Python - Elliptic Curve Cryptography - Coding Mathematical Groups - closure、order

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 3(Elliptic Curve Cryptography)、Mathematical Groups、Exercises 5(56)の解答を求めてみる。

コード

Python 3

#!/usr/bin/env python3
from ecc import FieldElement, Point

prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
x = FieldElement(15, prime)
y = FieldElement(86, prime)
p = Point(x, y, a, b)
t = p
order = 1

print(t)

while t != Point(None, None, a, b):
    t += p
    print(t)
    order += 1

print(f'order: {order}')

print(t + p)

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

C:\Users\...>py sample5.py
Point(15,86)_0_7 FieldElement(223)
Point(139,86)_0_7 FieldElement(223)
Point(69,137)_0_7 FieldElement(223)
Point(69,86)_0_7 FieldElement(223)
Point(139,137)_0_7 FieldElement(223)
Point(15,137)_0_7 FieldElement(223)
Point(infinity)
order: 7
Point(15,86)_0_7 FieldElement(223)

C:\Users\...>