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).

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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:

ledbit

'use strict';


function writeUTF8ToBuf(str, buf, off=0) {
   for (let i=0; i < str.length; i++) {
       const charcode = str.charCodeAt(i);
       if (charcode < 0x80) buf[off++] = charcode;
       else if (charcode < 0x800) {
         buf[off++] = 0xc0 | (charcode >> 6); 
         buf[off++] = 0x80 | (charcode & 0x3f);

roramigator

'use strict';

/**
 * TTTTTTTTTTTTTTTTTTTTTTTHHHHHHHHH     HHHHHHHHHEEEEEEEEEEEEEEEEEEEEEE
 * T:::::::::::::::::::::TH:::::::H     H:::::::HE::::::::::::::::::::E
 * T:::::::::::::::::::::TH:::::::H     H:::::::HE::::::::::::::::::::E
 * T:::::TT:::::::TT:::::THH::::::H     H::::::HHEE::::::EEEEEEEEE::::E
 * TTTTTT  T:::::T  TTTTTT  H:::::H     H:::::H    E:::::E       EEEEEE
 *         T:::::T          H:::::H     H:::::H    E:::::E
 *         T:::::T          H::::::HHHHH::::::H    E::::::EEEEEEEEEE