Matthew Raymer
12 months ago
6 changed files with 5026 additions and 5297 deletions
File diff suppressed because it is too large
File diff suppressed because it is too large
@ -1,283 +0,0 @@ |
|||
(function () { |
|||
randomBytes = (length) => self.crypto.getRandomValues(new Uint8Array(length)); |
|||
self.Secp256k1 = exports = {}; |
|||
|
|||
function uint256(x, base) { |
|||
return new BN(x, base); |
|||
} |
|||
|
|||
function rnd(P) { |
|||
return uint256(randomBytes(32)).umod(P); //TODO red
|
|||
} |
|||
|
|||
const A = uint256(0); |
|||
const B = uint256(7); |
|||
const GX = uint256( |
|||
"79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", |
|||
16, |
|||
); |
|||
const GY = uint256( |
|||
"483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", |
|||
16, |
|||
); |
|||
const P = uint256( |
|||
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", |
|||
16, |
|||
); |
|||
const N = uint256( |
|||
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", |
|||
16, |
|||
); |
|||
//const RED = BN.red(P)
|
|||
const _0 = uint256(0); |
|||
const _1 = uint256(1); |
|||
|
|||
// function for elliptic curve multiplication in jacobian coordinates using Double-and-add method
|
|||
function ecmul(_p, _d) { |
|||
let R = [_0, _0, _0]; |
|||
|
|||
//return (0,0) if d=0 or (x1,y1)=(0,0)
|
|||
if (_d == 0 || (_p[0] == 0 && _p[1] == 0)) { |
|||
return R; |
|||
} |
|||
let T = [ |
|||
_p[0], //x-coordinate temp
|
|||
_p[1], //y-coordinate temp
|
|||
_p[2], //z-coordinate temp
|
|||
]; |
|||
|
|||
const d = _d.clone(); |
|||
while (d != 0) { |
|||
if (d.testn(0)) { |
|||
//if last bit is 1 add T to result
|
|||
R = ecadd(T, R); |
|||
} |
|||
T = ecdouble(T); //double temporary coordinates
|
|||
d.iushrn(1); //"cut off" last bit
|
|||
} |
|||
|
|||
return R; |
|||
} |
|||
|
|||
function mulmod(a, b, P) { |
|||
return a.mul(b).umod(P); //TODO red
|
|||
} |
|||
|
|||
function addmod(a, b, P) { |
|||
return a.add(b).umod(P); //TODO red
|
|||
} |
|||
|
|||
function invmod(a, P) { |
|||
return a.invm(P); //TODO redq
|
|||
} |
|||
|
|||
function mulG(k) { |
|||
const GinJ = AtoJ(GX, GY); |
|||
const PUBinJ = ecmul(GinJ, k); |
|||
return JtoA(PUBinJ); |
|||
} |
|||
|
|||
function assert(cond, msg) { |
|||
if (!cond) { |
|||
throw Error("assertion failed: " + msg); |
|||
} |
|||
} |
|||
|
|||
function ecsign(d, z) { |
|||
assert(d != 0, "d must not be 0"); |
|||
assert(z != 0, "z must not be 0"); |
|||
while (true) { |
|||
const k = rnd(P); |
|||
const R = mulG(k); |
|||
if (R[0] == 0) continue; |
|||
const s = mulmod(invmod(k, N), addmod(z, mulmod(R[0], d, N), N), N); |
|||
if (s == 0) continue; |
|||
//FIXME: why do I need this
|
|||
if (s.testn(255)) continue; |
|||
return { r: toHex(R[0]), s: toHex(s), v: R[1].testn(0) ? 1 : 0 }; |
|||
} |
|||
} |
|||
|
|||
function JtoA(p) { |
|||
const zInv = invmod(p[2], P); |
|||
const zInv2 = mulmod(zInv, zInv, P); |
|||
return [mulmod(p[0], zInv2, P), mulmod(p[1], mulmod(zInv, zInv2, P), P)]; |
|||
} |
|||
|
|||
//point doubling for elliptic curve in jacobian coordinates
|
|||
//formula from https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
|
|||
function ecdouble(_p) { |
|||
if (_p[1] == 0) { |
|||
//return point at infinity
|
|||
return [_1, _1, _0]; |
|||
} |
|||
|
|||
const z2 = mulmod(_p[2], _p[2], P); |
|||
const m = addmod( |
|||
mulmod(A, mulmod(z2, z2, P), P), |
|||
mulmod(uint256(3), mulmod(_p[0], _p[0], P), P), |
|||
P, |
|||
); |
|||
const y2 = mulmod(_p[1], _p[1], P); |
|||
const s = mulmod(uint256(4), mulmod(_p[0], y2, P), P); |
|||
|
|||
const x = addmod(mulmod(m, m, P), negmod(mulmod(s, uint256(2), P), P), P); |
|||
return [ |
|||
x, |
|||
addmod( |
|||
mulmod(m, addmod(s, negmod(x, P), P), P), |
|||
negmod(mulmod(uint256(8), mulmod(y2, y2, P), P), P), |
|||
P, |
|||
), |
|||
mulmod(uint256(2), mulmod(_p[1], _p[2], P), P), |
|||
]; |
|||
} |
|||
|
|||
function negmod(a, P) { |
|||
return P.sub(a); |
|||
} |
|||
|
|||
// point addition for elliptic curve in jacobian coordinates
|
|||
// formula from https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
|
|||
function ecadd(_p, _q) { |
|||
if (_q[0] == 0 && _q[1] == 0 && _q[2] == 0) { |
|||
return _p; |
|||
} |
|||
|
|||
let z2 = mulmod(_q[2], _q[2], P); |
|||
const u1 = mulmod(_p[0], z2, P); |
|||
const s1 = mulmod(_p[1], mulmod(z2, _q[2], P), P); |
|||
z2 = mulmod(_p[2], _p[2], P); |
|||
let u2 = mulmod(_q[0], z2, P); |
|||
let s2 = mulmod(_q[1], mulmod(z2, _p[2], P), P); |
|||
|
|||
if (u1.eq(u2)) { |
|||
if (!s1.eq(s2)) { |
|||
//return point at infinity
|
|||
return [_1, _1, _0]; |
|||
} else { |
|||
return ecdouble(_p); |
|||
} |
|||
} |
|||
|
|||
u2 = addmod(u2, negmod(u1, P), P); |
|||
z2 = mulmod(u2, u2, P); |
|||
const t2 = mulmod(u1, z2, P); |
|||
z2 = mulmod(u2, z2, P); |
|||
s2 = addmod(s2, negmod(s1, P), P); |
|||
const x = addmod( |
|||
addmod(mulmod(s2, s2, P), negmod(z2, P), P), |
|||
negmod(mulmod(uint256(2), t2, P), P), |
|||
P, |
|||
); |
|||
return [ |
|||
x, |
|||
addmod( |
|||
mulmod(s2, addmod(t2, negmod(x, P), P), P), |
|||
negmod(mulmod(s1, z2, P), P), |
|||
P, |
|||
), |
|||
mulmod(u2, mulmod(_p[2], _q[2], P), P), |
|||
]; |
|||
} |
|||
|
|||
function AtoJ(x, y) { |
|||
return [uint256(x), uint256(y), _1]; |
|||
} |
|||
|
|||
function isValidPoint(x, y) { |
|||
const yy = addmod(mulmod(mulmod(x, x, P), x, P), B, P); |
|||
return yy.eq(mulmod(y, y, P)); |
|||
} |
|||
|
|||
function toHex(bn) { |
|||
return ( |
|||
"00000000000000000000000000000000000000000000000000000000000000000000000000000000" + |
|||
bn.toString(16) |
|||
).slice(-64); |
|||
} |
|||
|
|||
function decompressKey(x, yBit) { |
|||
let redP = BN.red("k256"); |
|||
x = x.toRed(redP); |
|||
const y = x.redMul(x).redMul(x).redAdd(B.toRed(redP)).redSqrt(); |
|||
const sign = y.testn(0); |
|||
return (sign != yBit ? y.redNeg() : y).fromRed(); |
|||
} |
|||
|
|||
function generatePublicKeyFromPrivateKeyData(pk) { |
|||
const p = mulG(pk); |
|||
return { x: toHex(p[0]), y: toHex(p[1]) }; |
|||
} |
|||
|
|||
function ecrecover(recId, sigr, sigs, message) { |
|||
assert(recId >= 0 && recId <= 3, "recId must be 0..3"); |
|||
assert(sigr != 0, "sigr must not be 0"); |
|||
assert(sigs != 0, "sigs must not be 0"); |
|||
// 1.0 For j from 0 to h (h == recId here and the loop is outside this function)
|
|||
// 1.1 Let x = r + jn
|
|||
const x = addmod(uint256(sigr), P.muln(recId >> 1), P); |
|||
// 1.2. Convert the integer x to an octet string X of length mlen using the conversion routine
|
|||
// specified in Section 2.3.7, where mlen = ⌈(log2 p)/8⌉ or mlen = ⌈m/8⌉.
|
|||
// 1.3. Convert the octet string (16 set binary digits)||X to an elliptic curve point R using the
|
|||
// conversion routine specified in Section 2.3.4. If this conversion routine outputs “invalid”, then
|
|||
// do another iteration of Step 1.
|
|||
//
|
|||
// More concisely, what these points mean is to use X as a compressed public key.
|
|||
if (x.gte(P)) { |
|||
// Cannot have point co-ordinates larger than this as everything takes place modulo Q.
|
|||
return null; |
|||
} |
|||
// Compressed keys require you to know an extra bit of data about the y-coord as there are two possibilities.
|
|||
// So it's encoded in the recId.
|
|||
const y = decompressKey(x, (recId & 1) == 1); |
|||
// 1.4. If nR != point at infinity, then do another iteration of Step 1 (callers responsibility).
|
|||
// if (!R.mul(N).isInfinity())
|
|||
// return null
|
|||
// 1.5. Compute e from M using Steps 2 and 3 of ECDSA signature verification.
|
|||
const e = uint256(message); |
|||
// 1.6. For k from 1 to 2 do the following. (loop is outside this function via iterating recId)
|
|||
// 1.6.1. Compute a candidate public key as:
|
|||
// Q = mi(r) * (sR - eG)
|
|||
//
|
|||
// Where mi(x) is the modular multiplicative inverse. We transform this into the following:
|
|||
// Q = (mi(r) * s ** R) + (mi(r) * -e ** G)
|
|||
// Where -e is the modular additive inverse of e, that is z such that z + e = 0 (mod n). In the above equation
|
|||
// ** is point multiplication and + is point addition (the EC group operator).
|
|||
//
|
|||
// We can find the additive inverse by subtracting e from zero then taking the mod. For example the additive
|
|||
// inverse of 3 modulo 11 is 8 because 3 + 8 mod 11 = 0, and -3 mod 11 = 8.
|
|||
const eNeg = negmod(e, N); |
|||
const rInv = invmod(sigr, N); |
|||
const srInv = mulmod(rInv, sigs, N); |
|||
const eNegrInv = mulmod(rInv, eNeg, N); |
|||
const R = AtoJ(x, y); |
|||
const G = AtoJ(GX, GY); |
|||
const qinJ = ecadd(ecmul(G, eNegrInv), ecmul(R, srInv)); |
|||
const p = JtoA(qinJ); |
|||
return { x: toHex(p[0]), y: toHex(p[1]) }; |
|||
} |
|||
|
|||
function ecverify(Qx, Qy, sigr, sigs, z) { |
|||
if (sigs == 0 || sigr == 0) { |
|||
return false; |
|||
} |
|||
const w = invmod(sigs, N); |
|||
const u1 = mulmod(z, w, N); |
|||
const u2 = mulmod(sigr, w, N); |
|||
const Q = AtoJ(Qx, Qy); |
|||
const G = AtoJ(GX, GY); |
|||
const RinJ = ecadd(ecmul(G, u1), ecmul(Q, u2)); |
|||
const r = JtoA(RinJ); |
|||
return sigr.eq(r[0]); |
|||
} |
|||
|
|||
exports.uint256 = uint256; |
|||
exports.ecsign = ecsign; |
|||
exports.ecrecover = ecrecover; |
|||
exports.generatePublicKeyFromPrivateKeyData = |
|||
generatePublicKeyFromPrivateKeyData; |
|||
exports.decompressKey = decompressKey; |
|||
exports.isValidPoint = isValidPoint; |
|||
exports.ecverify = ecverify; |
|||
})(); |
|||
File diff suppressed because it is too large
Loading…
Reference in new issue