_(sa,0);
-
- //the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large keys
- for (i=0; i<kn; i++) {
- t=sa[0]+x[i]*y[0];
- ui=((t & mask) * np) & mask; //the inner "& mask" is needed on Macintosh MSIE, but not windows MSIE
- c=(t+ui*n[0]) >> bpe;
- t=x[i];
-
- //do sa=(sa+x[i]*y+ui*n)/b where b=2**bpe
- for (j=1;j<ky;j++) {
- c+=sa[j]+t*y[j]+ui*n[j];
- sa[j-1]=c & mask;
- c>>=bpe;
- }
- for (;j<kn;j++) {
- c+=sa[j]+ui*n[j];
- sa[j-1]=c & mask;
- c>>=bpe;
- }
- sa[j-1]=c & mask;
- }
-
- if (!greater(n,sa))
- sub_(sa,n);
- copy_(x,sa);
-};
-
-
diff --git a/javascript/jsbn.js b/javascript/jsbn.js
new file mode 100644
index 0000000..928cc4f
--- /dev/null
+++ b/javascript/jsbn.js
@@ -0,0 +1,559 @@
+// Copyright (c) 2005 Tom Wu
+// All Rights Reserved.
+// See "LICENSE" for details.
+
+// Basic JavaScript BN library - subset useful for RSA encryption.
+
+// Bits per digit
+var dbits;
+
+// JavaScript engine analysis
+var canary = 0xdeadbeefcafe;
+var j_lm = ((canary&0xffffff)==0xefcafe);
+
+// (public) Constructor
+function BigInteger(a,b,c) {
+ if(a != null)
+ if("number" == typeof a) this.fromNumber(a,b,c);
+ else if(b == null && "string" != typeof a) this.fromString(a,256);
+ else this.fromString(a,b);
+}
+
+// return new, unset BigInteger
+function nbi() { return new BigInteger(null); }
+
+// am: Compute w_j += (x*this_i), propagate carries,
+// c is initial carry, returns final carry.
+// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
+// We need to select the fastest one that works in this environment.
+
+// am1: use a single mult and divide to get the high bits,
+// max digit bits should be 26 because
+// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
+function am1(i,x,w,j,c,n) {
+ while(--n >= 0) {
+ var v = x*this[i++]+w[j]+c;
+ c = Math.floor(v/0x4000000);
+ w[j++] = v&0x3ffffff;
+ }
+ return c;
+}
+// am2 avoids a big mult-and-extract completely.
+// Max digit bits should be <= 30 because we do bitwise ops
+// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
+function am2(i,x,w,j,c,n) {
+ var xl = x&0x7fff, xh = x>>15;
+ while(--n >= 0) {
+ var l = this[i]&0x7fff;
+ var h = this[i++]>>15;
+ var m = xh*l+h*xl;
+ l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
+ c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
+ w[j++] = l&0x3fffffff;
+ }
+ return c;
+}
+// Alternately, set max digit bits to 28 since some
+// browsers slow down when dealing with 32-bit numbers.
+function am3(i,x,w,j,c,n) {
+ var xl = x&0x3fff, xh = x>>14;
+ while(--n >= 0) {
+ var l = this[i]&0x3fff;
+ var h = this[i++]>>14;
+ var m = xh*l+h*xl;
+ l = xl*l+((m&0x3fff)<<14)+w[j]+c;
+ c = (l>>28)+(m>>14)+xh*h;
+ w[j++] = l&0xfffffff;
+ }
+ return c;
+}
+if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
+ BigInteger.prototype.am = am2;
+ dbits = 30;
+}
+else if(j_lm && (navigator.appName != "Netscape")) {
+ BigInteger.prototype.am = am1;
+ dbits = 26;
+}
+else { // Mozilla/Netscape seems to prefer am3
+ BigInteger.prototype.am = am3;
+ dbits = 28;
+}
+
+BigInteger.prototype.DB = dbits;
+BigInteger.prototype.DM = ((1<<dbits)-1);
+BigInteger.prototype.DV = (1<<dbits);
+
+var BI_FP = 52;
+BigInteger.prototype.FV = Math.pow(2,BI_FP);
+BigInteger.prototype.F1 = BI_FP-dbits;
+BigInteger.prototype.F2 = 2*dbits-BI_FP;
+
+// Digit conversions
+var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
+var BI_RC = new Array();
+var rr,vv;
+rr = "0".charCodeAt(0);
+for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
+rr = "a".charCodeAt(0);
+for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
+rr = "A".charCodeAt(0);
+for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
+
+function int2char(n) { return BI_RM.charAt(n); }
+function intAt(s,i) {
+ var c = BI_RC[s.charCodeAt(i)];
+ return (c==null)?-1:c;
+}
+
+// (protected) copy this to r
+function bnpCopyTo(r) {
+ for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
+ r.t = this.t;
+ r.s = this.s;
+}
+
+// (protected) set from integer value x, -DV <= x < DV
+function bnpFromInt(x) {
+ this.t = 1;
+ this.s = (x<0)?-1:0;
+ if(x > 0) this[0] = x;
+ else if(x < -1) this[0] = x+DV;
+ else this.t = 0;
+}
+
+// return bigint initialized to value
+function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
+
+// (protected) set from string and radix
+function bnpFromString(s,b) {
+ var k;
+ if(b == 16) k = 4;
+ else if(b == 8) k = 3;
+ else if(b == 256) k = 8; // byte array
+ else if(b == 2) k = 1;
+ else if(b == 32) k = 5;
+ else if(b == 4) k = 2;
+ else { this.fromRadix(s,b); return; }
+ this.t = 0;
+ this.s = 0;
+ var i = s.length, mi = false, sh = 0;
+ while(--i >= 0) {
+ var x = (k==8)?s[i]&0xff:intAt(s,i);
+ if(x < 0) {
+ if(s.charAt(i) == "-") mi = true;
+ continue;
+ }
+ mi = false;
+ if(sh == 0)
+ this[this.t++] = x;
+ else if(sh+k > this.DB) {
+ this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
+ this[this.t++] = (x>>(this.DB-sh));
+ }
+ else
+ this[this.t-1] |= x<<sh;
+ sh += k;
+ if(sh >= this.DB) sh -= this.DB;
+ }
+ if(k == 8 && (s[0]&0x80) != 0) {
+ this.s = -1;
+ if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
+ }
+ this.clamp();
+ if(mi) BigInteger.ZERO.subTo(this,this);
+}
+
+// (protected) clamp off excess high words
+function bnpClamp() {
+ var c = this.s&this.DM;
+ while(this.t > 0 && this[this.t-1] == c) --this.t;
+}
+
+// (public) return string representation in given radix
+function bnToString(b) {
+ if(this.s < 0) return "-"+this.negate().toString(b);
+ var k;
+ if(b == 16) k = 4;
+ else if(b == 8) k = 3;
+ else if(b == 2) k = 1;
+ else if(b == 32) k = 5;
+ else if(b == 4) k = 2;
+ else return this.toRadix(b);
+ var km = (1<<k)-1, d, m = false, r = "", i = this.t;
+ var p = this.DB-(i*this.DB)%k;
+ if(i-- > 0) {
+ if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
+ while(i >= 0) {
+ if(p < k) {
+ d = (this[i]&((1<<p)-1))<<(k-p);
+ d |= this[--i]>>(p+=this.DB-k);
+ }
+ else {
+ d = (this[i]>>(p-=k))&km;
+ if(p <= 0) { p += this.DB; --i; }
+ }
+ if(d > 0) m = true;
+ if(m) r += int2char(d);
+ }
+ }
+ return m?r:"0";
+}
+
+// (public) -this
+function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
+
+// (public) |this|
+function bnAbs() { return (this.s<0)?this.negate():this; }
+
+// (public) return + if this > a, - if this < a, 0 if equal
+function bnCompareTo(a) {
+ var r = this.s-a.s;
+ if(r != 0) return r;
+ var i = this.t;
+ r = i-a.t;
+ if(r != 0) return r;
+ while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
+ return 0;
+}
+
+// returns bit length of the integer x
+function nbits(x) {
+ var r = 1, t;
+ if((t=x>>>16) != 0) { x = t; r += 16; }
+ if((t=x>>8) != 0) { x = t; r += 8; }
+ if((t=x>>4) != 0) { x = t; r += 4; }
+ if((t=x>>2) != 0) { x = t; r += 2; }
+ if((t=x>>1) != 0) { x = t; r += 1; }
+ return r;
+}
+
+// (public) return the number of bits in "this"
+function bnBitLength() {
+ if(this.t <= 0) return 0;
+ return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
+}
+
+// (protected) r = this << n*DB
+function bnpDLShiftTo(n,r) {
+ var i;
+ for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
+ for(i = n-1; i >= 0; --i) r[i] = 0;
+ r.t = this.t+n;
+ r.s = this.s;
+}
+
+// (protected) r = this >> n*DB
+function bnpDRShiftTo(n,r) {
+ for(var i = n; i < this.t; ++i) r[i-n] = this[i];
+ r.t = Math.max(this.t-n,0);
+ r.s = this.s;
+}
+
+// (protected) r = this << n
+function bnpLShiftTo(n,r) {
+ var bs = n%this.DB;
+ var cbs = this.DB-bs;
+ var bm = (1<<cbs)-1;
+ var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
+ for(i = this.t-1; i >= 0; --i) {
+ r[i+ds+1] = (this[i]>>cbs)|c;
+ c = (this[i]&bm)<<bs;
+ }
+ for(i = ds-1; i >= 0; --i) r[i] = 0;
+ r[ds] = c;
+ r.t = this.t+ds+1;
+ r.s = this.s;
+ r.clamp();
+}
+
+// (protected) r = this >> n
+function bnpRShiftTo(n,r) {
+ r.s = this.s;
+ var ds = Math.floor(n/this.DB);
+ if(ds >= this.t) { r.t = 0; return; }
+ var bs = n%this.DB;
+ var cbs = this.DB-bs;
+ var bm = (1<<bs)-1;
+ r[0] = this[ds]>>bs;
+ for(var i = ds+1; i < this.t; ++i) {
+ r[i-ds-1] |= (this[i]&bm)<<cbs;
+ r[i-ds] = this[i]>>bs;
+ }
+ if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
+ r.t = this.t-ds;
+ r.clamp();
+}
+
+// (protected) r = this - a
+function bnpSubTo(a,r) {
+ var i = 0, c = 0, m = Math.min(a.t,this.t);
+ while(i < m) {
+ c += this[i]-a[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ if(a.t < this.t) {
+ c -= a.s;
+ while(i < this.t) {
+ c += this[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ c += this.s;
+ }
+ else {
+ c += this.s;
+ while(i < a.t) {
+ c -= a[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ c -= a.s;
+ }
+ r.s = (c<0)?-1:0;
+ if(c < -1) r[i++] = this.DV+c;
+ else if(c > 0) r[i++] = c;
+ r.t = i;
+ r.clamp();
+}
+
+// (protected) r = this * a, r != this,a (HAC 14.12)
+// "this" should be the larger one if appropriate.
+function bnpMultiplyTo(a,r) {
+ var x = this.abs(), y = a.abs();
+ var i = x.t;
+ r.t = i+y.t;
+ while(--i >= 0) r[i] = 0;
+ for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
+ r.s = 0;
+ r.clamp();
+ if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
+}
+
+// (protected) r = this^2, r != this (HAC 14.16)
+function bnpSquareTo(r) {
+ var x = this.abs();
+ var i = r.t = 2*x.t;
+ while(--i >= 0) r[i] = 0;
+ for(i = 0; i < x.t-1; ++i) {
+ var c = x.am(i,x[i],r,2*i,0,1);
+ if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
+ r[i+x.t] -= x.DV;
+ r[i+x.t+1] = 1;
+ }
+ }
+ if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
+ r.s = 0;
+ r.clamp();
+}
+
+// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
+// r != q, this != m. q or r may be null.
+function bnpDivRemTo(m,q,r) {
+ var pm = m.abs();
+ if(pm.t <= 0) return;
+ var pt = this.abs();
+ if(pt.t < pm.t) {
+ if(q != null) q.fromInt(0);
+ if(r != null) this.copyTo(r);
+ return;
+ }
+ if(r == null) r = nbi();
+ var y = nbi(), ts = this.s, ms = m.s;
+ var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
+ if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
+ else { pm.copyTo(y); pt.copyTo(r); }
+ var ys = y.t;
+ var y0 = y[ys-1];
+ if(y0 == 0) return;
+ var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
+ var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
+ var i = r.t, j = i-ys, t = (q==null)?nbi():q;
+ y.dlShiftTo(j,t);
+ if(r.compareTo(t) >= 0) {
+ r[r.t++] = 1;
+ r.subTo(t,r);
+ }
+ BigInteger.ONE.dlShiftTo(ys,t);
+ t.subTo(y,y); // "negative" y so we can replace sub with am later
+ while(y.t < ys) y[y.t++] = 0;
+ while(--j >= 0) {
+ // Estimate quotient digit
+ var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
+ if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
+ y.dlShiftTo(j,t);
+ r.subTo(t,r);
+ while(r[i] < --qd) r.subTo(t,r);
+ }
+ }
+ if(q != null) {
+ r.drShiftTo(ys,q);
+ if(ts != ms) BigInteger.ZERO.subTo(q,q);
+ }
+ r.t = ys;
+ r.clamp();
+ if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
+ if(ts < 0) BigInteger.ZERO.subTo(r,r);
+}
+
+// (public) this mod a
+function bnMod(a) {
+ var r = nbi();
+ this.abs().divRemTo(a,null,r);
+ if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
+ return r;
+}
+
+// Modular reduction using "classic" algorithm
+function Classic(m) { this.m = m; }
+function cConvert(x) {
+ if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
+ else return x;
+}
+function cRevert(x) { return x; }
+function cReduce(x) { x.divRemTo(this.m,null,x); }
+function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+Classic.prototype.convert = cConvert;
+Classic.prototype.revert = cRevert;
+Classic.prototype.reduce = cReduce;
+Classic.prototype.mulTo = cMulTo;
+Classic.prototype.sqrTo = cSqrTo;
+
+// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
+// justification:
+// xy == 1 (mod m)
+// xy = 1+km
+// xy(2-xy) = (1+km)(1-km)
+// x[y(2-xy)] = 1-k^2m^2
+// x[y(2-xy)] == 1 (mod m^2)
+// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
+// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
+// JS multiply "overflows" differently from C/C++, so care is needed here.
+function bnpInvDigit() {
+ if(this.t < 1) return 0;
+ var x = this[0];
+ if((x&1) == 0) return 0;
+ var y = x&3; // y == 1/x mod 2^2
+ y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
+ y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
+ y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
+ // last step - calculate inverse mod DV directly;
+ // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
+ y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
+ // we really want the negative inverse, and -DV < y < DV
+ return (y>0)?this.DV-y:-y;
+}
+
+// Montgomery reduction
+function Montgomery(m) {
+ this.m = m;
+ this.mp = m.invDigit();
+ this.mpl = this.mp&0x7fff;
+ this.mph = this.mp>>15;
+ this.um = (1<<(m.DB-15))-1;
+ this.mt2 = 2*m.t;
+}
+
+// xR mod m
+function montConvert(x) {
+ var r = nbi();
+ x.abs().dlShiftTo(this.m.t,r);
+ r.divRemTo(this.m,null,r);
+ if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
+ return r;
+}
+
+// x/R mod m
+function montRevert(x) {
+ var r = nbi();
+ x.copyTo(r);
+ this.reduce(r);
+ return r;
+}
+
+// x = x/R mod m (HAC 14.32)
+function montReduce(x) {
+ while(x.t <= this.mt2) // pad x so am has enough room later
+ x[x.t++] = 0;
+ for(var i = 0; i < this.m.t; ++i) {
+ // faster way of calculating u0 = x[i]*mp mod DV
+ var j = x[i]&0x7fff;
+ var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
+ // use am to combine the multiply-shift-add into one call
+ j = i+this.m.t;
+ x[j] += this.m.am(0,u0,x,i,0,this.m.t);
+ // propagate carry
+ while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
+ }
+ x.clamp();
+ x.drShiftTo(this.m.t,x);
+ if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
+}
+
+// r = "x^2/R mod m"; x != r
+function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+// r = "xy/R mod m"; x,y != r
+function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+
+Montgomery.prototype.convert = montConvert;
+Montgomery.prototype.revert = montRevert;
+Montgomery.prototype.reduce = montReduce;
+Montgomery.prototype.mulTo = montMulTo;
+Montgomery.prototype.sqrTo = montSqrTo;
+
+// (protected) true iff this is even
+function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
+
+// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
+function bnpExp(e,z) {
+ if(e > 0xffffffff || e < 1) return BigInteger.ONE;
+ var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
+ g.copyTo(r);
+ while(--i >= 0) {
+ z.sqrTo(r,r2);
+ if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
+ else { var t = r; r = r2; r2 = t; }
+ }
+ return z.revert(r);
+}
+
+// (public) this^e % m, 0 <= e < 2^32
+function bnModPowInt(e,m) {
+ var z;
+ if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
+ return this.exp(e,z);
+}
+
+// protected
+BigInteger.prototype.copyTo = bnpCopyTo;
+BigInteger.prototype.fromInt = bnpFromInt;
+BigInteger.prototype.fromString = bnpFromString;
+BigInteger.prototype.clamp = bnpClamp;
+BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
+BigInteger.prototype.drShiftTo = bnpDRShiftTo;
+BigInteger.prototype.lShiftTo = bnpLShiftTo;
+BigInteger.prototype.rShiftTo = bnpRShiftTo;
+BigInteger.prototype.subTo = bnpSubTo;
+BigInteger.prototype.multiplyTo = bnpMultiplyTo;
+BigInteger.prototype.squareTo = bnpSquareTo;
+BigInteger.prototype.divRemTo = bnpDivRemTo;
+BigInteger.prototype.invDigit = bnpInvDigit;
+BigInteger.prototype.isEven = bnpIsEven;
+BigInteger.prototype.exp = bnpExp;
+
+// public
+BigInteger.prototype.toString = bnToString;
+BigInteger.prototype.negate = bnNegate;
+BigInteger.prototype.abs = bnAbs;
+BigInteger.prototype.compareTo = bnCompareTo;
+BigInteger.prototype.bitLength = bnBitLength;
+BigInteger.prototype.mod = bnMod;
+BigInteger.prototype.modPowInt = bnModPowInt;
+
+// "constants"
+BigInteger.ZERO = nbv(0);
+BigInteger.ONE = nbv(1);
diff --git a/javascript/jsbn2.js b/javascript/jsbn2.js
new file mode 100644
index 0000000..cad0d7b
--- /dev/null
+++ b/javascript/jsbn2.js
@@ -0,0 +1,645 @@
+// Copyright (c) 2005 Tom Wu
+// All Rights Reserved.
+// See "LICENSE" for details.
+
+// Extended JavaScript BN functions, required for RSA private ops.
+
+// (public)
+function bnClone() { var r = nbi(); this.copyTo(r); return r; }
+
+// (public) return value as integer
+function bnIntValue() {
+ if(this.s < 0) {
+ if(this.t == 1) return this[0]-this.DV;
+ else if(this.t == 0) return -1;
+ }
+ else if(this.t == 1) return this[0];
+ else if(this.t == 0) return 0;
+ // assumes 16 < DB < 32
+ return ((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0];
+}
+
+// (public) return value as byte
+function bnByteValue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }
+
+// (public) return value as short (assumes DB>=16)
+function bnShortValue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }
+
+// (protected) return x s.t. r^x < DV
+function bnpChunkSize(r) { return Math.floor(Math.LN2*this.DB/Math.log(r)); }
+
+// (public) 0 if this == 0, 1 if this > 0
+function bnSigNum() {
+ if(this.s < 0) return -1;
+ else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
+ else return 1;
+}
+
+// (protected) convert to radix string
+function bnpToRadix(b) {
+ if(b == null) b = 10;
+ if(this.signum() == 0 || b < 2 || b > 36) return "0";
+ var cs = this.chunkSize(b);
+ var a = Math.pow(b,cs);
+ var d = nbv(a), y = nbi(), z = nbi(), r = "";
+ this.divRemTo(d,y,z);
+ while(y.signum() > 0) {
+ r = (a+z.intValue()).toString(b).substr(1) + r;
+ y.divRemTo(d,y,z);
+ }
+ return z.intValue().toString(b) + r;
+}
+
+// (protected) convert from radix string
+function bnpFromRadix(s,b) {
+ this.fromInt(0);
+ if(b == null) b = 10;
+ var cs = this.chunkSize(b);
+ var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
+ for(var i = 0; i < s.length; ++i) {
+ var x = intAt(s,i);
+ if(x < 0) {
+ if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
+ continue;
+ }
+ w = b*w+x;
+ if(++j >= cs) {
+ this.dMultiply(d);
+ this.dAddOffset(w,0);
+ j = 0;
+ w = 0;
+ }
+ }
+ if(j > 0) {
+ this.dMultiply(Math.pow(b,j));
+ this.dAddOffset(w,0);
+ }
+ if(mi) BigInteger.ZERO.subTo(this,this);
+}
+
+// (protected) alternate constructor
+function bnpFromNumber(a,b,c) {
+ if("number" == typeof b) {
+ // new BigInteger(int,int,RNG)
+ if(a < 2) this.fromInt(1);
+ else {
+ this.fromNumber(a,c);
+ if(!this.testBit(a-1)) // force MSB set
+ this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
+ if(this.isEven()) this.dAddOffset(1,0); // force odd
+ while(!this.isProbablePrime(b)) {
+ this.dAddOffset(2,0);
+ if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
+ }
+ }
+ }
+ else {
+ // new BigInteger(int,RNG)
+ var x = new Array(), t = a&7;
+ x.length = (a>>3)+1;
+ b.nextBytes(x);
+ if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
+ this.fromString(x,256);
+ }
+}
+
+// (public) convert to bigendian byte array
+function bnToByteArray() {
+ var i = this.t, r = new Array();
+ r[0] = this.s;
+ var p = this.DB-(i*this.DB)%8, d, k = 0;
+ if(i-- > 0) {
+ if(p < this.DB && (d = this[i]>>p) != (this.s&this.DM)>>p)
+ r[k++] = d|(this.s<<(this.DB-p));
+ while(i >= 0) {
+ if(p < 8) {
+ d = (this[i]&((1<<p)-1))<<(8-p);
+ d |= this[--i]>>(p+=this.DB-8);
+ }
+ else {
+ d = (this[i]>>(p-=8))&0xff;
+ if(p <= 0) { p += this.DB; --i; }
+ }
+ if((d&0x80) != 0) d |= -256;
+ if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
+ if(k > 0 || d != this.s) r[k++] = d;
+ }
+ }
+ return r;
+}
+
+function bnEquals(a) { return(this.compareTo(a)==0); }
+function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
+function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
+
+// (protected) r = this op a (bitwise)
+function bnpBitwiseTo(a,op,r) {
+ var i, f, m = Math.min(a.t,this.t);
+ for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
+ if(a.t < this.t) {
+ f = a.s&this.DM;
+ for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
+ r.t = this.t;
+ }
+ else {
+ f = this.s&this.DM;
+ for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
+ r.t = a.t;
+ }
+ r.s = op(this.s,a.s);
+ r.clamp();
+}
+
+// (public) this & a
+function op_and(x,y) { return x&y; }
+function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
+
+// (public) this | a
+function op_or(x,y) { return x|y; }
+function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
+
+// (public) this ^ a
+function op_xor(x,y) { return x^y; }
+function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
+
+// (public) this & ~a
+function op_andnot(x,y) { return x&~y; }
+function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
+
+// (public) ~this
+function bnNot() {
+ var r = nbi();
+ for(var i = 0; i < this.t; ++i) r[i] = this.DM&~this[i];
+ r.t = this.t;
+ r.s = ~this.s;
+ return r;
+}
+
+// (public) this << n
+function bnShiftLeft(n) {
+ var r = nbi();
+ if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
+ return r;
+}
+
+// (public) this >> n
+function bnShiftRight(n) {
+ var r = nbi();
+ if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
+ return r;
+}
+
+// return index of lowest 1-bit in x, x < 2^31
+function lbit(x) {
+ if(x == 0) return -1;
+ var r = 0;
+ if((x&0xffff) == 0) { x >>= 16; r += 16; }
+ if((x&0xff) == 0) { x >>= 8; r += 8; }
+ if((x&0xf) == 0) { x >>= 4; r += 4; }
+ if((x&3) == 0) { x >>= 2; r += 2; }
+ if((x&1) == 0) ++r;
+ return r;
+}
+
+// (public) returns index of lowest 1-bit (or -1 if none)
+function bnGetLowestSetBit() {
+ for(var i = 0; i < this.t; ++i)
+ if(this[i] != 0) return i*this.DB+lbit(this[i]);
+ if(this.s < 0) return this.t*this.DB;
+ return -1;
+}
+
+// return number of 1 bits in x
+function cbit(x) {
+ var r = 0;
+ while(x != 0) { x &= x-1; ++r; }
+ return r;
+}
+
+// (public) return number of set bits
+function bnBitCount() {
+ var r = 0, x = this.s&this.DM;
+ for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
+ return r;
+}
+
+// (public) true iff nth bit is set
+function bnTestBit(n) {
+ var j = Math.floor(n/this.DB);
+ if(j >= this.t) return(this.s!=0);
+ return((this[j]&(1<<(n%this.DB)))!=0);
+}
+
+// (protected) this op (1<<n)
+function bnpChangeBit(n,op) {
+ var r = BigInteger.ONE.shiftLeft(n);
+ this.bitwiseTo(r,op,r);
+ return r;
+}
+
+// (public) this | (1<<n)
+function bnSetBit(n) { return this.changeBit(n,op_or); }
+
+// (public) this & ~(1<<n)
+function bnClearBit(n) { return this.changeBit(n,op_andnot); }
+
+// (public) this ^ (1<<n)
+function bnFlipBit(n) { return this.changeBit(n,op_xor); }
+
+// (protected) r = this + a
+function bnpAddTo(a,r) {
+ var i = 0, c = 0, m = Math.min(a.t,this.t);
+ while(i < m) {
+ c += this[i]+a[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ if(a.t < this.t) {
+ c += a.s;
+ while(i < this.t) {
+ c += this[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ c += this.s;
+ }
+ else {
+ c += this.s;
+ while(i < a.t) {
+ c += a[i];
+ r[i++] = c&this.DM;
+ c >>= this.DB;
+ }
+ c += a.s;
+ }
+ r.s = (c<0)?-1:0;
+ if(c > 0) r[i++] = c;
+ else if(c < -1) r[i++] = this.DV+c;
+ r.t = i;
+ r.clamp();
+}
+
+// (public) this + a
+function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
+
+// (public) this - a
+function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
+
+// (public) this * a
+function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
+
+// (public) this / a
+function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
+
+// (public) this % a
+function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
+
+// (public) [this/a,this%a]
+function bnDivideAndRemainder(a) {
+ var q = nbi(), r = nbi();
+ this.divRemTo(a,q,r);
+ return new Array(q,r);
+}
+
+// (protected) this *= n, this >= 0, 1 < n < DV
+function bnpDMultiply(n) {
+ this[this.t] = this.am(0,n-1,this,0,0,this.t);
+ ++this.t;
+ this.clamp();
+}
+
+// (protected) this += n << w words, this >= 0
+function bnpDAddOffset(n,w) {
+ while(this.t <= w) this[this.t++] = 0;
+ this[w] += n;
+ while(this[w] >= this.DV) {
+ this[w] -= this.DV;
+ if(++w >= this.t) this[this.t++] = 0;
+ ++this[w];
+ }
+}
+
+// A "null" reducer
+function NullExp() {}
+function nNop(x) { return x; }
+function nMulTo(x,y,r) { x.multiplyTo(y,r); }
+function nSqrTo(x,r) { x.squareTo(r); }
+
+NullExp.prototype.convert = nNop;
+NullExp.prototype.revert = nNop;
+NullExp.prototype.mulTo = nMulTo;
+NullExp.prototype.sqrTo = nSqrTo;
+
+// (public) this^e
+function bnPow(e) { return this.exp(e,new NullExp()); }
+
+// (protected) r = lower n words of "this * a", a.t <= n
+// "this" should be the larger one if appropriate.
+function bnpMultiplyLowerTo(a,n,r) {
+ var i = Math.min(this.t+a.t,n);
+ r.s = 0; // assumes a,this >= 0
+ r.t = i;
+ while(i > 0) r[--i] = 0;
+ var j;
+ for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
+ for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
+ r.clamp();
+}
+
+// (protected) r = "this * a" without lower n words, n > 0
+// "this" should be the larger one if appropriate.
+function bnpMultiplyUpperTo(a,n,r) {
+ --n;
+ var i = r.t = this.t+a.t-n;
+ r.s = 0; // assumes a,this >= 0
+ while(--i >= 0) r[i] = 0;
+ for(i = Math.max(n-this.t,0); i < a.t; ++i)
+ r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
+ r.clamp();
+ r.drShiftTo(1,r);
+}
+
+// Barrett modular reduction
+function Barrett(m) {
+ // setup Barrett
+ this.r2 = nbi();
+ this.q3 = nbi();
+ BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
+ this.mu = this.r2.divide(m);
+ this.m = m;
+}
+
+function barrettConvert(x) {
+ if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
+ else if(x.compareTo(this.m) < 0) return x;
+ else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
+}
+
+function barrettRevert(x) { return x; }
+
+// x = x mod m (HAC 14.42)
+function barrettReduce(x) {
+ x.drShiftTo(this.m.t-1,this.r2);
+ if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
+ this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
+ this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
+ while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
+ x.subTo(this.r2,x);
+ while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
+}
+
+// r = x^2 mod m; x != r
+function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+// r = x*y mod m; x,y != r
+function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+
+Barrett.prototype.convert = barrettConvert;
+Barrett.prototype.revert = barrettRevert;
+Barrett.prototype.reduce = barrettReduce;
+Barrett.prototype.mulTo = barrettMulTo;
+Barrett.prototype.sqrTo = barrettSqrTo;
+
+// (public) this^e % m (HAC 14.85)
+function bnModPow(e,m) {
+ var i = e.bitLength(), k, r = nbv(1), z;
+ if(i <= 0) return r;
+ else if(i < 18) k = 1;
+ else if(i < 48) k = 3;
+ else if(i < 144) k = 4;
+ else if(i < 768) k = 5;
+ else k = 6;
+ if(i < 8)
+ z = new Classic(m);
+ else if(m.isEven())
+ z = new Barrett(m);
+ else
+ z = new Montgomery(m);
+
+ // precomputation
+ var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
+ g[1] = z.convert(this);
+ if(k > 1) {
+ var g2 = nbi();
+ z.sqrTo(g[1],g2);
+ while(n <= km) {
+ g[n] = nbi();
+ z.mulTo(g2,g[n-2],g[n]);
+ n += 2;
+ }
+ }
+
+ var j = e.t-1, w, is1 = true, r2 = nbi(), t;
+ i = nbits(e[j])-1;
+ while(j >= 0) {
+ if(i >= k1) w = (e[j]>>(i-k1))&km;
+ else {
+ w = (e[j]&((1<<(i+1))-1))<<(k1-i);
+ if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
+ }
+
+ n = k;
+ while((w&1) == 0) { w >>= 1; --n; }
+ if((i -= n) < 0) { i += this.DB; --j; }
+ if(is1) { // ret == 1, don't bother squaring or multiplying it
+ g[w].copyTo(r);
+ is1 = false;
+ }
+ else {
+ while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
+ if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
+ z.mulTo(r2,g[w],r);
+ }
+
+ while(j >= 0 && (e[j]&(1<<i)) == 0) {
+ z.sqrTo(r,r2); t = r; r = r2; r2 = t;
+ if(--i < 0) { i = this.DB-1; --j; }
+ }
+ }
+ return z.revert(r);
+}
+
+// (public) gcd(this,a) (HAC 14.54)
+function bnGCD(a) {
+ var x = (this.s<0)?this.negate():this.clone();
+ var y = (a.s<0)?a.negate():a.clone();
+ if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
+ var i = x.getLowestSetBit(), g = y.getLowestSetBit();
+ if(g < 0) return x;
+ if(i < g) g = i;
+ if(g > 0) {
+ x.rShiftTo(g,x);
+ y.rShiftTo(g,y);
+ }
+ while(x.signum() > 0) {
+ if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
+ if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
+ if(x.compareTo(y) >= 0) {
+ x.subTo(y,x);
+ x.rShiftTo(1,x);
+ }
+ else {
+ y.subTo(x,y);
+ y.rShiftTo(1,y);
+ }
+ }
+ if(g > 0) y.lShiftTo(g,y);
+ return y;
+}
+
+// (protected) this % n, n < 2^26
+function bnpModInt(n) {
+ if(n <= 0) return 0;
+ var d = this.DV%n, r = (this.s<0)?n-1:0;
+ if(this.t > 0)
+ if(d == 0) r = this[0]%n;
+ else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
+ return r;
+}
+
+// (public) 1/this % m (HAC 14.61)
+function bnModInverse(m) {
+ var ac = m.isEven();
+ if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
+ var u = m.clone(), v = this.clone();
+ var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
+ while(u.signum() != 0) {
+ while(u.isEven()) {
+ u.rShiftTo(1,u);
+ if(ac) {
+ if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
+ a.rShiftTo(1,a);
+ }
+ else if(!b.isEven()) b.subTo(m,b);
+ b.rShiftTo(1,b);
+ }
+ while(v.isEven()) {
+ v.rShiftTo(1,v);
+ if(ac) {
+ if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
+ c.rShiftTo(1,c);
+ }
+ else if(!d.isEven()) d.subTo(m,d);
+ d.rShiftTo(1,d);
+ }
+ if(u.compareTo(v) >= 0) {
+ u.subTo(v,u);
+ if(ac) a.subTo(c,a);
+ b.subTo(d,b);
+ }
+ else {
+ v.subTo(u,v);
+ if(ac) c.subTo(a,c);
+ d.subTo(b,d);
+ }
+ }
+ if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
+ if(d.compareTo(m) >= 0) return d.subtract(m);
+ if(d.signum() < 0) d.addTo(m,d); else return d;
+ if(d.signum() < 0) return d.add(m); else return d;
+}
+
+var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
+var lplim = (1<<26)/lowprimes[lowprimes.length-1];
+
+// (public) test primality with certainty >= 1-.5^t
+function bnIsProbablePrime(t) {
+ var i, x = this.abs();
+ if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
+ for(i = 0; i < lowprimes.length; ++i)
+ if(x[0] == lowprimes[i]) return true;
+ return false;
+ }
+ if(x.isEven()) return false;
+ i = 1;
+ while(i < lowprimes.length) {
+ var m = lowprimes[i], j = i+1;
+ while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
+ m = x.modInt(m);
+ while(i < j) if(m%lowprimes[i++] == 0) return false;
+ }
+ return x.millerRabin(t);
+}
+
+// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
+function bnpMillerRabin(t) {
+ var n1 = this.subtract(BigInteger.ONE);
+ var k = n1.getLowestSetBit();
+ if(k <= 0) return false;
+ var r = n1.shiftRight(k);
+ t = (t+1)>>1;
+ if(t > lowprimes.length) t = lowprimes.length;
+ var a = nbi();
+ for(var i = 0; i < t; ++i) {
+ a.fromInt(lowprimes[i]);
+ var y = a.modPow(r,this);
+ if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
+ var j = 1;
+ while(j++ < k && y.compareTo(n1) != 0) {
+ y = y.modPowInt(2,this);
+ if(y.compareTo(BigInteger.ONE) == 0) return false;
+ }
+ if(y.compareTo(n1) != 0) return false;
+ }
+ }
+ return true;
+}
+
+// protected
+BigInteger.prototype.chunkSize = bnpChunkSize;
+BigInteger.prototype.toRadix = bnpToRadix;
+BigInteger.prototype.fromRadix = bnpFromRadix;
+BigInteger.prototype.fromNumber = bnpFromNumber;
+BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
+BigInteger.prototype.changeBit = bnpChangeBit;
+BigInteger.prototype.addTo = bnpAddTo;
+BigInteger.prototype.dMultiply = bnpDMultiply;
+BigInteger.prototype.dAddOffset = bnpDAddOffset;
+BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
+BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
+BigInteger.prototype.modInt = bnpModInt;
+BigInteger.prototype.millerRabin = bnpMillerRabin;
+
+// public
+BigInteger.prototype.clone = bnClone;
+BigInteger.prototype.intValue = bnIntValue;
+BigInteger.prototype.byteValue = bnByteValue;
+BigInteger.prototype.shortValue = bnShortValue;
+BigInteger.prototype.signum = bnSigNum;
+BigInteger.prototype.toByteArray = bnToByteArray;
+BigInteger.prototype.equals = bnEquals;
+BigInteger.prototype.min = bnMin;
+BigInteger.prototype.max = bnMax;
+BigInteger.prototype.and = bnAnd;
+BigInteger.prototype.or = bnOr;
+BigInteger.prototype.xor = bnXor;
+BigInteger.prototype.andNot = bnAndNot;
+BigInteger.prototype.not = bnNot;
+BigInteger.prototype.shiftLeft = bnShiftLeft;
+BigInteger.prototype.shiftRight = bnShiftRight;
+BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
+BigInteger.prototype.bitCount = bnBitCount;
+BigInteger.prototype.testBit = bnTestBit;
+BigInteger.prototype.setBit = bnSetBit;
+BigInteger.prototype.clearBit = bnClearBit;
+BigInteger.prototype.flipBit = bnFlipBit;
+BigInteger.prototype.add = bnAdd;
+BigInteger.prototype.subtract = bnSubtract;
+BigInteger.prototype.multiply = bnMultiply;
+BigInteger.prototype.divide = bnDivide;
+BigInteger.prototype.remainder = bnRemainder;
+BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
+BigInteger.prototype.modPow = bnModPow;
+BigInteger.prototype.modInverse = bnModInverse;
+BigInteger.prototype.pow = bnPow;
+BigInteger.prototype.gcd = bnGCD;
+BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
+
+// BigInteger interfaces not implemented in jsbn:
+
+// BigInteger(int signum, byte[] magnitude)
+// double doubleValue()
+// float floatValue()
+// int hashCode()
+// long longValue()
+// static BigInteger valueOf(long val)
diff --git a/javascript/prng4.js b/javascript/prng4.js
new file mode 100644
index 0000000..3034f3f
--- /dev/null
+++ b/javascript/prng4.js
@@ -0,0 +1,45 @@
+// prng4.js - uses Arcfour as a PRNG
+
+function Arcfour() {
+ this.i = 0;
+ this.j = 0;
+ this.S = new Array();
+}
+
+// Initialize arcfour context from key, an array of ints, each from [0..255]
+function ARC4init(key) {
+ var i, j, t;
+ for(i = 0; i < 256; ++i)
+ this.S[i] = i;
+ j = 0;
+ for(i = 0; i < 256; ++i) {
+ j = (j + this.S[i] + key[i % key.length]) & 255;
+ t = this.S[i];
+ this.S[i] = this.S[j];
+ this.S[j] = t;
+ }
+ this.i = 0;
+ this.j = 0;
+}
+
+function ARC4next() {
+ var t;
+ this.i = (this.i + 1) & 255;
+ this.j = (this.j + this.S[this.i]) & 255;
+ t = this.S[this.i];
+ this.S[this.i] = this.S[this.j];
+ this.S[this.j] = t;
+ return this.S[(t + this.S[this.i]) & 255];
+}
+
+Arcfour.prototype.init = ARC4init;
+Arcfour.prototype.next = ARC4next;
+
+// Plug in your RNG constructor here
+function prng_newstate() {
+ return new Arcfour();
+}
+
+// Pool size must be a multiple of 4 and greater than 32.
+// An array of bytes the size of the pool will be passed to init()
+var rng_psize = 256;
diff --git a/javascript/rng.js b/javascript/rng.js
new file mode 100644
index 0000000..03afc3a
--- /dev/null
+++ b/javascript/rng.js
@@ -0,0 +1,68 @@
+// Random number generator - requires a PRNG backend, e.g. prng4.js
+
+// For best results, put code like
+// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
+// in your main HTML document.
+
+var rng_state;
+var rng_pool;
+var rng_pptr;
+
+// Mix in a 32-bit integer into the pool
+function rng_seed_int(x) {
+ rng_pool[rng_pptr++] ^= x & 255;
+ rng_pool[rng_pptr++] ^= (x >> 8) & 255;
+ rng_pool[rng_pptr++] ^= (x >> 16) & 255;
+ rng_pool[rng_pptr++] ^= (x >> 24) & 255;
+ if(rng_pptr >= rng_psize) rng_pptr -= rng_psize;
+}
+
+// Mix in the current time (w/milliseconds) into the pool
+function rng_seed_time() {
+ rng_seed_int(new Date().getTime());
+}
+
+// Initialize the pool with junk if needed.
+if(rng_pool == null) {
+ rng_pool = new Array();
+ rng_pptr = 0;
+ var t;
+ if(navigator.appName == "Netscape" && navigator.appVersion < "5" && window.crypto) {
+ // Extract entropy (256 bits) from NS4 RNG if available
+ var z = window.crypto.random(32);
+ for(t = 0; t < z.length; ++t)
+ rng_pool[rng_pptr++] = z.charCodeAt(t) & 255;
+ }
+ while(rng_pptr < rng_psize) { // extract some randomness from Math.random()
+ t = Math.floor(65536 * Math.random());
+ rng_pool[rng_pptr++] = t >>> 8;
+ rng_pool[rng_pptr++] = t & 255;
+ }
+ rng_pptr = 0;
+ rng_seed_time();
+ //rng_seed_int(window.screenX);
+ //rng_seed_int(window.screenY);
+}
+
+function rng_get_byte() {
+ if(rng_state == null) {
+ rng_seed_time();
+ rng_state = prng_newstate();
+ rng_state.init(rng_pool);
+ for(rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
+ rng_pool[rng_pptr] = 0;
+ rng_pptr = 0;
+ //rng_pool = null;
+ }
+ // TODO: allow reseeding after first request
+ return rng_state.next();
+}
+
+function rng_get_bytes(ba) {
+ var i;
+ for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
+}
+
+function SecureRandom() {}
+
+SecureRandom.prototype.nextBytes = rng_get_bytes;
diff --git a/javascript/srp.js b/javascript/srp.js
index 9c84aa9..4fcc1c9 100644
--- a/javascript/srp.js
+++ b/javascript/srp.js
@@ -17,12 +17,14 @@ var srp_K = null;
var srp_M = null;
var srp_M2 = null;
var xhr;
+var rng;
+
var srp_url = window.location.protocol+"//"+window.location.host+"/srp/";
function srp_register()
{
- srp_N = str2bigInt(srp_Nstr, 16, 0);
- srp_g = str2bigInt("2", 10, 0);
- srp_k = str2bigInt("c46d46600d87fef149bd79b81119842f3c20241fda67d06ef412d8f6d9479c58", 16, 0);
+ srp_N = new BigInteger(srp_Nstr, 16);
+ srp_g = new BigInteger("2");
+ srp_k = new BigInteger("c46d46600d87fef149bd79b81119842f3c20241fda67d06ef412d8f6d9479c58", 16);
srp_I = document.getElementById("srp_username").value;
srp_register_salt(srp_I);
return false;
@@ -64,8 +66,8 @@ function srp_register_receive_salt()
{
s = innerxml(xhr.responseXML.getElementsByTagName("salt")[0]);
srp_x = srp_calculate_x(s);
- v = powMod(srp_g, srp_x, srp_N);
- srp_register_send_verifier(bigInt2str(v, 16));
+ v = srp_g.modPow(srp_x, srp_N);
+ srp_register_send_verifier(v.toString(16));
}
else if(xhr.responseXML.getElementsByTagName("error").length > 0)
{
@@ -115,15 +117,16 @@ function srp_register_user()
};
function srp_identify()
{
- srp_N = str2bigInt(srp_Nstr, 16, 0);
- srp_g = str2bigInt("2", 10, 0);
- srp_k = str2bigInt("c46d46600d87fef149bd79b81119842f3c20241fda67d06ef412d8f6d9479c58", 16, 0);
- srp_a = randBigInt(32, 1);
+ srp_N = new BigInteger(srp_Nstr, 16);
+ srp_g = new BigInteger("2");
+ srp_k = new BigInteger("c46d46600d87fef149bd79b81119842f3c20241fda67d06ef412d8f6d9479c58", 16);
+ rng = new SecureRandom();
+ srp_a = new BigInteger(32, rng);
// A = g**a % N
- srp_A = powMod(srp_g,srp_a,srp_N);
+ srp_A = srp_g.modPow(srp_a, srp_N);
srp_I = document.getElementById("srp_username").value;
- srp_Astr = bigInt2str(srp_A, 16)
+ srp_Astr = srp_A.toString(16);
// C -> S: A | I
srp_send_identity(srp_Astr, srp_I);
return false;
@@ -178,29 +181,28 @@ function srp_receive_salts()
function srp_calculate_x(s)
{
var p = document.getElementById("srp_password").value;
- return str2bigInt(SHA256(s + SHA256(srp_I + ":" + p)), 16, 0);
+ return new BigInteger(SHA256(s + SHA256(srp_I + ":" + p)), 16);
};
function srp_calculations(s, B)
-{
-
+{
//S -> C: s | B
- srp_B = str2bigInt(B, 16, 0);
+ srp_B = new BigInteger(B, 16);
srp_Bstr = B;
// u = H(A,B)
- srp_u = str2bigInt(SHA256(srp_Astr + srp_Bstr), 16, 0);
+ srp_u = new BigInteger(SHA256(srp_Astr + srp_Bstr), 16);
// x = H(s, H(I:p))
srp_x = srp_calculate_x(s);
//S = (B - kg^x) ^ (a + ux)
- var kgx = mult(srp_k, powMod(srp_g, srp_x, srp_N));
- var aux = add(srp_a, mult(srp_u, srp_x));
- srp_S = powMod(sub(srp_B, kgx), aux, srp_N);
+ var kgx = srp_k.multiply(srp_g.modPow(srp_x, srp_N));
+ var aux = srp_a.add(srp_u.multiply(srp_x));
+ srp_S = srp_B.subtract(kgx).modPow(aux, srp_N);
// M = H(H(N) xor H(g), H(I), s, A, B, K)
- var Mstr = bigInt2str(srp_A, 16) + bigInt2str(srp_B,16) + bigInt2str(srp_S,16);
+ var Mstr = srp_A.toString(16) + srp_B.toString(16) + srp_S.toString(16);
srp_M = SHA256(Mstr);
srp_send_hash(srp_M);
//M2 = H(A, M, K)
- srp_M2 = SHA256(bigInt2str(srp_A, 16)+srp_M+bigInt2str(srp_S, 16));
+ srp_M2 = SHA256(srp_A.toString(16) + srp_M + srp_S.toString(16));
};
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-29 08:41:46 +0000