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JavaScript
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// 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; } var inBrowser = typeof navigator !== "undefined"; if(inBrowser && j_lm && (navigator.appName == "Microsoft Internet Explorer")) { BigInteger.prototype.am = am2; dbits = 30; } else if(inBrowser && 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+this.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 (this.s<0)?-r: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);
// Copyright (c) 2005-2009 Tom Wu // All Rights Reserved. // See "LICENSE" for details.
// Extended JavaScript BN functions, required for RSA private ops.
// Version 1.1: new BigInteger("0", 10) returns "proper" zero // Version 1.2: square() API, isProbablePrime fix
// (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^2 function bnSquare() { var r = nbi(); this.squareTo(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) { if(n == 0) return; 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 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997]; 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) { //Pick bases at random, instead of starting at 2 a.fromInt(lowprimes[Math.floor(Math.random()*lowprimes.length)]); 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;
// JSBN-specific extension BigInteger.prototype.square = bnSquare;
// Expose the Barrett function BigInteger.prototype.Barrett = Barrett
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude) // double doubleValue() // float floatValue() // int hashCode() // long longValue() // static BigInteger valueOf(long val)
// 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(typeof window !== "undefined" && window.crypto) { if (window.crypto.getRandomValues) { // Use webcrypto if available var ua = new Uint8Array(32); window.crypto.getRandomValues(ua); for(t = 0; t < 32; ++t) rng_pool[rng_pptr++] = ua[t]; } else if(navigator.appName == "Netscape" && navigator.appVersion < "5") { // 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;
// 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;
BigInteger.SecureRandom = SecureRandom; BigInteger.BigInteger = BigInteger; if (typeof exports !== 'undefined') { exports = module.exports = BigInteger; } else { this.BigInteger = BigInteger; this.SecureRandom = SecureRandom; }
}).call(this);