Python - Elliptic Curves - Coding Point Addition for When P1 = P2

Programming Bitcoin
Learn How to Program Bitcoin from Scratch
楽天ブックス(Kobo) 紀伊國屋書店(Kinoppy)

開発環境

• macOS Mojave - Apple (OS)
• Emacs (Text Editor)
• Windows 10 Pro (OS)
• Visual Studio Code (Text Editor)
• Python 3.7 (プログラミング言語)

Programming Bitcoin: Learn How to Program Bitcoin from Scratch (Jimmy Song(著)、O'Reilly Media)のChapter 2(Elliptic Curves)、Point Addition for When P1 = P2、Exercises 6(38)の解答を求めてみる。

コード

Python 3

#!/usr/bin/env python3
def slope(p1, a):
    x1, y1 = p1
    return (3 * x1 ** 2 + a) / (2 * y1)


def add(p1, a, b):
    x1, y1 = p1
    s = slope(p1, a)
    x3 = s ** 2 - x1 - x1
    y3 = s * (x1 - x3) - y1
    return (x3, y3)


p1 = (-1, -1)
p3 = add(p1, 5, 7)
x3, y3 = p3

for o in [p3, y3 ** 2 == x3 ** 3 + 5 * x3 + 7]:
    print(o)

入出力結果(cmd(コマンドプロンプト)、Terminal、Jupyter(IPython))

C:\Users\...>py sample6.py
(18.0, 77.0)

C:\Users\...>