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jsx

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a faster, safer, easier JavaScript

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// -*- mode: jsx; jsx-indent-level: 4; indent-tabs-mode: nil; -*- /* * Copyright (c) 2003-2005 Tom Wu * All Rights Reserved. * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. * * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL, * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. * * In addition, the following condition applies: * * All redistributions must retain an intact copy of this copyright notice * and disclaimer. */ import "./base.jsx"; // The code has been adapted for use as a benchmark by Google. class Crypto { static const nValue="a5261939975948bb7a58dffe5ff54e65f0498f9175f5a09288810b8975871e99af3b5dd94057b0fc07535f5f97444504fa35169d461d0d30cf0192e307727c065168c788771c561a9400fb49175e9e6aa4e23fe11af69e9412dd23b0cb6684c4c2429bce139e848ab26d0829073351f4acd36074eafd036a5eb83359d2a698d3"; static const eValue="10001"; static const dValue="8e9912f6d3645894e8d38cb58c0db81ff516cf4c7e5a14c7f1eddb1459d2cded4d8d293fc97aee6aefb861859c8b6a3d1dfe710463e1f9ddc72048c09751971c4a580aa51eb523357a3cc48d31cfad1d4a165066ed92d4748fb6571211da5cb14bc11b6e2df7c1a559e6d5ac1cd5c94703a22891464fba23d0d965086277a161"; static const pValue="d090ce58a92c75233a6486cb0a9209bf3583b64f540c76f5294bb97d285eed33aec220bde14b2417951178ac152ceab6da7090905b478195498b352048f15e7d"; static const qValue="cab575dc652bb66df15a0359609d51d1db184750c00c6698b90ef3465c99655103edbf0d54c56aec0ce3c4d22592338092a126a0cc49f65a4a30d222b411e58f"; static const dmp1Value="1a24bca8e273df2f0e47c199bbf678604e7df7215480c77c8db39f49b000ce2cf7500038acfff5433b7d582a01f1826e6f4d42e1c57f5e1fef7b12aabc59fd25"; static const dmq1Value="3d06982efbbe47339e1f6d36b1216b8a741d410b0c662f54f7118b27b9a4ec9d914337eb39841d8666f3034408cf94f5b62f11c402fc994fe15a05493150d9fd"; static const coeffValue="3a3e731acd8960b7ff9eb81a7ff93bd1cfa74cbd56987db58b4594fb09c09084db1734c8143f98b602b981aaa9243ca28deb69b5b280ee8dcee0fd2625e53250"; function constructor() { Crypto.setup(); var TEXT = "The quick brown fox jumped over the extremely lazy frog! " + "Now is the time for all good men to come to the party."; var encrypted = ""; function encrypt() : void { var RSA = new RSAKey(); RSA.setPublic(Crypto.nValue, Crypto.eValue); RSA.setPrivateEx(Crypto.nValue, Crypto.eValue, Crypto.dValue, Crypto.pValue, Crypto.qValue, Crypto.dmp1Value, Crypto.dmq1Value, Crypto.coeffValue); encrypted = RSA.encrypt(TEXT); } function decrypt() : void { var RSA = new RSAKey(); RSA.setPublic(Crypto.nValue, Crypto.eValue); RSA.setPrivateEx(Crypto.nValue, Crypto.eValue, Crypto.dValue, Crypto.pValue, Crypto.qValue, Crypto.dmp1Value, Crypto.dmq1Value, Crypto.coeffValue); var decrypted = RSA.decrypt(encrypted); if (decrypted != TEXT) { throw new Error("Crypto operation failed"); } } var crypto = new BenchmarkSuite('Crypto', 266181, [ new Benchmark("Encrypt", encrypt), new Benchmark("Decrypt", decrypt) ]); } static function setup () : void { BigInteger.init(); // JavaScript engine analysis var canary = 0xdeadbeefcafe; var j_lm = ((canary&0xffffff)==0xefcafe); // am3/28 is best for SM, Rhino, but am4/26 is best for v8. // Kestrel (Opera 9.5) gets its best result with am4/26. // IE7 does 9% better with am3/28 than with am4/26. // Firefox (SM) gets 10% faster with am3/28 than with am4/26. function setupEngine(fn : (number[],number,number,BigInteger,number,number,number)->number, bits : number) : void { BigInteger.am = fn; var dbits = bits; BigInteger.DB = dbits; BigInteger.DM = ((1<<dbits)-1); BigInteger.DV = (1<<dbits); BigInteger.FP = 52; BigInteger.FV = Math.pow(2,BigInteger.FP); BigInteger.F1 = BigInteger.FP-dbits; BigInteger.F2 = 2*dbits-BigInteger.FP; } setupEngine(Crypto.am3, 28); } // 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) static function am1(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number { var w_array = w.array; while(--n >= 0) { var v = x*this_array[i++]+w_array[j]+c; c = Math.floor(v/0x4000000); w_array[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) static function am2(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number { var w_array = w.array; var xl = x&0x7fff, xh = x>>15; while(--n >= 0) { var l = this_array[i]&0x7fff; var h = this_array[i++]>>15; var m = xh*l+h*xl; l = xl*l+((m&0x7fff)<<15)+w_array[j]+(c&0x3fffffff); c = (l>>>30)+(m>>>15)+xh*h+(c>>>30); w_array[j++] = l&0x3fffffff; } return c; } // Alternately, set max digit bits to 28 since some // browsers slow down when dealing with 32-bit numbers. static function am3(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number{ var w_array = w.array; var xl = x&0x3fff, xh = x>>14; while(--n >= 0) { var l = this_array[i]&0x3fff; var h = this_array[i++]>>14; var m = xh*l+h*xl; l = xl*l+((m&0x3fff)<<14)+w_array[j]+c; c = (l>>28)+(m>>14)+xh*h; w_array[j++] = l&0xfffffff; } return c; } // This is tailored to VMs with 2-bit tagging. It makes sure // that all the computations stay within the 29 bits available. static function am4(this_array : number[], i : number, x : number, w : BigInteger, j : number, c : number, n : number) : number { var w_array = w.array; var xl = x&0x1fff, xh = x>>13; while(--n >= 0) { var l = this_array[i]&0x1fff; var h = this_array[i++]>>13; var m = xh*l+h*xl; l = xl*l+((m&0x1fff)<<13)+w_array[j]+c; c = (l>>26)+(m>>13)+xh*h; w_array[j++] = l&0x3ffffff; } return c; } } class BigInteger { // "constants" static const ZERO = BigInteger.nbv(0); static const ONE = BigInteger.nbv(1); static var DB : number; static var DM : number; static var DV : number; static var FP : number; static var FV : number; static var F1 : number; static var F2 : number; static var am : (number[],number,number,BigInteger,number,number,number)->number; var array : number[]; var s : number; var t : number; // (public) Constructors function constructor() { this.array = new Array.<number>(); } function constructor(a : number, b : number, c : SecureRandom) { this(); this.fromNumber(a,b,c); } function constructor(a : number[]) { // when b == null && "string" != typeof a, this(); this.fromNumberArray(a); } function constructor(a : string, b : number) { this(); this.fromString(a,b); } // return new, unset BigInteger static function nbi() : BigInteger { return new BigInteger(); } // Digit conversion static const RM = "0123456789abcdefghijklmnopqrstuvwxyz"; static const RC = new Array.<number>(); static function init() : void { var rr,vv; rr = "0".charCodeAt(0); for(vv = 0; vv <= 9; ++vv) BigInteger.RC[rr++] = vv; rr = "a".charCodeAt(0); for(vv = 10; vv < 36; ++vv) BigInteger.RC[rr++] = vv; rr = "A".charCodeAt(0); for(vv = 10; vv < 36; ++vv) BigInteger.RC[rr++] = vv; } static function int2char(n : number) : string { return BigInteger.RM.charAt(n); } static function intAt(s : string,i : number) : number { var c = BigInteger.RC[s.charCodeAt(i)]; return (c==null)?-1:c as number; } // (protected) copy this to r function copyTo(r : BigInteger) : void { var this_array = this.array; var r_array = r.array; for(var i = this.t-1; i >= 0; --i) r_array[i] = this_array[i]; r.t = this.t; r.s = this.s; } // convert a (hex) string to a bignum object static function parseBigInt(str : string, r : number) : BigInteger { return new BigInteger(str,r); } // (protected) set from integer value x, -DV <= x < DV function fromInt(x : number) : void { var this_array = this.array; this.t = 1; this.s = (x<0)?-1:0; if(x > 0) this_array[0] = x; else if(x < -1) this_array[0] = x+BigInteger.DV; else this.t = 0; } // return bigint initialized to value static function nbv(i : number) : BigInteger { var r = BigInteger.nbi(); r.fromInt(i); return r; } // (protected) set from string and radix function fromString(s : string, b : number) : void { var this_array = this.array; 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.charAt(i) as number&0xff:BigInteger.intAt(s,i); if(x < 0) { if(s.charAt(i) == "-") mi = true; continue; } mi = false; if(sh == 0) this_array[this.t++] = x; else if(sh+k > BigInteger.DB) { this_array[this.t-1] |= (x&((1<<(BigInteger.DB-sh))-1))<<sh; this_array[this.t++] = (x>>(BigInteger.DB-sh)); } else this_array[this.t-1] |= x<<sh; sh += k; if(sh >= BigInteger.DB) sh -= BigInteger.DB; } if(k == 8 && (s.charAt(0) as number&0x80) != 0) { this.s = -1; if(sh > 0) this_array[this.t-1] |= ((1<<(BigInteger.DB-sh))-1)<<sh; } this.clamp(); if(mi) BigInteger.ZERO.subTo(this,this); } function fromNumberArray(s : number[]) : void { this.fromRadix(s,256); } // (protected) clamp off excess high words function clamp() : void { var this_array = this.array; var c = this.s&BigInteger.DM; while(this.t > 0 && this_array[this.t-1] == c) --this.t; } // (public) return string representation in given radix function toString(b : number) : string { var this_array = this.array; 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 = BigInteger.DB-(i*BigInteger.DB)%k; if(i-- > 0) { if(p < BigInteger.DB && (d = this_array[i]>>p) > 0) { m = true; r = BigInteger.int2char(d); } while(i >= 0) { if(p < k) { d = (this_array[i]&((1<<p)-1))<<(k-p); d |= this_array[--i]>>(p+=BigInteger.DB-k); } else { d = (this_array[i]>>(p-=k))&km; if(p <= 0) { p += BigInteger.DB; --i; } } if(d > 0) m = true; if(m) r += BigInteger.int2char(d); } } return m?r:"0"; } // (public) -this function negate() : BigInteger { var r = BigInteger.nbi(); BigInteger.ZERO.subTo(this,r); return r; } // (public) |this| function abs() : BigInteger { return (this.s<0)?this.negate():this; } // (public) return + if this > a, - if this < a, 0 if equal function compareTo(a : BigInteger) : number { var this_array = this.array; var a_array = a.array; 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_array[i]-a_array[i]) != 0) return r; return 0; } // returns bit length of the integer x static function nbits(x : number) : number { 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 bitLength() : number { var this_array = this.array; if(this.t <= 0) return 0; return BigInteger.DB*(this.t-1)+BigInteger.nbits(this_array[this.t-1]^(this.s&BigInteger.DM)); } // (protected) r = this << n*DB function dlShiftTo(n : number, r : BigInteger) : void { var this_array = this.array; var r_array = r.array; var i; for(i = this.t-1; i >= 0; --i) r_array[i+n] = this_array[i]; for(i = n-1; i >= 0; --i) r_array[i] = 0; r.t = this.t+n; r.s = this.s; } // (protected) r = this >> n*DB function drShiftTo(n : number, r : BigInteger) : void { var this_array = this.array; var r_array = r.array; for(var i = n; i < this.t; ++i) r_array[i-n] = this_array[i]; r.t = Math.max(this.t-n,0); r.s = this.s; } // (protected) r = this << n function lShiftTo(n : number, r : BigInteger) : void { var this_array = this.array; var r_array = r.array; var bs = n%BigInteger.DB; var cbs = BigInteger.DB-bs; var bm = (1<<cbs)-1; var ds = Math.floor(n/BigInteger.DB), c = (this.s<<bs)&BigInteger.DM, i; for(i = this.t-1; i >= 0; --i) { r_array[i+ds+1] = (this_array[i]>>cbs)|c; c = (this_array[i]&bm)<<bs; } for(i = ds-1; i >= 0; --i) r_array[i] = 0; r_array[ds] = c; r.t = this.t+ds+1; r.s = this.s; r.clamp(); } // (protected) r = this >> n function rShiftTo(n : number, r : BigInteger) : void { var this_array = this.array; var r_array = r.array; r.s = this.s; var ds = Math.floor(n/BigInteger.DB); if(ds >= this.t) { r.t = 0; return; } var bs = n%BigInteger.DB; var cbs = BigInteger.DB-bs; var bm = (1<<bs)-1; r_array[0] = this_array[ds]>>bs; for(var i = ds+1; i < this.t; ++i) { r_array[i-ds-1] |= (this_array[i]&bm)<<cbs; r_array[i-ds] = this_array[i]>>bs; } if(bs > 0) r_array[this.t-ds-1] |= (this.s&bm)<<cbs; r.t = this.t-ds; r.clamp(); } // (protected) r = this - a function subTo(a : BigInteger, r : BigInteger) : void { var this_array = this.array; var r_array = r.array; var a_array = a.array; var i = 0, c = 0, m = Math.min(a.t,this.t); while(i < m) { c += this_array[i]-a_array[i]; r_array[i++] = c&BigInteger.DM; c >>= BigInteger.DB; } if(a.t < this.t) { c -= a.s; while(i < this.t) { c += this_array[i]; r_array[i++] = c&BigInteger.DM; c >>= BigInteger.DB; } c += this.s; } else { c += this.s; while(i < a.t) { c -= a_array[i]; r_array[i++] = c&BigInteger.DM; c >>= BigInteger.DB; } c -= a.s; } r.s = (c<0)?-1:0; if(c < -1) r_array[i++] = BigInteger.DV+c; else if(c > 0) r_array[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 multiplyTo(a : BigInteger, r : BigInteger) : void { var this_array = this.array; var r_array = r.array; var x = this.abs(), y = a.abs(); var y_array = y.array; var i = x.t; r.t = i+y.t; while(--i >= 0) r_array[i] = 0; for(i = 0; i < y.t; ++i) r_array[i+x.t] = BigInteger.am(x.array,0,y_array[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 squareTo(r : BigInteger) : void { var x = this.abs(); var x_array = x.array; var r_array = r.array; var i = r.t = 2*x.t; while(--i >= 0) r_array[i] = 0; for(i = 0; i < x.t-1; ++i) { var c = BigInteger.am(x.array,i,x_array[i],r,2*i,0,1); if((r_array[i+x.t]+=BigInteger.am(x.array,i+1,2*x_array[i],r,2*i+1,c,x.t-i-1)) >= BigInteger.DV) { r_array[i+x.t] -= BigInteger.DV; r_array[i+x.t+1] = 1; } } if(r.t > 0) r_array[r.t-1] += BigInteger.am(x.array,i,x_array[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 divRemTo(m : BigInteger, q : BigInteger, r : BigInteger) : void { 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 = BigInteger.nbi(); var y = BigInteger.nbi(), ts = this.s, ms = m.s; var pm_array = pm.array; var nsh = BigInteger.DB-BigInteger.nbits(pm_array[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 y_array = y.array; var y0 = y_array[ys-1]; if(y0 == 0) return; var yt = y0*(1<<BigInteger.F1)+((ys>1)?y_array[ys-2]>>BigInteger.F2:0); var d1 = BigInteger.FV/yt, d2 = (1<<BigInteger.F1)/yt, e = 1<<BigInteger.F2; var i = r.t, j = i-ys, t = (q==null)?BigInteger.nbi():q; y.dlShiftTo(j,t); var r_array = r.array; if(r.compareTo(t) >= 0) { r_array[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_array[y.t++] = 0; while(--j >= 0) { // Estimate quotient digit var qd = (r_array[--i]==y0)?BigInteger.DM:Math.floor(r_array[i]*d1+(r_array[i-1]+e)*d2); if((r_array[i]+=BigInteger.am(y.array,0,qd,r,j,0,ys)) < qd) { // Try it out y.dlShiftTo(j,t); r.subTo(t,r); while(r_array[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 mod(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.abs().divRemTo(a,null,r); if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r); return r; } // (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 invDigit() : number { var this_array = this.array; if(this.t < 1) return 0; var x = this_array[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%BigInteger.DV))%BigInteger.DV; // y == 1/x mod 2^dbits // we really want the negative inverse, and -DV < y < DV return (y>0)?BigInteger.DV-y:-y; } // (protected) true iff this is even function isEven() : boolean { var this_array = this.array; return ((this.t>0)?(this_array[0]&1):this.s) == 0; } // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79) function exp(e : number, z : Reducer) : BigInteger { if(e > 0xffffffff || e < 1) return BigInteger.ONE; var r = BigInteger.nbi(), r2 = BigInteger.nbi(), g = z.convert(this), i = BigInteger.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 modPowInt(e : number, m : BigInteger) : BigInteger { var z : Reducer; if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m); return this.exp(e,z); } //-------------------------------------------------------------------------- // Extended JavaScript BN functions, required for RSA private ops. //-------------------------------------------------------------------------- // (public) function clone() : BigInteger { var r = BigInteger.nbi(); this.copyTo(r); return r; } // (public) return value as integer function intValue() : number { var this_array = this.array; if(this.s < 0) { if(this.t == 1) return this_array[0]-BigInteger.DV; else if(this.t == 0) return -1; } else if(this.t == 1) return this_array[0]; else if(this.t == 0) return 0; // assumes 16 < DB < 32 return ((this_array[1]&((1<<(32-BigInteger.DB))-1))<<BigInteger.DB)|this_array[0]; } // (public) return value as byte function byteValue() : number { var this_array = this.array; return (this.t==0)?this.s:(this_array[0]<<24)>>24; } // (public) return value as short (assumes DB>=16) function shortValue() : number { var this_array = this.array; return (this.t==0)?this.s:(this_array[0]<<16)>>16; } // (protected) return x s.t. r^x < DV function chunkSize(r : number) : number { return Math.floor(Math.LN2*BigInteger.DB/Math.log(r)); } // (public) 0 if this == 0, 1 if this > 0 function signum() : number { var this_array = this.array; if(this.s < 0) return -1; else if(this.t <= 0 || (this.t == 1 && this_array[0] <= 0)) return 0; else return 1; } // (protected) convert to radix string function toRadix() : string { return this.toRadix(10); } function toRadix(b : number) : string { if(this.signum() == 0 || b < 2 || b > 36) return "0"; var cs = this.chunkSize(b); var a = Math.pow(b,cs); var d = BigInteger.nbv(a), y = BigInteger.nbi(), z = BigInteger.nbi(), r = ""; this.divRemTo(d,y,z); while(y.signum() > 0) { r = (a+z.intValue()).toString(b).substring(1) + r; y.divRemTo(d,y,z); } return z.intValue().toString(b) + r; } // (protected) convert from radix string function fromRadix(s : string) : void { this.fromRadix(s, 10); } function fromRadix(s : string, b : number) : void { this.fromInt(0); 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 = BigInteger.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); } function fromRadix(s : number[], b : number) : void { this.fromInt(0); 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 = s[i]; 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 fromNumber(a : number, b : number, c : SecureRandom) : void { // 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),BigInteger.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); } } } function fromNumber(a : number, b : SecureRandom) : void { // new BigInteger(int,RNG) var x = new Array.<number>(), t = a&7; x.length = (a>>3)+1; b.nextBytes(x); if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0; this.fromNumberArray(x); } // (public) convert to bigendian byte array function toByteArray() : number[] { var this_array = this.array; var i = this.t, r = new Array.<number>(); r[0] = this.s; var p = BigInteger.DB-(i*BigInteger.DB)%8, d, k = 0; if(i-- > 0) { if(p < BigInteger.DB && (d = this_array[i]>>p) != (this.s&BigInteger.DM)>>p) r[k++] = d|(this.s<<(BigInteger.DB-p)); while(i >= 0) { if(p < 8) { d = (this_array[i]&((1<<p)-1))<<(8-p); d |= this_array[--i]>>(p+=BigInteger.DB-8); } else { d = (this_array[i]>>(p-=8))&0xff; if(p <= 0) { p += BigInteger.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 equals(a : BigInteger) : boolean { return(this.compareTo(a)==0); } function min(a : BigInteger) : BigInteger { return(this.compareTo(a)<0)?this:a; } function max(a : BigInteger) : BigInteger { return(this.compareTo(a)>0)?this:a; } // (protected) r = this op a (bitwise) function bitwiseTo(a : BigInteger, op : (number, number) -> number, r : BigInteger) : void { var this_array = this.array; var a_array = a.array; var r_array = r.array; var i, f, m = Math.min(a.t,this.t); for(i = 0; i < m; ++i) r_array[i] = op(this_array[i],a_array[i]); if(a.t < this.t) { f = a.s&BigInteger.DM; for(i = m; i < this.t; ++i) r_array[i] = op(this_array[i],f); r.t = this.t; } else { f = this.s&BigInteger.DM; for(i = m; i < a.t; ++i) r_array[i] = op(f,a_array[i]); r.t = a.t; } r.s = op(this.s,a.s); r.clamp(); } static function op_and(x : number, y : number) : number { return x&y; } static function op_or(x : number, y : number) : number { return x|y; } static function op_xor(x : number, y : number) : number { return x^y; } static function op_andnot(x : number, y : number) : number { return x&~y; } // (public) this & a function and(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.bitwiseTo(a,BigInteger.op_and,r); return r; } // (public) this | a function or(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.bitwiseTo(a,BigInteger.op_or,r); return r; } // (public) this ^ a function xor(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.bitwiseTo(a,BigInteger.op_xor,r); return r; } // (public) this & ~a function andNot(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.bitwiseTo(a,BigInteger.op_andnot,r); return r; } // (public) ~this function not() : BigInteger { var this_array = this.array; var r = BigInteger.nbi(); var r_array = r.array; for(var i = 0; i < this.t; ++i) r_array[i] = BigInteger.DM&~this_array[i]; r.t = this.t; r.s = ~this.s; return r; } // (public) this << n function shiftLeft(n : number) : BigInteger { var r = BigInteger.nbi(); if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r); return r; } // (public) this >> n function shiftRight(n : number) : BigInteger { var r = BigInteger.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 static function lbit(x : number) : number { 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 getLowestSetBit() : number { var this_array = this.array; for(var i = 0; i < this.t; ++i) if(this_array[i] != 0) return i*BigInteger.DB+BigInteger.lbit(this_array[i]); if(this.s < 0) return this.t*BigInteger.DB; return -1; } // return number of 1 bits in x static function cbit(x : number) : number { var r = 0; while(x != 0) { x &= x-1; ++r; } return r; } // (public) return number of set bits function bitCount() : number { var this_array = this.array; var r = 0, x = this.s&BigInteger.DM; for(var i = 0; i < this.t; ++i) r += BigInteger.cbit(this_array[i]^x); return r; } // (public) true iff nth bit is set function testBit(n : number) : boolean { var this_array = this.array; var j = Math.floor(n/BigInteger.DB); if(j >= this.t) return(this.s!=0); return((this_array[j]&(1<<(n%BigInteger.DB)))!=0); } // (protected) this op (1<<n) function changeBit(n : number, op : (number,number) -> number) : BigInteger { var r = BigInteger.ONE.shiftLeft(n); this.bitwiseTo(r,op,r); return r; } // (public) this | (1<<n) function setBit(n : number) : BigInteger { return this.changeBit(n,BigInteger.op_or); } // (public) this & ~(1<<n) function clearBit(n : number) : BigInteger { return this.changeBit(n,BigInteger.op_andnot); } // (public) this ^ (1<<n) function flipBit(n : number) : BigInteger { return this.changeBit(n,BigInteger.op_xor); } // (protected) r = this + a function addTo(a : BigInteger, r : BigInteger) : void { var this_array = this.array; var a_array = a.array; var r_array = r.array; var i = 0, c = 0, m = Math.min(a.t,this.t); while(i < m) { c += this_array[i]+a_array[i]; r_array[i++] = c&BigInteger.DM; c >>= BigInteger.DB; } if(a.t < this.t) { c += a.s; while(i < this.t) { c += this_array[i]; r_array[i++] = c&BigInteger.DM; c >>= BigInteger.DB; } c += this.s; } else { c += this.s; while(i < a.t) { c += a_array[i]; r_array[i++] = c&BigInteger.DM; c >>= BigInteger.DB; } c += a.s; } r.s = (c<0)?-1:0; if(c > 0) r_array[i++] = c; else if(c < -1) r_array[i++] = BigInteger.DV+c; r.t = i; r.clamp(); } // (public) this + a function add(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.addTo(a,r); return r; } // (public) this - a function subtract(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.subTo(a,r); return r; } // (public) this * a function multiply(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.multiplyTo(a,r); return r; } // (public) this / a function divide(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.divRemTo(a,r,null); return r; } // (public) this % a function remainder(a : BigInteger) : BigInteger { var r = BigInteger.nbi(); this.divRemTo(a,null,r); return r; } // (public) [this/a,this%a] function divideAndRemainder(a : BigInteger) : BigInteger[] { var q = BigInteger.nbi(), r = BigInteger.nbi(); this.divRemTo(a,q,r); return [q,r]; } // (protected) this *= n, this >= 0, 1 < n < DV function dMultiply(n : number) : void { var this_array = this.array; this_array[this.t] = BigInteger.am(this.array,0,n-1,this,0,0,this.t); ++this.t; this.clamp(); } // (protected) this += n << w words, this >= 0 function dAddOffset(n : number, w : number) : void { var this_array = this.array; while(this.t <= w) this_array[this.t++] = 0; this_array[w] += n; while(this_array[w] >= BigInteger.DV) { this_array[w] -= BigInteger.DV; if(++w >= this.t) this_array[this.t++] = 0; ++this_array[w]; } } // (public) this^e function pow(e : number) : BigInteger { 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 multiplyLowerTo(a : BigInteger, n : number, r : BigInteger) : void { var r_array = r.array; var a_array = a.array; var i = Math.min(this.t+a.t,n); r.s = 0; // assumes a,this >= 0 r.t = i; while(i > 0) r_array[--i] = 0; var j; for(j = r.t-this.t; i < j; ++i) r_array[i+this.t] = BigInteger.am(this.array,0,a_array[i],r,i,0,this.t); for(j = Math.min(a.t,n); i < j; ++i) BigInteger.am(this.array,0,a_array[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 multiplyUpperTo(a : BigInteger, n : number, r : BigInteger) : void { var r_array = r.array; var a_array = a.array; --n; var i = r.t = this.t+a.t-n; r.s = 0; // assumes a,this >= 0 while(--i >= 0) r_array[i] = 0; for(i = Math.max(n-this.t,0); i < a.t; ++i) r_array[this.t+i-n] = BigInteger.am(this.array,n-i,a_array[i],r,0,0,this.t+i-n); r.clamp(); r.drShiftTo(1,r); } // (public) this^e % m (HAC 14.85) function modPow(e : BigInteger, m : BigInteger) : BigInteger { var e_array = e.array; var i = e.bitLength(), k, r = BigInteger.nbv(1), z = null : Reducer; 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.<BigInteger>(), n = 3, k1 = k-1, km = (1<<k)-1; g[1] = z.convert(this); if(k > 1) { var g2 = BigInteger.nbi(); z.sqrTo(g[1],g2); while(n <= km) { g[n] = BigInteger.nbi(); z.mulTo(g2,g[n-2],g[n]); n += 2; } } var j = e.t-1, w, is1 = true, r2 = BigInteger.nbi(), t; i = BigInteger.nbits(e_array[j])-1; while(j >= 0) { if(i >= k1) w = (e_array[j]>>(i-k1))&km; else { w = (e_array[j]&((1<<(i+1))-1))<<(k1-i); if(j > 0) w |= e_array[j-1]>>(BigInteger.DB+i-k1); } n = k; while((w&1) == 0) { w >>= 1; --n; } if((i -= n) < 0) { i += BigInteger.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_array[j]&(1<<i)) == 0) { z.sqrTo(r,r2); t = r; r = r2; r2 = t; if(--i < 0) { i = BigInteger.DB-1; --j; } } } return z.revert(r); } // (public) gcd(this,a) (HAC 14.54) function gcd(a : BigInteger) : BigInteger { 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 modInt(n : number) : number { var this_array = this.array; if(n <= 0) return 0; var d = BigInteger.DV%n, r = (this.s<0)?n-1:0; if(this.t > 0) if(d == 0) r = this_array[0]%n; else for(var i = this.t-1; i >= 0; --i) r = (d*r+this_array[i])%n; return r; } // (public) 1/this % m (HAC 14.61) function modInverse(m : BigInteger) : BigInteger { var ac = m.isEven(); if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO; var u = m.clone(), v = this.clone(); var a = BigInteger.nbv(1), b = BigInteger.nbv(0), c = BigInteger.nbv(0), d = BigInteger.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; } static const 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]; static const lplim = (1<<26)/BigInteger.lowprimes[BigInteger.lowprimes.length-1]; // (public) test primality with certainty >= 1-.5^t function isProbablePrime(t : number) : boolean { var i, x = this.abs(); var x_array = x.array; if(x.t == 1 && x_array[0] <= BigInteger.lowprimes[BigInteger.lowprimes.length-1]) { for(i = 0; i < BigInteger.lowprimes.length; ++i) if(x_array[0] == BigInteger.lowprimes[i]) return true; return false; } if(x.isEven()) return false; i = 1; while(i < BigInteger.lowprimes.length) { var m = BigInteger.lowprimes[i], j = i+1; while(j < BigInteger.lowprimes.length && m < BigInteger.lplim) m *= BigInteger.lowprimes[j++]; m = x.modInt(m); while(i < j) if(m%BigInteger.lowprimes[i++] == 0) return false; } return x.millerRabin(t); } // (protected) true if probably prime (HAC 4.24, Miller-Rabin) function millerRabin(t : number) : boolean { 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 > BigInteger.lowprimes.length) t = BigInteger.lowprimes.length; var a = BigInteger.nbi(); for(var i = 0; i < t; ++i) { a.fromInt(BigInteger.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; } // BigInteger interfaces not implemented in jsbn: // BigInteger(int signum, byte[] magnitude) // double doubleValue() // float floatValue() // int hashCode() // long longValue() // static BigInteger valueOf(long val) } abstract class Reducer { abstract function convert(x : BigInteger) : BigInteger; abstract function revert(x : BigInteger) : BigInteger; abstract function reduce(x : BigInteger) : void; abstract function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void; abstract function sqrTo(x : BigInteger, r : BigInteger) : void; } // Modular reduction using "classic" algorithm class Classic extends Reducer { var m : BigInteger; function constructor(m : BigInteger) { this.m = m; } override function convert(x : BigInteger) : BigInteger { if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m); else return x; } override function revert(x : BigInteger) : BigInteger { return x; } override function reduce(x : BigInteger) : void { x.divRemTo(this.m,null,x); } override function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void { x.multiplyTo(y,r); this.reduce(r); } override function sqrTo(x : BigInteger, r : BigInteger) : void { x.squareTo(r); this.reduce(r); } } // Montgomery reduction class Montgomery extends Reducer { var m : BigInteger; var mp : number; var mpl : number; var mph : number; var um : number; var mt2 : number; function constructor(m : BigInteger) { this.m = m; this.mp = m.invDigit(); this.mpl = this.mp&0x7fff; this.mph = this.mp>>15; this.um = (1<<(BigInteger.DB-15))-1; this.mt2 = 2*m.t; } // xR mod m override function convert(x : BigInteger) : BigInteger { var r = BigInteger.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 override function revert(x : BigInteger) : BigInteger { var r = BigInteger.nbi(); x.copyTo(r); this.reduce(r); return r; } // x = x/R mod m (HAC 14.32) override function reduce(x : BigInteger) : void { var x_array = x.array; while(x.t <= this.mt2) // pad x so am has enough room later x_array[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_array[i]&0x7fff; var u0 = (j*this.mpl+(((j*this.mph+(x_array[i]>>15)*this.mpl)&this.um)<<15))&BigInteger.DM; // use am to combine the multiply-shift-add into one call j = i+this.m.t; x_array[j] += BigInteger.am(this.m.array,0,u0,x,i,0,this.m.t); // propagate carry while(x_array[j] >= BigInteger.DV) { x_array[j] -= BigInteger.DV; x_array[++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 override function sqrTo(x : BigInteger, r : BigInteger) : void { x.squareTo(r); this.reduce(r); } // r = "xy/R mod m"; x,y != r override function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void { x.multiplyTo(y,r); this.reduce(r); } } // A "null" reducer class NullExp extends Reducer { function constructor() { } override function convert(x : BigInteger) : BigInteger { return x; } override function revert(x : BigInteger) : BigInteger { return x; } override function reduce(x : BigInteger) : void { } override function mulTo(x : BigInteger, y : BigInteger, r : BigInteger) : void { x.multiplyTo(y,r); } override function sqrTo(x : BigInteger, r : BigInteger) : void { x.squareTo(r); } } // Barrett modular reduction class Barrett extends Reducer { var r2 : BigInteger; var q3 : BigInteger; var mu : BigInteger; var m : BigInteger; function constructor(m : BigInteger) { // setup Barrett this.r2 = BigInteger.nbi(); this.q3 = BigInteger.nbi(); BigInteger.ONE.dlShiftTo(2*m.t,this.r2); this.mu = this.r2.divide(m); this.m = m; } override function convert(x : BigInteger) : BigInteger { 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 = BigInteger.nbi(); x.copyTo(r); this.reduce(r); return r; } } override function revert(x : BigInteger) : BigInteger { return x; } // x = x mod m (HAC 14.42) override function reduce(x : BigInteger) : void { 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); thi