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							|  | @ -0,0 +1,40 @@ | |||
| Licensing | ||||
| --------- | ||||
| 
 | ||||
| This software is covered under the following copyright: | ||||
| 
 | ||||
| /* | ||||
|  * Copyright (c) 2003-2005  Tom Wu | ||||
|  * All Rights Reserved. | ||||
|  * | ||||
|  * Permission is hereby granted, free of charge, to any person obtaining | ||||
|  * a copy of this software and associated documentation files (the | ||||
|  * "Software"), to deal in the Software without restriction, including | ||||
|  * without limitation the rights to use, copy, modify, merge, publish, | ||||
|  * distribute, sublicense, and/or sell copies of the Software, and to | ||||
|  * permit persons to whom the Software is furnished to do so, subject to | ||||
|  * the following conditions: | ||||
|  * | ||||
|  * The above copyright notice and this permission notice shall be | ||||
|  * included in all copies or substantial portions of the Software. | ||||
|  * | ||||
|  * THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,  | ||||
|  * EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY  | ||||
|  * WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.   | ||||
|  * | ||||
|  * IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL, | ||||
|  * INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER | ||||
|  * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF | ||||
|  * THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT | ||||
|  * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. | ||||
|  * | ||||
|  * In addition, the following condition applies: | ||||
|  * | ||||
|  * All redistributions must retain an intact copy of this copyright notice | ||||
|  * and disclaimer. | ||||
|  */ | ||||
| 
 | ||||
| Address all questions regarding this license to: | ||||
| 
 | ||||
|   Tom Wu | ||||
|   tjw@cs.Stanford.EDU | ||||
							
								
								
									
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								node_modules/ecc-jsbn/lib/ec.js
									
										
									
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							|  | @ -0,0 +1,561 @@ | |||
| // 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
 | ||||
| var BigInteger = require('jsbn').BigInteger | ||||
| var Barrett = BigInteger.prototype.Barrett | ||||
| 
 | ||||
| // ----------------
 | ||||
| // 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); | ||||
|     } | ||||
|     var r = this.x.toBigInteger().multiply(this.zinv); | ||||
|     this.curve.reduce(r); | ||||
|     return this.curve.fromBigInteger(r); | ||||
| } | ||||
| 
 | ||||
| function pointFpGetY() { | ||||
|     if(this.zinv == null) { | ||||
|       this.zinv = this.z.modInverse(this.curve.q); | ||||
|     } | ||||
|     var r = this.y.toBigInteger().multiply(this.zinv); | ||||
|     this.curve.reduce(r); | ||||
|     return this.curve.fromBigInteger(r); | ||||
| } | ||||
| 
 | ||||
| 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); | ||||
|     //this.curve.reduce(w);
 | ||||
|     // 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); | ||||
|     this.reducer = new Barrett(this.q); | ||||
| } | ||||
| 
 | ||||
| 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); | ||||
| } | ||||
| 
 | ||||
| function curveReduce(x) { | ||||
|     this.reducer.reduce(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; | ||||
|     } | ||||
| } | ||||
| 
 | ||||
| function curveFpEncodePointHex(p) { | ||||
| 	if (p.isInfinity()) return "00"; | ||||
| 	var xHex = p.getX().toBigInteger().toString(16); | ||||
| 	var yHex = p.getY().toBigInteger().toString(16); | ||||
| 	var oLen = this.getQ().toString(16).length; | ||||
| 	if ((oLen % 2) != 0) oLen++; | ||||
| 	while (xHex.length < oLen) { | ||||
| 		xHex = "0" + xHex; | ||||
| 	} | ||||
| 	while (yHex.length < oLen) { | ||||
| 		yHex = "0" + yHex; | ||||
| 	} | ||||
| 	return "04" + xHex + yHex; | ||||
| } | ||||
| 
 | ||||
| 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.reduce = curveReduce; | ||||
| //ECCurveFp.prototype.decodePointHex = curveFpDecodePointHex;
 | ||||
| ECCurveFp.prototype.encodePointHex = curveFpEncodePointHex; | ||||
| 
 | ||||
| // from: https://github.com/kaielvin/jsbn-ec-point-compression
 | ||||
| ECCurveFp.prototype.decodePointHex = function(s) | ||||
| { | ||||
| 	var yIsEven; | ||||
|     switch(parseInt(s.substr(0,2), 16)) { // first byte
 | ||||
|     case 0: | ||||
| 	return this.infinity; | ||||
|     case 2: | ||||
| 	yIsEven = false; | ||||
|     case 3: | ||||
| 	if(yIsEven == undefined) yIsEven = true; | ||||
| 	var len = s.length - 2; | ||||
| 	var xHex = s.substr(2, len); | ||||
| 	var x = this.fromBigInteger(new BigInteger(xHex,16)); | ||||
| 	var alpha = x.multiply(x.square().add(this.getA())).add(this.getB()); | ||||
| 	var beta = alpha.sqrt(); | ||||
| 
 | ||||
|     if (beta == null) throw "Invalid point compression"; | ||||
| 
 | ||||
|     var betaValue = beta.toBigInteger(); | ||||
|     if (betaValue.testBit(0) != yIsEven) | ||||
|     { | ||||
|         // Use the other root
 | ||||
|         beta = this.fromBigInteger(this.getQ().subtract(betaValue)); | ||||
|     } | ||||
|     return new ECPointFp(this,x,beta); | ||||
|     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.encodeCompressedPointHex = function(p) | ||||
| { | ||||
| 	if (p.isInfinity()) return "00"; | ||||
| 	var xHex = p.getX().toBigInteger().toString(16); | ||||
| 	var oLen = this.getQ().toString(16).length; | ||||
| 	if ((oLen % 2) != 0) oLen++; | ||||
| 	while (xHex.length < oLen) | ||||
| 		xHex = "0" + xHex; | ||||
| 	var yPrefix; | ||||
| 	if(p.getY().toBigInteger().isEven()) yPrefix = "02"; | ||||
| 	else                                 yPrefix = "03"; | ||||
| 
 | ||||
| 	return yPrefix + xHex; | ||||
| } | ||||
| 
 | ||||
| 
 | ||||
| ECFieldElementFp.prototype.getR = function() | ||||
| { | ||||
| 	if(this.r != undefined) return this.r; | ||||
| 
 | ||||
|     this.r = null; | ||||
|     var bitLength = this.q.bitLength(); | ||||
|     if (bitLength > 128) | ||||
|     { | ||||
|         var firstWord = this.q.shiftRight(bitLength - 64); | ||||
|         if (firstWord.intValue() == -1) | ||||
|         { | ||||
|             this.r = BigInteger.ONE.shiftLeft(bitLength).subtract(this.q); | ||||
|         } | ||||
|     } | ||||
|     return this.r; | ||||
| } | ||||
| ECFieldElementFp.prototype.modMult = function(x1,x2) | ||||
| { | ||||
|     return this.modReduce(x1.multiply(x2)); | ||||
| } | ||||
| ECFieldElementFp.prototype.modReduce = function(x) | ||||
| { | ||||
|     if (this.getR() != null) | ||||
|     { | ||||
|         var qLen = q.bitLength(); | ||||
|         while (x.bitLength() > (qLen + 1)) | ||||
|         { | ||||
|             var u = x.shiftRight(qLen); | ||||
|             var v = x.subtract(u.shiftLeft(qLen)); | ||||
|             if (!this.getR().equals(BigInteger.ONE)) | ||||
|             { | ||||
|                 u = u.multiply(this.getR()); | ||||
|             } | ||||
|             x = u.add(v);  | ||||
|         } | ||||
|         while (x.compareTo(q) >= 0) | ||||
|         { | ||||
|             x = x.subtract(q); | ||||
|         } | ||||
|     } | ||||
|     else | ||||
|     { | ||||
|         x = x.mod(q); | ||||
|     } | ||||
|     return x; | ||||
| } | ||||
| ECFieldElementFp.prototype.sqrt = function() | ||||
| { | ||||
|     if (!this.q.testBit(0)) throw "unsupported"; | ||||
| 
 | ||||
|     // p mod 4 == 3
 | ||||
|     if (this.q.testBit(1)) | ||||
|     { | ||||
|     	var z = new ECFieldElementFp(this.q,this.x.modPow(this.q.shiftRight(2).add(BigInteger.ONE),this.q)); | ||||
|     	return z.square().equals(this) ? z : null; | ||||
|     } | ||||
| 
 | ||||
|     // p mod 4 == 1
 | ||||
|     var qMinusOne = this.q.subtract(BigInteger.ONE); | ||||
| 
 | ||||
|     var legendreExponent = qMinusOne.shiftRight(1); | ||||
|     if (!(this.x.modPow(legendreExponent, this.q).equals(BigInteger.ONE))) | ||||
|     { | ||||
|         return null; | ||||
|     } | ||||
| 
 | ||||
|     var u = qMinusOne.shiftRight(2); | ||||
|     var k = u.shiftLeft(1).add(BigInteger.ONE); | ||||
| 
 | ||||
|     var Q = this.x; | ||||
|     var fourQ = modDouble(modDouble(Q)); | ||||
| 
 | ||||
|     var U, V; | ||||
|     do | ||||
|     { | ||||
|         var P; | ||||
|         do | ||||
|         { | ||||
|             P = new BigInteger(this.q.bitLength(), new SecureRandom()); | ||||
|         } | ||||
|         while (P.compareTo(this.q) >= 0 | ||||
|             || !(P.multiply(P).subtract(fourQ).modPow(legendreExponent, this.q).equals(qMinusOne))); | ||||
| 
 | ||||
|         var result = this.lucasSequence(P, Q, k); | ||||
|         U = result[0]; | ||||
|         V = result[1]; | ||||
| 
 | ||||
|         if (this.modMult(V, V).equals(fourQ)) | ||||
|         { | ||||
|             // Integer division by 2, mod q
 | ||||
|             if (V.testBit(0)) | ||||
|             { | ||||
|                 V = V.add(q); | ||||
|             } | ||||
| 
 | ||||
|             V = V.shiftRight(1); | ||||
| 
 | ||||
|             return new ECFieldElementFp(q,V); | ||||
|         } | ||||
|     } | ||||
|     while (U.equals(BigInteger.ONE) || U.equals(qMinusOne)); | ||||
| 
 | ||||
|     return null; | ||||
| } | ||||
| ECFieldElementFp.prototype.lucasSequence = function(P,Q,k) | ||||
| { | ||||
|     var n = k.bitLength(); | ||||
|     var s = k.getLowestSetBit(); | ||||
| 
 | ||||
|     var Uh = BigInteger.ONE; | ||||
|     var Vl = BigInteger.TWO; | ||||
|     var Vh = P; | ||||
|     var Ql = BigInteger.ONE; | ||||
|     var Qh = BigInteger.ONE; | ||||
| 
 | ||||
|     for (var j = n - 1; j >= s + 1; --j) | ||||
|     { | ||||
|         Ql = this.modMult(Ql, Qh); | ||||
| 
 | ||||
|         if (k.testBit(j)) | ||||
|         { | ||||
|             Qh = this.modMult(Ql, Q); | ||||
|             Uh = this.modMult(Uh, Vh); | ||||
|             Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql))); | ||||
|             Vh = this.modReduce(Vh.multiply(Vh).subtract(Qh.shiftLeft(1))); | ||||
|         } | ||||
|         else | ||||
|         { | ||||
|             Qh = Ql; | ||||
|             Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql)); | ||||
|             Vh = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql))); | ||||
|             Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1))); | ||||
|         } | ||||
|     } | ||||
| 
 | ||||
|     Ql = this.modMult(Ql, Qh); | ||||
|     Qh = this.modMult(Ql, Q); | ||||
|     Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql)); | ||||
|     Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql))); | ||||
|     Ql = this.modMult(Ql, Qh); | ||||
| 
 | ||||
|     for (var j = 1; j <= s; ++j) | ||||
|     { | ||||
|         Uh = this.modMult(Uh, Vl); | ||||
|         Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1))); | ||||
|         Ql = this.modMult(Ql, Ql); | ||||
|     } | ||||
| 
 | ||||
|     return [ Uh, Vl ]; | ||||
| } | ||||
| 
 | ||||
| var exports = { | ||||
|   ECCurveFp: ECCurveFp, | ||||
|   ECPointFp: ECPointFp, | ||||
|   ECFieldElementFp: ECFieldElementFp | ||||
| } | ||||
| 
 | ||||
| module.exports = exports | ||||
							
								
								
									
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							|  | @ -0,0 +1,170 @@ | |||
| // Named EC curves
 | ||||
| 
 | ||||
| // Requires ec.js, jsbn.js, and jsbn2.js
 | ||||
| var BigInteger = require('jsbn').BigInteger | ||||
| var ECCurveFp = require('./ec.js').ECCurveFp | ||||
| 
 | ||||
| 
 | ||||
| // ----------------
 | ||||
| // 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 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 == "secp256r1") return secp256r1(); | ||||
|     return null; | ||||
| } | ||||
| 
 | ||||
| module.exports = { | ||||
|   "secp128r1":secp128r1, | ||||
|   "secp160k1":secp160k1, | ||||
|   "secp160r1":secp160r1, | ||||
|   "secp192k1":secp192k1, | ||||
|   "secp192r1":secp192r1, | ||||
|   "secp224r1":secp224r1, | ||||
|   "secp256r1":secp256r1 | ||||
| } | ||||
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