1 line
52 KiB
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1 line
52 KiB
JSON
{"ast":null,"code":"// Basic Javascript Elliptic Curve implementation\n// Ported loosely from BouncyCastle's Java EC code\n// Only Fp curves implemented for now\n// Requires jsbn.js and jsbn2.js\nvar BigInteger = require('jsbn').BigInteger;\n\nvar Barrett = BigInteger.prototype.Barrett; // ----------------\n// ECFieldElementFp\n// constructor\n\nfunction ECFieldElementFp(q, x) {\n this.x = x; // TODO if(x.compareTo(q) >= 0) error\n\n this.q = q;\n}\n\nfunction feFpEquals(other) {\n if (other == this) return true;\n return this.q.equals(other.q) && this.x.equals(other.x);\n}\n\nfunction feFpToBigInteger() {\n return this.x;\n}\n\nfunction feFpNegate() {\n return new ECFieldElementFp(this.q, this.x.negate().mod(this.q));\n}\n\nfunction feFpAdd(b) {\n return new ECFieldElementFp(this.q, this.x.add(b.toBigInteger()).mod(this.q));\n}\n\nfunction feFpSubtract(b) {\n return new ECFieldElementFp(this.q, this.x.subtract(b.toBigInteger()).mod(this.q));\n}\n\nfunction feFpMultiply(b) {\n return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q));\n}\n\nfunction feFpSquare() {\n return new ECFieldElementFp(this.q, this.x.square().mod(this.q));\n}\n\nfunction feFpDivide(b) {\n return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q));\n}\n\nECFieldElementFp.prototype.equals = feFpEquals;\nECFieldElementFp.prototype.toBigInteger = feFpToBigInteger;\nECFieldElementFp.prototype.negate = feFpNegate;\nECFieldElementFp.prototype.add = feFpAdd;\nECFieldElementFp.prototype.subtract = feFpSubtract;\nECFieldElementFp.prototype.multiply = feFpMultiply;\nECFieldElementFp.prototype.square = feFpSquare;\nECFieldElementFp.prototype.divide = feFpDivide; // ----------------\n// ECPointFp\n// constructor\n\nfunction ECPointFp(curve, x, y, z) {\n this.curve = curve;\n this.x = x;\n this.y = y; // Projective coordinates: either zinv == null or z * zinv == 1\n // z and zinv are just BigIntegers, not fieldElements\n\n if (z == null) {\n this.z = BigInteger.ONE;\n } else {\n this.z = z;\n }\n\n this.zinv = null; //TODO: compression flag\n}\n\nfunction pointFpGetX() {\n if (this.zinv == null) {\n this.zinv = this.z.modInverse(this.curve.q);\n }\n\n var r = this.x.toBigInteger().multiply(this.zinv);\n this.curve.reduce(r);\n return this.curve.fromBigInteger(r);\n}\n\nfunction pointFpGetY() {\n if (this.zinv == null) {\n this.zinv = this.z.modInverse(this.curve.q);\n }\n\n var r = this.y.toBigInteger().multiply(this.zinv);\n this.curve.reduce(r);\n return this.curve.fromBigInteger(r);\n}\n\nfunction pointFpEquals(other) {\n if (other == this) return true;\n if (this.isInfinity()) return other.isInfinity();\n if (other.isInfinity()) return this.isInfinity();\n var u, v; // u = Y2 * Z1 - Y1 * Z2\n\n u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q);\n if (!u.equals(BigInteger.ZERO)) return false; // v = X2 * Z1 - X1 * Z2\n\n v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q);\n return v.equals(BigInteger.ZERO);\n}\n\nfunction pointFpIsInfinity() {\n if (this.x == null && this.y == null) return true;\n return this.z.equals(BigInteger.ZERO) && !this.y.toBigInteger().equals(BigInteger.ZERO);\n}\n\nfunction pointFpNegate() {\n return new ECPointFp(this.curve, this.x, this.y.negate(), this.z);\n}\n\nfunction pointFpAdd(b) {\n if (this.isInfinity()) return b;\n if (b.isInfinity()) return this; // u = Y2 * Z1 - Y1 * Z2\n\n var u = b.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(b.z)).mod(this.curve.q); // v = X2 * Z1 - X1 * Z2\n\n var v = b.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(b.z)).mod(this.curve.q);\n\n if (BigInteger.ZERO.equals(v)) {\n if (BigInteger.ZERO.equals(u)) {\n return this.twice(); // this == b, so double\n }\n\n return this.curve.getInfinity(); // this = -b, so infinity\n }\n\n var THREE = new BigInteger(\"3\");\n var x1 = this.x.toBigInteger();\n var y1 = this.y.toBigInteger();\n var x2 = b.x.toBigInteger();\n var y2 = b.y.toBigInteger();\n var v2 = v.square();\n var v3 = v2.multiply(v);\n var x1v2 = x1.multiply(v2);\n var zu2 = u.square().multiply(this.z); // x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)\n\n 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\n\n 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\n\n var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q);\n return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);\n}\n\nfunction pointFpTwice() {\n if (this.isInfinity()) return this;\n if (this.y.toBigInteger().signum() == 0) return this.curve.getInfinity(); // TODO: optimized handling of constants\n\n var THREE = new BigInteger(\"3\");\n var x1 = this.x.toBigInteger();\n var y1 = this.y.toBigInteger();\n var y1z1 = y1.multiply(this.z);\n var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q);\n var a = this.curve.a.toBigInteger(); // w = 3 * x1^2 + a * z1^2\n\n var w = x1.square().multiply(THREE);\n\n if (!BigInteger.ZERO.equals(a)) {\n w = w.add(this.z.square().multiply(a));\n }\n\n w = w.mod(this.curve.q); //this.curve.reduce(w);\n // x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)\n\n 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\n\n 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\n\n var z3 = y1z1.square().multiply(y1z1).shiftLeft(3).mod(this.curve.q);\n return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);\n} // Simple NAF (Non-Adjacent Form) multiplication algorithm\n// TODO: modularize the multiplication algorithm\n\n\nfunction pointFpMultiply(k) {\n if (this.isInfinity()) return this;\n if (k.signum() == 0) return this.curve.getInfinity();\n var e = k;\n var h = e.multiply(new BigInteger(\"3\"));\n var neg = this.negate();\n var R = this;\n var i;\n\n for (i = h.bitLength() - 2; i > 0; --i) {\n R = R.twice();\n var hBit = h.testBit(i);\n var eBit = e.testBit(i);\n\n if (hBit != eBit) {\n R = R.add(hBit ? this : neg);\n }\n }\n\n return R;\n} // Compute this*j + x*k (simultaneous multiplication)\n\n\nfunction pointFpMultiplyTwo(j, x, k) {\n var i;\n if (j.bitLength() > k.bitLength()) i = j.bitLength() - 1;else i = k.bitLength() - 1;\n var R = this.curve.getInfinity();\n var both = this.add(x);\n\n while (i >= 0) {\n R = R.twice();\n\n if (j.testBit(i)) {\n if (k.testBit(i)) {\n R = R.add(both);\n } else {\n R = R.add(this);\n }\n } else {\n if (k.testBit(i)) {\n R = R.add(x);\n }\n }\n\n --i;\n }\n\n return R;\n}\n\nECPointFp.prototype.getX = pointFpGetX;\nECPointFp.prototype.getY = pointFpGetY;\nECPointFp.prototype.equals = pointFpEquals;\nECPointFp.prototype.isInfinity = pointFpIsInfinity;\nECPointFp.prototype.negate = pointFpNegate;\nECPointFp.prototype.add = pointFpAdd;\nECPointFp.prototype.twice = pointFpTwice;\nECPointFp.prototype.multiply = pointFpMultiply;\nECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo; // ----------------\n// ECCurveFp\n// constructor\n\nfunction ECCurveFp(q, a, b) {\n this.q = q;\n this.a = this.fromBigInteger(a);\n this.b = this.fromBigInteger(b);\n this.infinity = new ECPointFp(this, null, null);\n this.reducer = new Barrett(this.q);\n}\n\nfunction curveFpGetQ() {\n return this.q;\n}\n\nfunction curveFpGetA() {\n return this.a;\n}\n\nfunction curveFpGetB() {\n return this.b;\n}\n\nfunction curveFpEquals(other) {\n if (other == this) return true;\n return this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b);\n}\n\nfunction curveFpGetInfinity() {\n return this.infinity;\n}\n\nfunction curveFpFromBigInteger(x) {\n return new ECFieldElementFp(this.q, x);\n}\n\nfunction curveReduce(x) {\n this.reducer.reduce(x);\n} // for now, work with hex strings because they're easier in JS\n\n\nfunction curveFpDecodePointHex(s) {\n switch (parseInt(s.substr(0, 2), 16)) {\n // first byte\n case 0:\n return this.infinity;\n\n case 2:\n case 3:\n // point compression not supported yet\n return null;\n\n case 4:\n case 6:\n case 7:\n var len = (s.length - 2) / 2;\n var xHex = s.substr(2, len);\n var yHex = s.substr(len + 2, len);\n return new ECPointFp(this, this.fromBigInteger(new BigInteger(xHex, 16)), this.fromBigInteger(new BigInteger(yHex, 16)));\n\n default:\n // unsupported\n return null;\n }\n}\n\nfunction curveFpEncodePointHex(p) {\n if (p.isInfinity()) return \"00\";\n var xHex = p.getX().toBigInteger().toString(16);\n var yHex = p.getY().toBigInteger().toString(16);\n var oLen = this.getQ().toString(16).length;\n if (oLen % 2 != 0) oLen++;\n\n while (xHex.length < oLen) {\n xHex = \"0\" + xHex;\n }\n\n while (yHex.length < oLen) {\n yHex = \"0\" + yHex;\n }\n\n return \"04\" + xHex + yHex;\n}\n\nECCurveFp.prototype.getQ = curveFpGetQ;\nECCurveFp.prototype.getA = curveFpGetA;\nECCurveFp.prototype.getB = curveFpGetB;\nECCurveFp.prototype.equals = curveFpEquals;\nECCurveFp.prototype.getInfinity = curveFpGetInfinity;\nECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger;\nECCurveFp.prototype.reduce = curveReduce; //ECCurveFp.prototype.decodePointHex = curveFpDecodePointHex;\n\nECCurveFp.prototype.encodePointHex = curveFpEncodePointHex; // from: https://github.com/kaielvin/jsbn-ec-point-compression\n\nECCurveFp.prototype.decodePointHex = function (s) {\n var yIsEven;\n\n switch (parseInt(s.substr(0, 2), 16)) {\n // first byte\n case 0:\n return this.infinity;\n\n case 2:\n yIsEven = false;\n\n case 3:\n if (yIsEven == undefined) yIsEven = true;\n var len = s.length - 2;\n var xHex = s.substr(2, len);\n var x = this.fromBigInteger(new BigInteger(xHex, 16));\n var alpha = x.multiply(x.square().add(this.getA())).add(this.getB());\n var beta = alpha.sqrt();\n if (beta == null) throw \"Invalid point compression\";\n var betaValue = beta.toBigInteger();\n\n if (betaValue.testBit(0) != yIsEven) {\n // Use the other root\n beta = this.fromBigInteger(this.getQ().subtract(betaValue));\n }\n\n return new ECPointFp(this, x, beta);\n\n case 4:\n case 6:\n case 7:\n var len = (s.length - 2) / 2;\n var xHex = s.substr(2, len);\n var yHex = s.substr(len + 2, len);\n return new ECPointFp(this, this.fromBigInteger(new BigInteger(xHex, 16)), this.fromBigInteger(new BigInteger(yHex, 16)));\n\n default:\n // unsupported\n return null;\n }\n};\n\nECCurveFp.prototype.encodeCompressedPointHex = function (p) {\n if (p.isInfinity()) return \"00\";\n var xHex = p.getX().toBigInteger().toString(16);\n var oLen = this.getQ().toString(16).length;\n if (oLen % 2 != 0) oLen++;\n\n while (xHex.length < oLen) xHex = \"0\" + xHex;\n\n var yPrefix;\n if (p.getY().toBigInteger().isEven()) yPrefix = \"02\";else yPrefix = \"03\";\n return yPrefix + xHex;\n};\n\nECFieldElementFp.prototype.getR = function () {\n if (this.r != undefined) return this.r;\n this.r = null;\n var bitLength = this.q.bitLength();\n\n if (bitLength > 128) {\n var firstWord = this.q.shiftRight(bitLength - 64);\n\n if (firstWord.intValue() == -1) {\n this.r = BigInteger.ONE.shiftLeft(bitLength).subtract(this.q);\n }\n }\n\n return this.r;\n};\n\nECFieldElementFp.prototype.modMult = function (x1, x2) {\n return this.modReduce(x1.multiply(x2));\n};\n\nECFieldElementFp.prototype.modReduce = function (x) {\n if (this.getR() != null) {\n var qLen = q.bitLength();\n\n while (x.bitLength() > qLen + 1) {\n var u = x.shiftRight(qLen);\n var v = x.subtract(u.shiftLeft(qLen));\n\n if (!this.getR().equals(BigInteger.ONE)) {\n u = u.multiply(this.getR());\n }\n\n x = u.add(v);\n }\n\n while (x.compareTo(q) >= 0) {\n x = x.subtract(q);\n }\n } else {\n x = x.mod(q);\n }\n\n return x;\n};\n\nECFieldElementFp.prototype.sqrt = function () {\n if (!this.q.testBit(0)) throw \"unsupported\"; // p mod 4 == 3\n\n if (this.q.testBit(1)) {\n var z = new ECFieldElementFp(this.q, this.x.modPow(this.q.shiftRight(2).add(BigInteger.ONE), this.q));\n return z.square().equals(this) ? z : null;\n } // p mod 4 == 1\n\n\n var qMinusOne = this.q.subtract(BigInteger.ONE);\n var legendreExponent = qMinusOne.shiftRight(1);\n\n if (!this.x.modPow(legendreExponent, this.q).equals(BigInteger.ONE)) {\n return null;\n }\n\n var u = qMinusOne.shiftRight(2);\n var k = u.shiftLeft(1).add(BigInteger.ONE);\n var Q = this.x;\n var fourQ = modDouble(modDouble(Q));\n var U, V;\n\n do {\n var P;\n\n do {\n P = new BigInteger(this.q.bitLength(), new SecureRandom());\n } while (P.compareTo(this.q) >= 0 || !P.multiply(P).subtract(fourQ).modPow(legendreExponent, this.q).equals(qMinusOne));\n\n var result = this.lucasSequence(P, Q, k);\n U = result[0];\n V = result[1];\n\n if (this.modMult(V, V).equals(fourQ)) {\n // Integer division by 2, mod q\n if (V.testBit(0)) {\n V = V.add(q);\n }\n\n V = V.shiftRight(1);\n return new ECFieldElementFp(q, V);\n }\n } while (U.equals(BigInteger.ONE) || U.equals(qMinusOne));\n\n return null;\n};\n\nECFieldElementFp.prototype.lucasSequence = function (P, Q, k) {\n var n = k.bitLength();\n var s = k.getLowestSetBit();\n var Uh = BigInteger.ONE;\n var Vl = BigInteger.TWO;\n var Vh = P;\n var Ql = BigInteger.ONE;\n var Qh = BigInteger.ONE;\n\n for (var j = n - 1; j >= s + 1; --j) {\n Ql = this.modMult(Ql, Qh);\n\n if (k.testBit(j)) {\n Qh = this.modMult(Ql, Q);\n Uh = this.modMult(Uh, Vh);\n Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));\n Vh = this.modReduce(Vh.multiply(Vh).subtract(Qh.shiftLeft(1)));\n } else {\n Qh = Ql;\n Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));\n Vh = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));\n Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));\n }\n }\n\n Ql = this.modMult(Ql, Qh);\n Qh = this.modMult(Ql, Q);\n Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));\n Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));\n Ql = this.modMult(Ql, Qh);\n\n for (var j = 1; j <= s; ++j) {\n Uh = this.modMult(Uh, Vl);\n Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));\n Ql = this.modMult(Ql, Ql);\n }\n\n return [Uh, Vl];\n};\n\nvar exports = {\n ECCurveFp: ECCurveFp,\n ECPointFp: ECPointFp,\n ECFieldElementFp: ECFieldElementFp\n};\nmodule.exports = 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// TODO: optimized handling of constants\n var THREE = new BigInteger(\"3\");\n var x1 = this.x.toBigInteger();\n var y1 = this.y.toBigInteger();\n\n var y1z1 = y1.multiply(this.z);\n var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q);\n var a = this.curve.a.toBigInteger();\n\n // w = 3 * x1^2 + a * z1^2\n var w = x1.square().multiply(THREE);\n if(!BigInteger.ZERO.equals(a)) {\n w = w.add(this.z.square().multiply(a));\n }\n w = w.mod(this.curve.q);\n //this.curve.reduce(w);\n // x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)\n var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.q);\n // y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3\n var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.square().multiply(w)).mod(this.curve.q);\n // z3 = 8 * (y1 * z1)^3\n var z3 = y1z1.square().multiply(y1z1).shiftLeft(3).mod(this.curve.q);\n\n return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);\n}\n\n// Simple NAF (Non-Adjacent Form) multiplication algorithm\n// TODO: modularize the multiplication algorithm\nfunction pointFpMultiply(k) {\n if(this.isInfinity()) return this;\n if(k.signum() == 0) return this.curve.getInfinity();\n\n var e = k;\n var h = e.multiply(new BigInteger(\"3\"));\n\n var neg = this.negate();\n var R = this;\n\n var i;\n for(i = h.bitLength() - 2; i > 0; --i) {\n\tR = R.twice();\n\n\tvar hBit = h.testBit(i);\n\tvar eBit = e.testBit(i);\n\n\tif (hBit != eBit) {\n\t R = R.add(hBit ? this : neg);\n\t}\n }\n\n return R;\n}\n\n// Compute this*j + x*k (simultaneous multiplication)\nfunction pointFpMultiplyTwo(j,x,k) {\n var i;\n if(j.bitLength() > k.bitLength())\n i = j.bitLength() - 1;\n else\n i = k.bitLength() - 1;\n\n var R = this.curve.getInfinity();\n var both = this.add(x);\n while(i >= 0) {\n R = R.twice();\n if(j.testBit(i)) {\n if(k.testBit(i)) {\n R = R.add(both);\n }\n else {\n R = R.add(this);\n }\n }\n else {\n if(k.testBit(i)) {\n R = R.add(x);\n }\n }\n --i;\n }\n\n return R;\n}\n\nECPointFp.prototype.getX = pointFpGetX;\nECPointFp.prototype.getY = pointFpGetY;\nECPointFp.prototype.equals = pointFpEquals;\nECPointFp.prototype.isInfinity = pointFpIsInfinity;\nECPointFp.prototype.negate = pointFpNegate;\nECPointFp.prototype.add = pointFpAdd;\nECPointFp.prototype.twice = pointFpTwice;\nECPointFp.prototype.multiply = pointFpMultiply;\nECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo;\n\n// ----------------\n// ECCurveFp\n\n// constructor\nfunction ECCurveFp(q,a,b) {\n this.q = q;\n this.a = this.fromBigInteger(a);\n this.b = this.fromBigInteger(b);\n this.infinity = new ECPointFp(this, null, null);\n this.reducer = new Barrett(this.q);\n}\n\nfunction curveFpGetQ() {\n return this.q;\n}\n\nfunction curveFpGetA() {\n return this.a;\n}\n\nfunction curveFpGetB() {\n return this.b;\n}\n\nfunction curveFpEquals(other) {\n if(other == this) return true;\n return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b));\n}\n\nfunction curveFpGetInfinity() {\n return this.infinity;\n}\n\nfunction curveFpFromBigInteger(x) {\n return new ECFieldElementFp(this.q, x);\n}\n\nfunction curveReduce(x) {\n this.reducer.reduce(x);\n}\n\n// for now, work with hex strings because they're easier in JS\nfunction curveFpDecodePointHex(s) {\n switch(parseInt(s.substr(0,2), 16)) { // first byte\n case 0:\n\treturn this.infinity;\n case 2:\n case 3:\n\t// point compression not supported yet\n\treturn null;\n case 4:\n case 6:\n case 7:\n\tvar len = (s.length - 2) / 2;\n\tvar xHex = s.substr(2, len);\n\tvar yHex = s.substr(len+2, len);\n\n\treturn new ECPointFp(this,\n\t\t\t this.fromBigInteger(new BigInteger(xHex, 16)),\n\t\t\t this.fromBigInteger(new BigInteger(yHex, 16)));\n\n default: // unsupported\n\treturn null;\n }\n}\n\nfunction curveFpEncodePointHex(p) {\n\tif (p.isInfinity()) return \"00\";\n\tvar xHex = p.getX().toBigInteger().toString(16);\n\tvar yHex = p.getY().toBigInteger().toString(16);\n\tvar oLen = this.getQ().toString(16).length;\n\tif ((oLen % 2) != 0) oLen++;\n\twhile (xHex.length < oLen) {\n\t\txHex = \"0\" + xHex;\n\t}\n\twhile (yHex.length < oLen) {\n\t\tyHex = \"0\" + yHex;\n\t}\n\treturn \"04\" + xHex + yHex;\n}\n\nECCurveFp.prototype.getQ = curveFpGetQ;\nECCurveFp.prototype.getA = curveFpGetA;\nECCurveFp.prototype.getB = curveFpGetB;\nECCurveFp.prototype.equals = curveFpEquals;\nECCurveFp.prototype.getInfinity = curveFpGetInfinity;\nECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger;\nECCurveFp.prototype.reduce = curveReduce;\n//ECCurveFp.prototype.decodePointHex = curveFpDecodePointHex;\nECCurveFp.prototype.encodePointHex = curveFpEncodePointHex;\n\n// from: https://github.com/kaielvin/jsbn-ec-point-compression\nECCurveFp.prototype.decodePointHex = function(s)\n{\n\tvar yIsEven;\n switch(parseInt(s.substr(0,2), 16)) { // first byte\n case 0:\n\treturn this.infinity;\n case 2:\n\tyIsEven = false;\n case 3:\n\tif(yIsEven == undefined) yIsEven = true;\n\tvar len = s.length - 2;\n\tvar xHex = s.substr(2, len);\n\tvar x = this.fromBigInteger(new BigInteger(xHex,16));\n\tvar alpha = x.multiply(x.square().add(this.getA())).add(this.getB());\n\tvar beta = alpha.sqrt();\n\n if (beta == null) throw \"Invalid point compression\";\n\n var betaValue = beta.toBigInteger();\n if (betaValue.testBit(0) != yIsEven)\n {\n // Use the other root\n beta = this.fromBigInteger(this.getQ().subtract(betaValue));\n }\n return new ECPointFp(this,x,beta);\n case 4:\n case 6:\n case 7:\n\tvar len = (s.length - 2) / 2;\n\tvar xHex = s.substr(2, len);\n\tvar yHex = s.substr(len+2, len);\n\n\treturn new ECPointFp(this,\n\t\t\t this.fromBigInteger(new BigInteger(xHex, 16)),\n\t\t\t this.fromBigInteger(new BigInteger(yHex, 16)));\n\n default: // unsupported\n\treturn null;\n }\n}\nECCurveFp.prototype.encodeCompressedPointHex = function(p)\n{\n\tif (p.isInfinity()) return \"00\";\n\tvar xHex = p.getX().toBigInteger().toString(16);\n\tvar oLen = this.getQ().toString(16).length;\n\tif ((oLen % 2) != 0) oLen++;\n\twhile (xHex.length < oLen)\n\t\txHex = \"0\" + xHex;\n\tvar yPrefix;\n\tif(p.getY().toBigInteger().isEven()) yPrefix = \"02\";\n\telse yPrefix = \"03\";\n\n\treturn yPrefix + xHex;\n}\n\n\nECFieldElementFp.prototype.getR = function()\n{\n\tif(this.r != undefined) return this.r;\n\n this.r = null;\n var bitLength = this.q.bitLength();\n if (bitLength > 128)\n {\n var firstWord = this.q.shiftRight(bitLength - 64);\n if (firstWord.intValue() == -1)\n {\n this.r = BigInteger.ONE.shiftLeft(bitLength).subtract(this.q);\n }\n }\n return this.r;\n}\nECFieldElementFp.prototype.modMult = function(x1,x2)\n{\n return this.modReduce(x1.multiply(x2));\n}\nECFieldElementFp.prototype.modReduce = function(x)\n{\n if (this.getR() != null)\n {\n var qLen = q.bitLength();\n while (x.bitLength() > (qLen + 1))\n {\n var u = x.shiftRight(qLen);\n var v = x.subtract(u.shiftLeft(qLen));\n if (!this.getR().equals(BigInteger.ONE))\n {\n u = u.multiply(this.getR());\n }\n x = u.add(v); \n }\n while (x.compareTo(q) >= 0)\n {\n x = x.subtract(q);\n }\n }\n else\n {\n x = x.mod(q);\n }\n return x;\n}\nECFieldElementFp.prototype.sqrt = function()\n{\n if (!this.q.testBit(0)) throw \"unsupported\";\n\n // p mod 4 == 3\n if (this.q.testBit(1))\n {\n \tvar z = new ECFieldElementFp(this.q,this.x.modPow(this.q.shiftRight(2).add(BigInteger.ONE),this.q));\n \treturn z.square().equals(this) ? z : null;\n }\n\n // p mod 4 == 1\n var qMinusOne = this.q.subtract(BigInteger.ONE);\n\n var legendreExponent = qMinusOne.shiftRight(1);\n if (!(this.x.modPow(legendreExponent, this.q).equals(BigInteger.ONE)))\n {\n return null;\n }\n\n var u = qMinusOne.shiftRight(2);\n var k = u.shiftLeft(1).add(BigInteger.ONE);\n\n var Q = this.x;\n var fourQ = modDouble(modDouble(Q));\n\n var U, V;\n do\n {\n var P;\n do\n {\n P = new BigInteger(this.q.bitLength(), new SecureRandom());\n }\n while (P.compareTo(this.q) >= 0\n || !(P.multiply(P).subtract(fourQ).modPow(legendreExponent, this.q).equals(qMinusOne)));\n\n var result = this.lucasSequence(P, Q, k);\n U = result[0];\n V = result[1];\n\n if (this.modMult(V, V).equals(fourQ))\n {\n // Integer division by 2, mod q\n if (V.testBit(0))\n {\n V = V.add(q);\n }\n\n V = V.shiftRight(1);\n\n return new ECFieldElementFp(q,V);\n }\n }\n while (U.equals(BigInteger.ONE) || U.equals(qMinusOne));\n\n return null;\n}\nECFieldElementFp.prototype.lucasSequence = function(P,Q,k)\n{\n var n = k.bitLength();\n var s = k.getLowestSetBit();\n\n var Uh = BigInteger.ONE;\n var Vl = BigInteger.TWO;\n var Vh = P;\n var Ql = BigInteger.ONE;\n var Qh = BigInteger.ONE;\n\n for (var j = n - 1; j >= s + 1; --j)\n {\n Ql = this.modMult(Ql, Qh);\n\n if (k.testBit(j))\n {\n Qh = this.modMult(Ql, Q);\n Uh = this.modMult(Uh, Vh);\n Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));\n Vh = this.modReduce(Vh.multiply(Vh).subtract(Qh.shiftLeft(1)));\n }\n else\n {\n Qh = Ql;\n Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));\n Vh = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));\n Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));\n }\n }\n\n Ql = this.modMult(Ql, Qh);\n Qh = this.modMult(Ql, Q);\n Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));\n Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));\n Ql = this.modMult(Ql, Qh);\n\n for (var j = 1; j <= s; ++j)\n {\n Uh = this.modMult(Uh, Vl);\n Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));\n Ql = this.modMult(Ql, Ql);\n }\n\n return [ Uh, Vl ];\n}\n\nvar exports = {\n ECCurveFp: ECCurveFp,\n ECPointFp: ECPointFp,\n ECFieldElementFp: ECFieldElementFp\n}\n\nmodule.exports = exports\n"]},"metadata":{},"sourceType":"script"} |