Matthew Raymer
10 months ago
7 changed files with 3848 additions and 10 deletions
@ -0,0 +1,256 @@ |
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(function () { |
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randomBytes = length => self.crypto.getRandomValues(new Uint8Array(length)) |
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self.Secp256k1 = exports = {} |
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function uint256(x, base) { |
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return new BN(x, base) |
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} |
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function rnd(P) { |
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return uint256(randomBytes(32)).umod(P)//TODO red
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} |
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const A = uint256(0) |
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const B = uint256(7) |
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const GX = uint256("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16) |
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const GY = uint256("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16) |
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const P = uint256("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16) |
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const N = uint256("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16) |
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//const RED = BN.red(P)
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const _0 = uint256(0) |
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const _1 = uint256(1) |
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// function for elliptic curve multiplication in jacobian coordinates using Double-and-add method
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function ecmul(_p, _d) { |
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let R = [_0,_0,_0] |
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//return (0,0) if d=0 or (x1,y1)=(0,0)
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if (_d == 0 || ((_p[0] == 0) && (_p[1] == 0)) ) { |
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return R |
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} |
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let T = [ |
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_p[0], //x-coordinate temp
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_p[1], //y-coordinate temp
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_p[2], //z-coordinate temp
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] |
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const d = _d.clone() |
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while (d != 0) { |
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if (d.testn(0)) { //if last bit is 1 add T to result
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R = ecadd(T,R) |
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} |
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T = ecdouble(T); //double temporary coordinates
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d.iushrn(1); //"cut off" last bit
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} |
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return R |
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} |
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function mulmod(a, b, P) { |
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return a.mul(b).umod(P)//TODO red
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} |
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function addmod(a, b, P) { |
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return a.add(b).umod(P)//TODO red
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} |
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function invmod(a, P) { |
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return a.invm(P)//TODO redq
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} |
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function mulG(k) { |
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const GinJ = AtoJ(GX, GY) |
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const PUBinJ = ecmul(GinJ, k) |
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return JtoA(PUBinJ) |
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} |
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function assert(cond, msg) { |
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if (!cond) { |
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throw Error("assertion failed: " + msg) |
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} |
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} |
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function ecsign(d, z) { |
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assert(d != 0, "d must not be 0") |
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assert(z != 0, "z must not be 0") |
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while (true) { |
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const k = rnd(P) |
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const R = mulG(k) |
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if (R[0] == 0) continue |
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const s = mulmod(invmod(k, N), addmod(z, mulmod(R[0], d, N), N), N) |
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if (s == 0) continue |
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//FIXME: why do I need this
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if (s.testn(255)) continue |
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return {r: toHex(R[0]), s: toHex(s), v: R[1].testn(0) ? 1 : 0} |
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} |
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} |
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function JtoA(p) { |
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const zInv = invmod(p[2], P) |
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const zInv2 = mulmod(zInv, zInv, P) |
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return [mulmod(p[0], zInv2, P), mulmod(p[1], mulmod(zInv, zInv2, P), P)] |
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} |
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//point doubling for elliptic curve in jacobian coordinates
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//formula from https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
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function ecdouble(_p) { |
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if (_p[1] == 0) { |
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//return point at infinity
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return [_1, _1, _0] |
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} |
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const z2 = mulmod(_p[2], _p[2], P) |
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const m = addmod(mulmod(A, mulmod(z2, z2, P), P), mulmod(uint256(3), mulmod(_p[0], _p[0], P), P), P) |
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const y2 = mulmod(_p[1], _p[1], P) |
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const s = mulmod(uint256(4), mulmod(_p[0], y2, P), P) |
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const x = addmod(mulmod(m, m, P), negmod(mulmod(s, uint256(2), P), P), P) |
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return [ |
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x, |
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addmod(mulmod(m, addmod(s, negmod(x, P), P), P), negmod(mulmod(uint256(8), mulmod(y2, y2, P), P), P), P), |
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mulmod(uint256(2), mulmod(_p[1], _p[2], P), P) |
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] |
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} |
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function negmod(a, P) { |
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return P.sub(a) |
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} |
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// point addition for elliptic curve in jacobian coordinates
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// formula from https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
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function ecadd(_p, _q) { |
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if (_q[0] == 0 && _q[1] == 0 && _q[2] == 0) { |
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return _p |
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} |
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let z2 = mulmod(_q[2], _q[2], P) |
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const u1 = mulmod(_p[0], z2, P) |
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const s1 = mulmod(_p[1], mulmod(z2, _q[2], P), P) |
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z2 = mulmod(_p[2], _p[2], P) |
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let u2 = mulmod(_q[0], z2, P) |
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let s2 = mulmod(_q[1], mulmod(z2, _p[2], P), P) |
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if (u1.eq(u2)) { |
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if (!s1.eq(s2)) { |
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//return point at infinity
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return [_1, _1, _0] |
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} |
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else { |
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return ecdouble(_p) |
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} |
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} |
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u2 = addmod(u2, negmod(u1, P), P) |
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z2 = mulmod(u2, u2, P) |
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const t2 = mulmod(u1, z2, P) |
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z2 = mulmod(u2, z2, P) |
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s2 = addmod(s2, negmod(s1, P), P) |
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const x = addmod(addmod(mulmod(s2, s2, P), negmod(z2, P), P), negmod(mulmod(uint256(2), t2, P), P), P) |
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return [ |
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x, |
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addmod(mulmod(s2, addmod(t2, negmod(x, P), P), P), negmod(mulmod(s1, z2, P), P), P), |
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mulmod(u2, mulmod(_p[2], _q[2], P), P) |
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] |
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} |
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function AtoJ(x, y) { |
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return [ |
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uint256(x), |
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uint256(y), |
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_1 |
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] |
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} |
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function isValidPoint(x, y) { |
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const yy = addmod(mulmod(mulmod(x, x, P), x, P), B, P) |
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return yy.eq(mulmod(y, y, P)) |
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} |
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function toHex(bn) { |
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return ('00000000000000000000000000000000000000000000000000000000000000000000000000000000' + bn.toString(16)).slice(-64) |
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} |
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function decompressKey(x, yBit) { |
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let redP = BN.red('k256'); |
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x = x.toRed(redP) |
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const y = x.redMul(x).redMul(x).redAdd(B.toRed(redP)).redSqrt() |
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const sign = y.testn(0) |
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return (sign != yBit ? y.redNeg() : y).fromRed() |
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} |
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function generatePublicKeyFromPrivateKeyData(pk) { |
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const p = mulG(pk) |
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return {x: toHex(p[0]), y: toHex(p[1])} |
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} |
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function ecrecover(recId, sigr, sigs, message) { |
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assert(recId >= 0 && recId <= 3, "recId must be 0..3") |
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assert(sigr != 0, "sigr must not be 0") |
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assert(sigs != 0, "sigs must not be 0") |
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// 1.0 For j from 0 to h (h == recId here and the loop is outside this function)
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// 1.1 Let x = r + jn
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const x = addmod(uint256(sigr), P.muln(recId >> 1), P) |
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// 1.2. Convert the integer x to an octet string X of length mlen using the conversion routine
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// specified in Section 2.3.7, where mlen = ⌈(log2 p)/8⌉ or mlen = ⌈m/8⌉.
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// 1.3. Convert the octet string (16 set binary digits)||X to an elliptic curve point R using the
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// conversion routine specified in Section 2.3.4. If this conversion routine outputs “invalid”, then
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// do another iteration of Step 1.
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//
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// More concisely, what these points mean is to use X as a compressed public key.
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if (x.gte(P)) { |
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// Cannot have point co-ordinates larger than this as everything takes place modulo Q.
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return null |
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} |
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// Compressed keys require you to know an extra bit of data about the y-coord as there are two possibilities.
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// So it's encoded in the recId.
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const y = decompressKey(x, (recId & 1) == 1) |
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// 1.4. If nR != point at infinity, then do another iteration of Step 1 (callers responsibility).
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// if (!R.mul(N).isInfinity())
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// return null
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// 1.5. Compute e from M using Steps 2 and 3 of ECDSA signature verification.
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const e = uint256(message) |
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// 1.6. For k from 1 to 2 do the following. (loop is outside this function via iterating recId)
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// 1.6.1. Compute a candidate public key as:
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// Q = mi(r) * (sR - eG)
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//
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// Where mi(x) is the modular multiplicative inverse. We transform this into the following:
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// Q = (mi(r) * s ** R) + (mi(r) * -e ** G)
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// Where -e is the modular additive inverse of e, that is z such that z + e = 0 (mod n). In the above equation
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// ** is point multiplication and + is point addition (the EC group operator).
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//
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// We can find the additive inverse by subtracting e from zero then taking the mod. For example the additive
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// inverse of 3 modulo 11 is 8 because 3 + 8 mod 11 = 0, and -3 mod 11 = 8.
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const eNeg = negmod(e, N) |
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const rInv = invmod(sigr, N) |
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const srInv = mulmod(rInv, sigs, N) |
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const eNegrInv = mulmod(rInv, eNeg, N) |
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const R = AtoJ(x, y) |
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const G = AtoJ(GX, GY) |
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const qinJ = ecadd(ecmul(G, eNegrInv), ecmul(R, srInv)) |
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const p = JtoA(qinJ) |
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return {x: toHex(p[0]), y: toHex(p[1])} |
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} |
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function ecverify (Qx, Qy, sigr, sigs, z) { |
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if (sigs == 0 || sigr == 0) { |
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return false |
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} |
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const w = invmod(sigs, N) |
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const u1 = mulmod(z, w, N) |
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const u2 = mulmod(sigr, w, N) |
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const Q = AtoJ(Qx, Qy) |
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const G = AtoJ(GX, GY) |
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const RinJ = ecadd(ecmul(G, u1), ecmul(Q, u2)) |
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const r = JtoA(RinJ) |
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return sigr.eq(r[0]) |
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} |
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exports.uint256 = uint256 |
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exports.ecsign = ecsign |
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exports.ecrecover = ecrecover |
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exports.generatePublicKeyFromPrivateKeyData = generatePublicKeyFromPrivateKeyData |
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exports.decompressKey = decompressKey |
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exports.isValidPoint = isValidPoint |
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exports.ecverify = ecverify |
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})() |
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