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bitcore/browser/bitcoinjs-lib.js

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browser ECDSA compressed key generated
2014-02-20 13:59:41 -08:00
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<<dbits)-1);
BigInteger.prototype.DV = (1<<dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2,BI_FP);
BigInteger.prototype.F1 = BI_FP-dbits;
BigInteger.prototype.F2 = 2*dbits-BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = new Array();
var rr,vv;
rr = "0".charCodeAt(0);
for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) { return BI_RM.charAt(n); }
function intAt(s,i) {
var c = BI_RC[s.charCodeAt(i)];
return (c==null)?-1:c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x<0)?-1:0;
if(x > 0) this[0] = x;
else if(x < -1) this[0] = x+DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
// (protected) set from string and radix
function bnpFromString(s,b) {
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 256) k = 8; // byte array
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else { this.fromRadix(s,b); return; }
this.t = 0;
this.s = 0;
var i = s.length, mi = false, sh = 0;
while(--i >= 0) {
var x = (k==8)?s[i]&0xff:intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if(sh == 0)
this[this.t++] = x;
else if(sh+k > this.DB) {
this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
this[this.t++] = (x>>(this.DB-sh));
}
else
this[this.t-1] |= x<<sh;
sh += k;
if(sh >= this.DB) sh -= this.DB;
}
if(k == 8 && (s[0]&0x80) != 0) {
this.s = -1;
if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
}
this.clamp();
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s&this.DM;
while(this.t > 0 && this[this.t-1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if(this.s < 0) return "-"+this.negate().toString(b);
var k;
if(b == 16) k = 4;
else if(b == 8) k = 3;
else if(b == 2) k = 1;
else if(b == 32) k = 5;
else if(b == 4) k = 2;
else return this.toRadix(b);
var km = (1<<k)-1, d, m = false, r = "", i = this.t;
var p = this.DB-(i*this.DB)%k;
if(i-- > 0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<<p)-1))<<(k-p);
d |= this[--i]>>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r += int2char(d);
}
}
return m?r:"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
r = i-a.t;
if(r != 0) return (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;
// 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
// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
// in your main HTML document.
var rng_state;
var rng_pool;
var rng_pptr;
// Mix in a 32-bit integer into the pool
function rng_seed_int(x) {
rng_pool[rng_pptr++] ^= x & 255;
rng_pool[rng_pptr++] ^= (x >> 8) & 255;
rng_pool[rng_pptr++] ^= (x >> 16) & 255;
rng_pool[rng_pptr++] ^= (x >> 24) & 255;
if(rng_pptr >= rng_psize) rng_pptr -= rng_psize;
}
// Mix in the current time (w/milliseconds) into the pool
function rng_seed_time() {
rng_seed_int(new Date().getTime());
}
// Initialize the pool with junk if needed.
if(rng_pool == null) {
rng_pool = new Array();
rng_pptr = 0;
var t;
if(navigator.appName == "Netscape" && navigator.appVersion < "5" && window.crypto) {
// Extract entropy (256 bits) from NS4 RNG if available
var z = window.crypto.random(32);
for(t = 0; t < z.length; ++t)
rng_pool[rng_pptr++] = z.charCodeAt(t) & 255;
}
while(rng_pptr < rng_psize) { // extract some randomness from Math.random()
t = Math.floor(65536 * Math.random());
rng_pool[rng_pptr++] = t >>> 8;
rng_pool[rng_pptr++] = t & 255;
}
rng_pptr = 0;
rng_seed_time();
//rng_seed_int(window.screenX);
//rng_seed_int(window.screenY);
}
function rng_get_byte() {
if(rng_state == null) {
rng_seed_time();
rng_state = prng_newstate();
rng_state.init(rng_pool);
for(rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr)
rng_pool[rng_pptr] = 0;
rng_pptr = 0;
//rng_pool = null;
}
// TODO: allow reseeding after first request
return rng_state.next();
}
function rng_get_bytes(ba) {
var i;
for(i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
}
function SecureRandom() {}
SecureRandom.prototype.nextBytes = rng_get_bytes;
// 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;