Last active
December 16, 2018 10:58
-
-
Save wilsonianb/3e7354ee08ad2a9325c2b311c96f7a65 to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
const brorand = require('brorand') | |
const elliptic = require('elliptic') | |
const Ed25519 = elliptic.eddsa('ed25519') | |
const hashjs = require('hash.js') | |
function hash(message) { | |
return hashjs.sha512().update(message).digest().slice(0, 32) | |
} | |
function getL(Xs) { | |
return Ed25519.hashInt.apply(Ed25519, Xs) | |
} | |
function getAggregatePublicKey(L, Xs) { | |
let X = Ed25519.decodePoint(Xs[0]).mul(Ed25519.hashInt(L, Xs[0])) | |
for (let i=1; i<Xs.length; i++) { | |
X = X.add(Ed25519.decodePoint(Xs[i]).mul(Ed25519.hashInt(L, Xs[i]))) | |
} | |
return Ed25519.encodePoint(X) | |
} | |
function getR(Rs) { | |
let R = Rs[0] | |
for (let i=1; i<Rs.length; i++) { | |
R = R.add(Rs[i]) | |
} | |
return Ed25519.encodePoint(R) | |
} | |
function getSi(ri, X, R, m, L, xi, Xi) { | |
const message = elliptic.utils.parseBytes(m); | |
var s_ = Ed25519.hashInt(R, X, message) | |
.mul(Ed25519.hashInt(L, Xi)) | |
.mul(xi) | |
var si = ri.add(s_).umod(Ed25519.curve.n) | |
return Ed25519.makeSignature({ R: Ed25519.decodePoint(R), S: si, Rencoded: R }) | |
} | |
function combine(sigs, R) { | |
let S = sigs[0].S() | |
for (let i=1; i<sigs.length; i++) { | |
S = S.add(sigs[i].S()) | |
} | |
return Ed25519.makeSignature({ R: Ed25519.decodePoint(R), S: S, Rencoded: R }) | |
} | |
// https://blockstream.com/2018/01/23/musig-key-aggregation-schnorr-signatures.html | |
const n = 7 | |
let xs = [] | |
let Xs = [] | |
for (let i=0; i<n; i++) { | |
const kp = Ed25519.keyFromSecret(hash(brorand(16))) | |
xs.push(kp.priv()) | |
Xs.push(kp.pubBytes()) | |
} | |
// Call L = H(X1,X2,…) | |
const L = getL(Xs) | |
// Call X the sum of all H(L,Xi)Xi | |
const X = getAggregatePublicKey(L, Xs) | |
// Each signer chooses a random nonce ri, and shares Ri = riG with the other signers | |
let rs = [] | |
let Rs = [] | |
let ts = [] | |
for (let i=0; i<n; i++) { | |
const kp = Ed25519.keyFromSecret(hash(brorand(16))) | |
rs.push(kp.priv()) | |
Rs.push(kp.pub()) | |
ts.push(Ed25519.hashInt(kp.pub())) | |
} | |
// Call R the sum of the Ri points | |
const R = getR(Rs) | |
const msg = Ed25519.hashInt('howdy') | |
// Each signer computes si = ri + H(X,R,m)H(L,Xi)xi | |
let sigs = [] | |
for (let i=0; i<n; i++) { | |
sigs.push(getSi(rs[i], X, R, msg, L, xs[i], Xs[i])) | |
} | |
// The final signature is (R,s) where s is the sum of the si values | |
const s = combine(sigs, R) | |
// Verification satisfies sG = R + H(X,R,m)X | |
console.log(Ed25519.verify(msg, s, X)) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment