nlitsme

Demonstrate how to calculate the messagehash for the two signatures in this transaction

See ecdsa_demo.py for code showing how to use this to crack the bitcoin secret key.

These are the values extracted from the example transaction below:

pk="04 db d0 c6 15 32 27 9c f7 29 81 c3 58 4f c3 22 16 e0 12 76 99 63 5c 27 89 f5 49 e0 73 0c 05 9b 81 ae 13 30 16 a6 9c 21 e2 3f 18 59 a9 5f 06 d5 2b 7b f1 49 a8 f2 fe 4e 85 35 c8 a8 29 b4 49 c5 ff"
r="d4 7c e4 c0 25 c3 5e c4 40 bc 81 d9 98 34 a6 24 87 51 61 a2 6b f5 6e f7 fd c0 f5 d5 2f 84 3a d1"
s1="44 e1 ff 2d fd 81 02 cf 7a 47 c2 1d 5c 9f d5 70 16 10 d0 49 53 c6 83 65 96 b4 fe 9d d2 f5 3e 3e"

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:

mimoo

Elliptic Curve Cryptography (ECC)

Abstract

ECC is about a group created via:

• a 2-dimension elliptic curve: an equation with unknowns x and y
  • every Elliptic Curve follows this formula: y² + a₁ x y + a₃ y = x³ + a₂ x² + a₄ x + a₆ (for some specified a₁, a₂, a₃, a₄, a₆)
  • actually, it can be shorten to this y² = x³ + a x + b (short weierstrass form) in practice because the characteristic (order of a prime field) 2 and 3 points in prime fields (except for binary (GF(2^x)) and GF(3^x) curves)

• a curve of characteristic 2 (defined over GF(2^x)) can be simplified to y² + xy = x³ + ax² + b

arnobaer

/*
 *  hex2bytes - hex string of unlimited length to a continous block of bytes
 *  Copyright (C) 2018  Bernhard Arnold <bernhard.arnold@cern.ch>
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,

oidualc

#TabsToolbar {
  direction: rtl;
}

#tabbrowser-tabs {
  direction: ltr;
}

.titlebar-buttonbox {
  display: flex;

pachadotdev

# Option 1: Use apt-get

# keys taken from https://software.intel.com/en-us/articles/installing-intel-free-libs-and-python-apt-repo
cd ~/GitHub/r-with-intel-mkl/
wget https://apt.repos.intel.com/intel-gpg-keys/GPG-PUB-KEY-INTEL-SW-PRODUCTS-2019.PUB
apt-key add GPG-PUB-KEY-INTEL-SW-PRODUCTS-2019.PUB

sudo sh -c 'echo deb https://apt.repos.intel.com/mkl all main > /etc/apt/sources.list.d/intel-mkl.list'
sudo apt-get update && sudo apt-get install intel-mkl-64bit

jproney

PicoCTF 2017: ECC2

A 1064CBread Writeup

Problem

In the file handout.txt, we are given the following parameters for an elliptic curve:

• y^2 = x^3 + A*x + B mod M -- the curve equation
• M -- the modulus of the curve

mdonkers

#!/usr/bin/env python3
"""
License: MIT License
Copyright (c) 2023 Miel Donkers

Very simple HTTP server in python for logging requests
Usage::
    ./server.py [<port>]
"""
from http.server import BaseHTTPRequestHandler, HTTPServer

web-hat

<?php

function whpp_track_post_views($post_id) {
    if (!is_single())
        return;
    if (empty($post_id)) {
        global $post;
        $post_id = $post->ID;
    }
    whpp_set_post_views($post_id);

Brainiarc7

Building Tensorflow from source on Ubuntu 16.04LTS for maximum performance:

TensorFlow is now distributed under an Apache v2 open source license on GitHub.

On Ubuntu 16.04LTS+:

Step 1. Install NVIDIA CUDA:

To use TensorFlow with NVIDIA GPUs, the first step is to install the CUDA Toolkit as shown: