paulmillr

### noble-secp256k1.py - MIT License (c) Paul Miller (paulmillr.com) ###

# initial:  0.177 / 36ms
# jacobian: 0.111 / 3.7ms
# + constant-time: 4ms
# + constant-time + precomputes: 2.6ms

class Curve:
    # Params: a, b
    a = 0

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BLS Signature for Busy People

Summary

• BLS stands for

  • Barreto-Lynn-Scott: BLS12, a Pairing Friendly Elliptic Curve.
  • Boneh-Lynn-Shacham: A Signature Scheme.

• Signature Aggregation

• It is possible to verify n aggregate signatures on the same message with just 2 pairings instead of n+1.

paulmillr

// PART 1
// secp256k1 curve parameters. Verify using https://www.secg.org/sec2-v2.pdf
const P = 2n ** 256n - 0x1000003d1n; // curve's field prime
const N = 2n ** 256n - 0x14551231950b75fc4402da1732fc9bebfn; // curve (group) order
const CURVE = { P: P, n: N, a: 0n, b: 7n };
const err = (m = ''): never => {
  throw new Error(m);
}; // error helper
const M = (a: bigint, b: bigint = P) => {
  // mod division

paulmillr

---------- Forwarded message ----------

From: Mark S. Miller <erights@google.com>
Date: Tue, Nov 16, 2010 at 3:44 PM
Subject: "Future of Javascript" doc from our internal "JavaScript Summit"
last week
To: javascript-standard@google.com

paulmillr

Hal Finney's explanation of secp256k1 "efficiently computable endomorphism" parameters used secp256k1 libraries, archived from source.

The same optimization could be applied to any Koblitz curve (e.g. Short Weistrass curve with a=0).

---

I implemented an optimized ECDSA verify for the secp256k1 curve, based on pages 125-129 of the Guide to Elliptic Curve Cryptography, by Hankerson, Menezes and Vanstone. I own the book but I also found a PDF on a Russian site which is more convenient.

secp256k1 uses the following prime for its x and y coordinates:

paulmillr

Fun parts of developing noble-hashes and scure-base

• Base58 is quadratic (O(n^2)). Basically you can’t encode 1MB of data with it. This has been found with our DoS tests, which we employ for scure-base and noble-hashes. See README for more details
• Hashes are additionally tested against huge multi-gig inputs, scrypt/pbkdf2 are tested against all possible combination of options. They take 2 hours to run on a decent machine
• Hashes are actually faster than many wasm alternatives. A single sha256 hashing of 32 bytes of data takes 888 nanoseconds on mac with M1
• The last fact is extremely remarkable, because we do not employ loop unrolls in the code. A loop unroll is when you’re writing code which could have been executed in loop like for (let step = 0; step < 64), but instead, you’re writing every iteration step-by-step. Which incr

paulmillr

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paulmillr

export { box_keyPair, sign_detached_verify, sign, box, box_open } from 'tweetnacl-ts';