if ("undefined" == typeof window) window = this; /*! * Crypto-JS v2.0.0 * http://code.google.com/p/crypto-js/ * Copyright (c) 2009, Jeff Mott. All rights reserved. * http://code.google.com/p/crypto-js/wiki/License */ var base64map = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"; // Global Crypto object var Crypto = window.Crypto = {}; // Crypto utilities var util = Crypto.util = { // Bit-wise rotate left rotl: function (n, b) { return (n << b) | (n >>> (32 - b)); }, // Bit-wise rotate right rotr: function (n, b) { return (n << (32 - b)) | (n >>> b); }, // Swap big-endian to little-endian and vice versa endian: function (n) { // If number given, swap endian if (n.constructor == Number) { return util.rotl(n, 8) & 0x00FF00FF | util.rotl(n, 24) & 0xFF00FF00; } // Else, assume array and swap all items for (var i = 0; i < n.length; i++) n[i] = util.endian(n[i]); return n; }, // Generate an array of any length of random bytes randomBytes: function (n) { for (var bytes = []; n > 0; n--) bytes.push(Math.floor(Math.random() * 256)); return bytes; }, // Convert a byte array to big-endian 32-bit words bytesToWords: function (bytes) { for (var words = [], i = 0, b = 0; i < bytes.length; i++, b += 8) words[b >>> 5] |= bytes[i] << (24 - b % 32); return words; }, // Convert big-endian 32-bit words to a byte array wordsToBytes: function (words) { for (var bytes = [], b = 0; b < words.length * 32; b += 8) bytes.push((words[b >>> 5] >>> (24 - b % 32)) & 0xFF); return bytes; }, // Convert a byte array to a hex string bytesToHex: function (bytes) { for (var hex = [], i = 0; i < bytes.length; i++) { hex.push((bytes[i] >>> 4).toString(16)); hex.push((bytes[i] & 0xF).toString(16)); } return hex.join(""); }, // Convert a hex string to a byte array hexToBytes: function (hex) { for (var bytes = [], c = 0; c < hex.length; c += 2) bytes.push(parseInt(hex.substr(c, 2), 16)); return bytes; }, // Convert a byte array to a base-64 string bytesToBase64: function (bytes) { // Use browser-native function if it exists if (typeof btoa == "function") return btoa(Binary.bytesToString(bytes)); for(var base64 = [], i = 0; i < bytes.length; i += 3) { var triplet = (bytes[i] << 16) | (bytes[i + 1] << 8) | bytes[i + 2]; for (var j = 0; j < 4; j++) { if (i * 8 + j * 6 <= bytes.length * 8) base64.push(base64map.charAt((triplet >>> 6 * (3 - j)) & 0x3F)); else base64.push("="); } } return base64.join(""); }, // Convert a base-64 string to a byte array base64ToBytes: function (base64) { // Use browser-native function if it exists if (typeof atob == "function") return Binary.stringToBytes(atob(base64)); // Remove non-base-64 characters base64 = base64.replace(/[^A-Z0-9+\/]/ig, ""); for (var bytes = [], i = 0, imod4 = 0; i < base64.length; imod4 = ++i % 4) { if (imod4 == 0) continue; bytes.push(((base64map.indexOf(base64.charAt(i - 1)) & (Math.pow(2, -2 * imod4 + 8) - 1)) << (imod4 * 2)) | (base64map.indexOf(base64.charAt(i)) >>> (6 - imod4 * 2))); } return bytes; } }; // Crypto mode namespace Crypto.mode = {}; // Crypto character encodings var charenc = Crypto.charenc = {}; // UTF-8 encoding var UTF8 = charenc.UTF8 = { // Convert a string to a byte array stringToBytes: function (str) { return Binary.stringToBytes(unescape(encodeURIComponent(str))); }, // Convert a byte array to a string bytesToString: function (bytes) { return decodeURIComponent(escape(Binary.bytesToString(bytes))); } }; // Binary encoding var Binary = charenc.Binary = { // Convert a string to a byte array stringToBytes: function (str) { for (var bytes = [], i = 0; i < str.length; i++) bytes.push(str.charCodeAt(i)); return bytes; }, // Convert a byte array to a string bytesToString: function (bytes) { for (var str = [], i = 0; i < bytes.length; i++) str.push(String.fromCharCode(bytes[i])); return str.join(""); } }; Bitcoin = {}; if (typeof navigator === 'undefined') { var navigator = {}; navigator.appName = 'NodeJS'; } // 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<= 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))<>(this.DB-sh)); } else this[this.t-1] |= x<= 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)< 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< 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+=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<= 0; --i) { r[i+ds+1] = (this[i]>>cbs)|c; c = (this[i]&bm)<= 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; for(var i = ds+1; i < this.t; ++i) { r[i-ds-1] |= (this[i]&bm)<>bs; } if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<>= 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<1)?y[ys-2]>>this.F2:0); var d1 = this.FV/yt, d2 = (1<= 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< 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))<>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< 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+=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<>= 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< 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< 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; // BigInteger interfaces not implemented in jsbn: // BigInteger(int signum, byte[] magnitude) // double doubleValue() // float floatValue() // int hashCode() // long longValue() // static BigInteger valueOf(long val) // 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 monkey patching BigInteger.valueOf = nbv; /** * Returns a byte array representation of the big integer. * * This returns the absolute of the contained value in big endian * form. A value of zero results in an empty array. */ BigInteger.prototype.toByteArrayUnsigned = function () { var ba = this.abs().toByteArray(); if (ba.length) { if (ba[0] == 0) { ba = ba.slice(1); } return ba.map(function (v) { return (v < 0) ? v + 256 : v; }); } else { // Empty array, nothing to do return ba; } }; /** * Turns a byte array into a big integer. * * This function will interpret a byte array as a big integer in big * endian notation and ignore leading zeros. */ BigInteger.fromByteArrayUnsigned = function (ba) { if (!ba.length) { return ba.valueOf(0); } else if (ba[0] & 0x80) { // Prepend a zero so the BigInteger class doesn't mistake this // for a negative integer. return new BigInteger([0].concat(ba)); } else { return new BigInteger(ba); } }; /** * Converts big integer to signed byte representation. * * The format for this value uses a the most significant bit as a sign * bit. If the most significant bit is already occupied by the * absolute value, an extra byte is prepended and the sign bit is set * there. * * Examples: * * 0 => 0x00 * 1 => 0x01 * -1 => 0x81 * 127 => 0x7f * -127 => 0xff * 128 => 0x0080 * -128 => 0x8080 * 255 => 0x00ff * -255 => 0x80ff * 16300 => 0x3fac * -16300 => 0xbfac * 62300 => 0x00f35c * -62300 => 0x80f35c */ BigInteger.prototype.toByteArraySigned = function () { var val = this.abs().toByteArrayUnsigned(); var neg = this.compareTo(BigInteger.ZERO) < 0; if (neg) { if (val[0] & 0x80) { val.unshift(0x80); } else { val[0] |= 0x80; } } else { if (val[0] & 0x80) { val.unshift(0x00); } } return val; }; /** * Parse a signed big integer byte representation. * * For details on the format please see BigInteger.toByteArraySigned. */ BigInteger.fromByteArraySigned = function (ba) { // Check for negative value if (ba[0] & 0x80) { // Remove sign bit ba[0] &= 0x7f; return BigInteger.fromByteArrayUnsigned(ba).negate(); } else { return BigInteger.fromByteArrayUnsigned(ba); } }; // Console ignore var names = ["log", "debug", "info", "warn", "error", "assert", "dir", "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", "profile", "profileEnd"]; if ("undefined" == typeof window.console) window.console = {}; for (var i = 0; i < names.length; ++i) if ("undefined" == typeof window.console[names[i]]) window.console[names[i]] = function() {}; // Bitcoin utility functions Bitcoin.Util = { /** * Cross-browser compatibility version of Array.isArray. */ isArray: Array.isArray || function(o) { return Object.prototype.toString.call(o) === '[object Array]'; }, /** * Create an array of a certain length filled with a specific value. */ makeFilledArray: function (len, val) { var array = []; var i = 0; while (i < len) { array[i++] = val; } return array; }, /** * Turn an integer into a "var_int". * * "var_int" is a variable length integer used by Bitcoin's binary format. * * Returns a byte array. */ numToVarInt: function (i) { if (i < 0xfd) { // unsigned char return [i]; } else if (i <= 1<<16) { // unsigned short (LE) return [0xfd, i >>> 8, i & 255]; } else if (i <= 1<<32) { // unsigned int (LE) return [0xfe].concat(Crypto.util.wordsToBytes([i])); } else { // unsigned long long (LE) return [0xff].concat(Crypto.util.wordsToBytes([i >>> 32, i])); } }, /** * Parse a Bitcoin value byte array, returning a BigInteger. */ valueToBigInt: function (valueBuffer) { if (valueBuffer instanceof BigInteger) return valueBuffer; // Prepend zero byte to prevent interpretation as negative integer return BigInteger.fromByteArrayUnsigned(valueBuffer); }, /** * Format a Bitcoin value as a string. * * Takes a BigInteger or byte-array and returns that amount of Bitcoins in a * nice standard formatting. * * Examples: * 12.3555 * 0.1234 * 900.99998888 * 34.00 */ formatValue: function (valueBuffer) { var value = this.valueToBigInt(valueBuffer).toString(); var integerPart = value.length > 8 ? value.substr(0, value.length-8) : '0'; var decimalPart = value.length > 8 ? value.substr(value.length-8) : value; while (decimalPart.length < 8) decimalPart = "0"+decimalPart; decimalPart = decimalPart.replace(/0*$/, ''); while (decimalPart.length < 2) decimalPart += "0"; return integerPart+"."+decimalPart; }, /** * Parse a floating point string as a Bitcoin value. * * Keep in mind that parsing user input is messy. You should always display * the parsed value back to the user to make sure we understood his input * correctly. */ parseValue: function (valueString) { // TODO: Detect other number formats (e.g. comma as decimal separator) var valueComp = valueString.split('.'); var integralPart = valueComp[0]; var fractionalPart = valueComp[1] || "0"; while (fractionalPart.length < 8) fractionalPart += "0"; fractionalPart = fractionalPart.replace(/^0+/g, ''); var value = BigInteger.valueOf(parseInt(integralPart)); value = value.multiply(BigInteger.valueOf(100000000)); value = value.add(BigInteger.valueOf(parseInt(fractionalPart))); return value; }, /** * Calculate RIPEMD160(SHA256(data)). * * Takes an arbitrary byte array as inputs and returns the hash as a byte * array. */ sha256ripe160: function (data) { return Crypto.RIPEMD160(Crypto.SHA256(data, {asBytes: true}), {asBytes: true}); } }; for (var i in Crypto.util) { if (Crypto.util.hasOwnProperty(i)) { Bitcoin.Util[i] = Crypto.util[i]; } } // Random number generator - requires a PRNG backend, e.g. prng4.js // For best results, put code like // // 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; // Basic Javascript Elliptic Curve implementation // Ported loosely from BouncyCastle's Java EC code // Only Fp curves implemented for now // Requires jsbn.js and jsbn2.js // ---------------- // ECFieldElementFp // constructor function ECFieldElementFp(q,x) { this.x = x; // TODO if(x.compareTo(q) >= 0) error this.q = q; } function feFpEquals(other) { if(other == this) return true; return (this.q.equals(other.q) && this.x.equals(other.x)); } function feFpToBigInteger() { return this.x; } function feFpNegate() { return new ECFieldElementFp(this.q, this.x.negate().mod(this.q)); } function feFpAdd(b) { return new ECFieldElementFp(this.q, this.x.add(b.toBigInteger()).mod(this.q)); } function feFpSubtract(b) { return new ECFieldElementFp(this.q, this.x.subtract(b.toBigInteger()).mod(this.q)); } function feFpMultiply(b) { return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q)); } function feFpSquare() { return new ECFieldElementFp(this.q, this.x.square().mod(this.q)); } function feFpDivide(b) { return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q)); } ECFieldElementFp.prototype.equals = feFpEquals; ECFieldElementFp.prototype.toBigInteger = feFpToBigInteger; ECFieldElementFp.prototype.negate = feFpNegate; ECFieldElementFp.prototype.add = feFpAdd; ECFieldElementFp.prototype.subtract = feFpSubtract; ECFieldElementFp.prototype.multiply = feFpMultiply; ECFieldElementFp.prototype.square = feFpSquare; ECFieldElementFp.prototype.divide = feFpDivide; // ---------------- // ECPointFp // constructor function ECPointFp(curve,x,y,z) { this.curve = curve; this.x = x; this.y = y; // Projective coordinates: either zinv == null or z * zinv == 1 // z and zinv are just BigIntegers, not fieldElements if(z == null) { this.z = BigInteger.ONE; } else { this.z = z; } this.zinv = null; //TODO: compression flag } function pointFpGetX() { if(this.zinv == null) { this.zinv = this.z.modInverse(this.curve.q); } return this.curve.fromBigInteger(this.x.toBigInteger().multiply(this.zinv).mod(this.curve.q)); } function pointFpGetY() { if(this.zinv == null) { this.zinv = this.z.modInverse(this.curve.q); } return this.curve.fromBigInteger(this.y.toBigInteger().multiply(this.zinv).mod(this.curve.q)); } function pointFpEquals(other) { if(other == this) return true; if(this.isInfinity()) return other.isInfinity(); if(other.isInfinity()) return this.isInfinity(); var u, v; // u = Y2 * Z1 - Y1 * Z2 u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q); if(!u.equals(BigInteger.ZERO)) return false; // v = X2 * Z1 - X1 * Z2 v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q); return v.equals(BigInteger.ZERO); } function pointFpIsInfinity() { if((this.x == null) && (this.y == null)) return true; return this.z.equals(BigInteger.ZERO) && !this.y.toBigInteger().equals(BigInteger.ZERO); } function pointFpNegate() { return new ECPointFp(this.curve, this.x, this.y.negate(), this.z); } function pointFpAdd(b) { if(this.isInfinity()) return b; if(b.isInfinity()) return this; // u = Y2 * Z1 - Y1 * Z2 var u = b.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(b.z)).mod(this.curve.q); // v = X2 * Z1 - X1 * Z2 var v = b.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(b.z)).mod(this.curve.q); if(BigInteger.ZERO.equals(v)) { if(BigInteger.ZERO.equals(u)) { return this.twice(); // this == b, so double } return this.curve.getInfinity(); // this = -b, so infinity } var THREE = new BigInteger("3"); var x1 = this.x.toBigInteger(); var y1 = this.y.toBigInteger(); var x2 = b.x.toBigInteger(); var y2 = b.y.toBigInteger(); var v2 = v.square(); var v3 = v2.multiply(v); var x1v2 = x1.multiply(v2); var zu2 = u.square().multiply(this.z); // x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3) var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.curve.q); // y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3 var y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.curve.q); // z3 = v^3 * z1 * z2 var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q); return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3); } function pointFpTwice() { if(this.isInfinity()) return this; if(this.y.toBigInteger().signum() == 0) return this.curve.getInfinity(); // TODO: optimized handling of constants var THREE = new BigInteger("3"); var x1 = this.x.toBigInteger(); var y1 = this.y.toBigInteger(); var y1z1 = y1.multiply(this.z); var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q); var a = this.curve.a.toBigInteger(); // w = 3 * x1^2 + a * z1^2 var w = x1.square().multiply(THREE); if(!BigInteger.ZERO.equals(a)) { w = w.add(this.z.square().multiply(a)); } w = w.mod(this.curve.q); // x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1) var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.q); // y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3 var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.square().multiply(w)).mod(this.curve.q); // z3 = 8 * (y1 * z1)^3 var z3 = y1z1.square().multiply(y1z1).shiftLeft(3).mod(this.curve.q); return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3); } // Simple NAF (Non-Adjacent Form) multiplication algorithm // TODO: modularize the multiplication algorithm function pointFpMultiply(k) { if(this.isInfinity()) return this; if(k.signum() == 0) return this.curve.getInfinity(); var e = k; var h = e.multiply(new BigInteger("3")); var neg = this.negate(); var R = this; var i; for(i = h.bitLength() - 2; i > 0; --i) { R = R.twice(); var hBit = h.testBit(i); var eBit = e.testBit(i); if (hBit != eBit) { R = R.add(hBit ? this : neg); } } return R; } // Compute this*j + x*k (simultaneous multiplication) function pointFpMultiplyTwo(j,x,k) { var i; if(j.bitLength() > k.bitLength()) i = j.bitLength() - 1; else i = k.bitLength() - 1; var R = this.curve.getInfinity(); var both = this.add(x); while(i >= 0) { R = R.twice(); if(j.testBit(i)) { if(k.testBit(i)) { R = R.add(both); } else { R = R.add(this); } } else { if(k.testBit(i)) { R = R.add(x); } } --i; } return R; } ECPointFp.prototype.getX = pointFpGetX; ECPointFp.prototype.getY = pointFpGetY; ECPointFp.prototype.equals = pointFpEquals; ECPointFp.prototype.isInfinity = pointFpIsInfinity; ECPointFp.prototype.negate = pointFpNegate; ECPointFp.prototype.add = pointFpAdd; ECPointFp.prototype.twice = pointFpTwice; ECPointFp.prototype.multiply = pointFpMultiply; ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo; // ---------------- // ECCurveFp // constructor function ECCurveFp(q,a,b) { this.q = q; this.a = this.fromBigInteger(a); this.b = this.fromBigInteger(b); this.infinity = new ECPointFp(this, null, null); } function curveFpGetQ() { return this.q; } function curveFpGetA() { return this.a; } function curveFpGetB() { return this.b; } function curveFpEquals(other) { if(other == this) return true; return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b)); } function curveFpGetInfinity() { return this.infinity; } function curveFpFromBigInteger(x) { return new ECFieldElementFp(this.q, x); } // for now, work with hex strings because they're easier in JS function curveFpDecodePointHex(s) { switch(parseInt(s.substr(0,2), 16)) { // first byte case 0: return this.infinity; case 2: case 3: // point compression not supported yet return null; case 4: case 6: case 7: var len = (s.length - 2) / 2; var xHex = s.substr(2, len); var yHex = s.substr(len+2, len); return new ECPointFp(this, this.fromBigInteger(new BigInteger(xHex, 16)), this.fromBigInteger(new BigInteger(yHex, 16))); default: // unsupported return null; } } ECCurveFp.prototype.getQ = curveFpGetQ; ECCurveFp.prototype.getA = curveFpGetA; ECCurveFp.prototype.getB = curveFpGetB; ECCurveFp.prototype.equals = curveFpEquals; ECCurveFp.prototype.getInfinity = curveFpGetInfinity; ECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger; ECCurveFp.prototype.decodePointHex = curveFpDecodePointHex; // Named EC curves // Requires ec.js, jsbn.js, and jsbn2.js // ---------------- // X9ECParameters // constructor function X9ECParameters(curve,g,n,h) { this.curve = curve; this.g = g; this.n = n; this.h = h; } function x9getCurve() { return this.curve; } function x9getG() { return this.g; } function x9getN() { return this.n; } function x9getH() { return this.h; } X9ECParameters.prototype.getCurve = x9getCurve; X9ECParameters.prototype.getG = x9getG; X9ECParameters.prototype.getN = x9getN; X9ECParameters.prototype.getH = x9getH; // ---------------- // SECNamedCurves function fromHex(s) { return new BigInteger(s, 16); } function secp128r1() { // p = 2^128 - 2^97 - 1 var p = fromHex("FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF"); var a = fromHex("FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC"); var b = fromHex("E87579C11079F43DD824993C2CEE5ED3"); //byte[] S = Hex.decode("000E0D4D696E6768756151750CC03A4473D03679"); var n = fromHex("FFFFFFFE0000000075A30D1B9038A115"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "161FF7528B899B2D0C28607CA52C5B86" + "CF5AC8395BAFEB13C02DA292DDED7A83"); return new X9ECParameters(curve, G, n, h); } function secp160k1() { // p = 2^160 - 2^32 - 2^14 - 2^12 - 2^9 - 2^8 - 2^7 - 2^3 - 2^2 - 1 var p = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73"); var a = BigInteger.ZERO; var b = fromHex("7"); //byte[] S = null; var n = fromHex("0100000000000000000001B8FA16DFAB9ACA16B6B3"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "3B4C382CE37AA192A4019E763036F4F5DD4D7EBB" + "938CF935318FDCED6BC28286531733C3F03C4FEE"); return new X9ECParameters(curve, G, n, h); } function secp160r1() { // p = 2^160 - 2^31 - 1 var p = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"); var a = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"); var b = fromHex("1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45"); //byte[] S = Hex.decode("1053CDE42C14D696E67687561517533BF3F83345"); var n = fromHex("0100000000000000000001F4C8F927AED3CA752257"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "4A96B5688EF573284664698968C38BB913CBFC82" + "23A628553168947D59DCC912042351377AC5FB32"); return new X9ECParameters(curve, G, n, h); } function secp192k1() { // p = 2^192 - 2^32 - 2^12 - 2^8 - 2^7 - 2^6 - 2^3 - 1 var p = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37"); var a = BigInteger.ZERO; var b = fromHex("3"); //byte[] S = null; var n = fromHex("FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D" + "9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D"); return new X9ECParameters(curve, G, n, h); } function secp192r1() { // p = 2^192 - 2^64 - 1 var p = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"); var a = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"); var b = fromHex("64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"); //byte[] S = Hex.decode("3045AE6FC8422F64ED579528D38120EAE12196D5"); var n = fromHex("FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012" + "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"); return new X9ECParameters(curve, G, n, h); } function secp224r1() { // p = 2^224 - 2^96 + 1 var p = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"); var a = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"); var b = fromHex("B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"); //byte[] S = Hex.decode("BD71344799D5C7FCDC45B59FA3B9AB8F6A948BC5"); var n = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21" + "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"); return new X9ECParameters(curve, G, n, h); } function secp256k1() { // p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1 var p = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F"); var a = BigInteger.ZERO; var b = fromHex("7"); //byte[] S = null; var n = fromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798" + "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"); return new X9ECParameters(curve, G, n, h); } function secp256r1() { // p = 2^224 (2^32 - 1) + 2^192 + 2^96 - 1 var p = fromHex("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"); var a = fromHex("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"); var b = fromHex("5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"); //byte[] S = Hex.decode("C49D360886E704936A6678E1139D26B7819F7E90"); var n = fromHex("FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"); var h = BigInteger.ONE; var curve = new ECCurveFp(p, a, b); var G = curve.decodePointHex("04" + "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296" + "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"); return new X9ECParameters(curve, G, n, h); } // TODO: make this into a proper hashtable function getSECCurveByName(name) { if(name == "secp128r1") return secp128r1(); if(name == "secp160k1") return secp160k1(); if(name == "secp160r1") return secp160r1(); if(name == "secp192k1") return secp192k1(); if(name == "secp192r1") return secp192r1(); if(name == "secp224r1") return secp224r1(); if(name == "secp256k1") return secp256k1(); if(name == "secp256r1") return secp256r1(); return null; } function integerToBytes(i, len) { var bytes = i.toByteArrayUnsigned(); if (len < bytes.length) { bytes = bytes.slice(bytes.length-len); } else while (len > bytes.length) { bytes.unshift(0); } return bytes; }; ECFieldElementFp.prototype.getByteLength = function () { return Math.floor((this.toBigInteger().bitLength() + 7) / 8); }; ECPointFp.prototype.getEncoded = function (compressed) { var x = this.getX().toBigInteger(); var y = this.getY().toBigInteger(); // Get value as a 32-byte Buffer // Fixed length based on a patch by bitaddress.org and Casascius var enc = integerToBytes(x, 32); if (compressed) { if (y.isEven()) { // Compressed even pubkey // M = 02 || X enc.unshift(0x02); } else { // Compressed uneven pubkey // M = 03 || X enc.unshift(0x03); } } else { // Uncompressed pubkey // M = 04 || X || Y enc.unshift(0x04); enc = enc.concat(integerToBytes(y, 32)); } return enc; }; ECPointFp.decodeFrom = function (curve, enc) { var type = enc[0]; var dataLen = enc.length-1; // Extract x and y as byte arrays var xBa = enc.slice(1, 1 + dataLen/2); var yBa = enc.slice(1 + dataLen/2, 1 + dataLen); // Prepend zero byte to prevent interpretation as negative integer xBa.unshift(0); yBa.unshift(0); // Convert to BigIntegers var x = new BigInteger(xBa); var y = new BigInteger(yBa); // Return point return new ECPointFp(curve, curve.fromBigInteger(x), curve.fromBigInteger(y)); }; ECPointFp.prototype.add2D = function (b) { if(this.isInfinity()) return b; if(b.isInfinity()) return this; if (this.x.equals(b.x)) { if (this.y.equals(b.y)) { // this = b, i.e. this must be doubled return this.twice(); } // this = -b, i.e. the result is the point at infinity return this.curve.getInfinity(); } var x_x = b.x.subtract(this.x); var y_y = b.y.subtract(this.y); var gamma = y_y.divide(x_x); var x3 = gamma.square().subtract(this.x).subtract(b.x); var y3 = gamma.multiply(this.x.subtract(x3)).subtract(this.y); return new ECPointFp(this.curve, x3, y3); }; ECPointFp.prototype.twice2D = function () { if (this.isInfinity()) return this; if (this.y.toBigInteger().signum() == 0) { // if y1 == 0, then (x1, y1) == (x1, -y1) // and hence this = -this and thus 2(x1, y1) == infinity return this.curve.getInfinity(); } var TWO = this.curve.fromBigInteger(BigInteger.valueOf(2)); var THREE = this.curve.fromBigInteger(BigInteger.valueOf(3)); var gamma = this.x.square().multiply(THREE).add(this.curve.a).divide(this.y.multiply(TWO)); var x3 = gamma.square().subtract(this.x.multiply(TWO)); var y3 = gamma.multiply(this.x.subtract(x3)).subtract(this.y); return new ECPointFp(this.curve, x3, y3); }; ECPointFp.prototype.multiply2D = function (k) { if(this.isInfinity()) return this; if(k.signum() == 0) return this.curve.getInfinity(); var e = k; var h = e.multiply(new BigInteger("3")); var neg = this.negate(); var R = this; var i; for (i = h.bitLength() - 2; i > 0; --i) { R = R.twice(); var hBit = h.testBit(i); var eBit = e.testBit(i); if (hBit != eBit) { R = R.add2D(hBit ? this : neg); } } return R; }; ECPointFp.prototype.isOnCurve = function () { var x = this.getX().toBigInteger(); var y = this.getY().toBigInteger(); var a = this.curve.getA().toBigInteger(); var b = this.curve.getB().toBigInteger(); var n = this.curve.getQ(); var lhs = y.multiply(y).mod(n); var rhs = x.multiply(x).multiply(x) .add(a.multiply(x)).add(b).mod(n); return lhs.equals(rhs); }; ECPointFp.prototype.toString = function () { return '('+this.getX().toBigInteger().toString()+','+ this.getY().toBigInteger().toString()+')'; }; /** * Validate an elliptic curve point. * * See SEC 1, section 3.2.2.1: Elliptic Curve Public Key Validation Primitive */ ECPointFp.prototype.validate = function () { var n = this.curve.getQ(); // Check Q != O if (this.isInfinity()) { throw new Error("Point is at infinity."); } // Check coordinate bounds var x = this.getX().toBigInteger(); var y = this.getY().toBigInteger(); if (x.compareTo(BigInteger.ONE) < 0 || x.compareTo(n.subtract(BigInteger.ONE)) > 0) { throw new Error('x coordinate out of bounds'); } if (y.compareTo(BigInteger.ONE) < 0 || y.compareTo(n.subtract(BigInteger.ONE)) > 0) { throw new Error('y coordinate out of bounds'); } // Check y^2 = x^3 + ax + b (mod n) if (!this.isOnCurve()) { throw new Error("Point is not on the curve."); } // Check nQ = 0 (Q is a scalar multiple of G) if (this.multiply(n).isInfinity()) { // TODO: This check doesn't work - fix. throw new Error("Point is not a scalar multiple of G."); } return true; }; function dmp(v) { if (!(v instanceof BigInteger)) v = v.toBigInteger(); return Crypto.util.bytesToHex(v.toByteArrayUnsigned()); }; Bitcoin.ECDSA = (function () { var ecparams = getSECCurveByName("secp256k1"); var rng = new SecureRandom(); var P_OVER_FOUR = null; function implShamirsTrick(P, k, Q, l) { var m = Math.max(k.bitLength(), l.bitLength()); var Z = P.add2D(Q); var R = P.curve.getInfinity(); for (var i = m - 1; i >= 0; --i) { R = R.twice2D(); R.z = BigInteger.ONE; if (k.testBit(i)) { if (l.testBit(i)) { R = R.add2D(Z); } else { R = R.add2D(P); } } else { if (l.testBit(i)) { R = R.add2D(Q); } } } return R; }; var ECDSA = { getBigRandom: function (limit) { return new BigInteger(limit.bitLength(), rng) .mod(limit.subtract(BigInteger.ONE)) .add(BigInteger.ONE) ; }, sign: function (hash, priv) { var d = priv; var n = ecparams.getN(); var e = BigInteger.fromByteArrayUnsigned(hash); do { var k = ECDSA.getBigRandom(n); var G = ecparams.getG(); var Q = G.multiply(k); var r = Q.getX().toBigInteger().mod(n); } while (r.compareTo(BigInteger.ZERO) <= 0); var s = k.modInverse(n).multiply(e.add(d.multiply(r))).mod(n); return ECDSA.serializeSig(r, s); }, verify: function (hash, sig, pubkey) { var r,s; if (Bitcoin.Util.isArray(sig)) { var obj = ECDSA.parseSig(sig); r = obj.r; s = obj.s; } else if ("object" === typeof sig && sig.r && sig.s) { r = sig.r; s = sig.s; } else { throw "Invalid value for signature"; } var Q; if (pubkey instanceof ECPointFp) { Q = pubkey; } else if (Bitcoin.Util.isArray(pubkey)) { Q = ECPointFp.decodeFrom(ecparams.getCurve(), pubkey); } else { throw "Invalid format for pubkey value, must be byte array or ECPointFp"; } var e = BigInteger.fromByteArrayUnsigned(hash); return ECDSA.verifyRaw(e, r, s, Q); }, verifyRaw: function (e, r, s, Q) { var n = ecparams.getN(); var G = ecparams.getG(); if (r.compareTo(BigInteger.ONE) < 0 || r.compareTo(n) >= 0) return false; if (s.compareTo(BigInteger.ONE) < 0 || s.compareTo(n) >= 0) return false; var c = s.modInverse(n); var u1 = e.multiply(c).mod(n); var u2 = r.multiply(c).mod(n); // TODO(!!!): For some reason Shamir's trick isn't working with // signed message verification!? Probably an implementation // error! //var point = implShamirsTrick(G, u1, Q, u2); var point = G.multiply(u1).add(Q.multiply(u2)); var v = point.getX().toBigInteger().mod(n); return v.equals(r); }, /** * Serialize a signature into DER format. * * Takes two BigIntegers representing r and s and returns a byte array. */ serializeSig: function (r, s) { var rBa = r.toByteArraySigned(); var sBa = s.toByteArraySigned(); var sequence = []; sequence.push(0x02); // INTEGER sequence.push(rBa.length); sequence = sequence.concat(rBa); sequence.push(0x02); // INTEGER sequence.push(sBa.length); sequence = sequence.concat(sBa); sequence.unshift(sequence.length); sequence.unshift(0x30); // SEQUENCE return sequence; }, /** * Parses a byte array containing a DER-encoded signature. * * This function will return an object of the form: * * { * r: BigInteger, * s: BigInteger * } */ parseSig: function (sig) { var cursor; if (sig[0] != 0x30) throw new Error("Signature not a valid DERSequence"); cursor = 2; if (sig[cursor] != 0x02) throw new Error("First element in signature must be a DERInteger");; var rBa = sig.slice(cursor+2, cursor+2+sig[cursor+1]); cursor += 2+sig[cursor+1]; if (sig[cursor] != 0x02) throw new Error("Second element in signature must be a DERInteger"); var sBa = sig.slice(cursor+2, cursor+2+sig[cursor+1]); cursor += 2+sig[cursor+1]; //if (cursor != sig.length) // throw new Error("Extra bytes in signature"); var r = BigInteger.fromByteArrayUnsigned(rBa); var s = BigInteger.fromByteArrayUnsigned(sBa); return {r: r, s: s}; }, parseSigCompact: function (sig) { if (sig.length !== 65) { throw "Signature has the wrong length"; } // Signature is prefixed with a type byte storing three bits of // information. var i = sig[0] - 27; if (i < 0 || i > 7) { throw "Invalid signature type"; } var n = ecparams.getN(); var r = BigInteger.fromByteArrayUnsigned(sig.slice(1, 33)).mod(n); var s = BigInteger.fromByteArrayUnsigned(sig.slice(33, 65)).mod(n); return {r: r, s: s, i: i}; }, /** * Recover a public key from a signature. * * See SEC 1: Elliptic Curve Cryptography, section 4.1.6, "Public * Key Recovery Operation". * * http://www.secg.org/download/aid-780/sec1-v2.pdf */ recoverPubKey: function (r, s, hash, i) { // The recovery parameter i has two bits. i = i & 3; // The less significant bit specifies whether the y coordinate // of the compressed point is even or not. var isYEven = i & 1; // The more significant bit specifies whether we should use the // first or second candidate key. var isSecondKey = i >> 1; var n = ecparams.getN(); var G = ecparams.getG(); var curve = ecparams.getCurve(); var p = curve.getQ(); var a = curve.getA().toBigInteger(); var b = curve.getB().toBigInteger(); // We precalculate (p + 1) / 4 where p is if the field order if (!P_OVER_FOUR) { P_OVER_FOUR = p.add(BigInteger.ONE).divide(BigInteger.valueOf(4)); } // 1.1 Compute x var x = isSecondKey ? r.add(n) : r; // 1.3 Convert x to point var alpha = x.multiply(x).multiply(x).add(a.multiply(x)).add(b).mod(p); var beta = alpha.modPow(P_OVER_FOUR, p); var xorOdd = beta.isEven() ? (i % 2) : ((i+1) % 2); // If beta is even, but y isn't or vice versa, then convert it, // otherwise we're done and y == beta. var y = (beta.isEven() ? !isYEven : isYEven) ? beta : p.subtract(beta); // 1.4 Check that nR is at infinity var R = new ECPointFp(curve, curve.fromBigInteger(x), curve.fromBigInteger(y)); R.validate(); // 1.5 Compute e from M var e = BigInteger.fromByteArrayUnsigned(hash); var eNeg = BigInteger.ZERO.subtract(e).mod(n); // 1.6 Compute Q = r^-1 (sR - eG) var rInv = r.modInverse(n); var Q = implShamirsTrick(R, s, G, eNeg).multiply(rInv); Q.validate(); if (!ECDSA.verifyRaw(e, r, s, Q)) { throw "Pubkey recovery unsuccessful"; } var pubKey = new Bitcoin.ECKey(); pubKey.pub = Q; return pubKey; }, /** * Calculate pubkey extraction parameter. * * When extracting a pubkey from a signature, we have to * distinguish four different cases. Rather than putting this * burden on the verifier, Bitcoin includes a 2-bit value with the * signature. * * This function simply tries all four cases and returns the value * that resulted in a successful pubkey recovery. */ calcPubkeyRecoveryParam: function (address, r, s, hash) { for (var i = 0; i < 4; i++) { try { var pubkey = Bitcoin.ECDSA.recoverPubKey(r, s, hash, i); if (pubkey.getBitcoinAddress().toString() == address) { return i; } } catch (e) {} } throw "Unable to find valid recovery factor"; } }; return ECDSA; })(); Bitcoin.ECKey = (function () { var ECDSA = Bitcoin.ECDSA; var ecparams = getSECCurveByName("secp256k1"); var rng = new SecureRandom(); var ECKey = function (input) { if (!input) { // Generate new key var n = ecparams.getN(); this.priv = ECDSA.getBigRandom(n); } else if (input instanceof BigInteger) { // Input is a private key value this.priv = input; } else if (Bitcoin.Util.isArray(input)) { // Prepend zero byte to prevent interpretation as negative integer this.priv = BigInteger.fromByteArrayUnsigned(input); } else if ("string" == typeof input) { if (input.length == 51 && input[0] == '5') { // Base58 encoded private key this.priv = BigInteger.fromByteArrayUnsigned(ECKey.decodeString(input)); } else { // Prepend zero byte to prevent interpretation as negative integer this.priv = BigInteger.fromByteArrayUnsigned(Crypto.util.base64ToBytes(input)); } } this.compressed = !!ECKey.compressByDefault; }; /** * Whether public keys should be returned compressed by default. */ ECKey.compressByDefault = false; /** * Set whether the public key should be returned compressed or not. */ ECKey.prototype.setCompressed = function (v) { this.compressed = !!v; }; /** * Return public key in DER encoding. */ ECKey.prototype.getPub = function () { return this.getPubPoint().getEncoded(this.compressed); }; /** * Return public point as ECPoint object. */ ECKey.prototype.getPubPoint = function () { if (!this.pub) this.pub = ecparams.getG().multiply(this.priv); return this.pub; }; /** * Get the pubKeyHash for this key. * * This is calculated as RIPE160(SHA256([encoded pubkey])) and returned as * a byte array. */ ECKey.prototype.getPubKeyHash = function () { if (this.pubKeyHash) return this.pubKeyHash; return this.pubKeyHash = Bitcoin.Util.sha256ripe160(this.getPub()); }; ECKey.prototype.getBitcoinAddress = function () { var hash = this.getPubKeyHash(); var addr = new Bitcoin.Address(hash); return addr; }; ECKey.prototype.getExportedPrivateKey = function () { var hash = this.priv.toByteArrayUnsigned(); while (hash.length < 32) hash.unshift(0); hash.unshift(0x80); var checksum = Crypto.SHA256(Crypto.SHA256(hash, {asBytes: true}), {asBytes: true}); var bytes = hash.concat(checksum.slice(0,4)); return Bitcoin.Base58.encode(bytes); }; ECKey.prototype.setPub = function (pub) { this.pub = ECPointFp.decodeFrom(ecparams.getCurve(), pub); }; ECKey.prototype.toString = function (format) { if (format === "base64") { return Crypto.util.bytesToBase64(this.priv.toByteArrayUnsigned()); } else { return Crypto.util.bytesToHex(this.priv.toByteArrayUnsigned()); } }; ECKey.prototype.sign = function (hash) { return ECDSA.sign(hash, this.priv); }; ECKey.prototype.verify = function (hash, sig) { return ECDSA.verify(hash, sig, this.getPub()); }; /** * Parse an exported private key contained in a string. */ ECKey.decodeString = function (string) { var bytes = Bitcoin.Base58.decode(string); var hash = bytes.slice(0, 33); var checksum = Crypto.SHA256(Crypto.SHA256(hash, {asBytes: true}), {asBytes: true}); if (checksum[0] != bytes[33] || checksum[1] != bytes[34] || checksum[2] != bytes[35] || checksum[3] != bytes[36]) { throw "Checksum validation failed!"; } var version = hash.shift(); if (version != 0x80) { throw "Version "+version+" not supported!"; } return hash; }; return ECKey; })(); module.exports.ECKey = Bitcoin.ECKey;