Python - Elliptic Curves - Coding Elliptic Curves in Python - 特殊メソッド、拡張比較、比較演算子、不等号、__ne__メソッド

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)、Coding Elliptic Curves in Python、Exercises 2(27)の解答を求めてみる。

コード

Python 3

ecc_test.py

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


class PointTest(TestCase):
    def setUp(self):
        pass

    def tearDown(self):
        pass

    def test_ne1(self):
        p1 = Point(0, 0, 0, 0)
        p2 = Point(1, 1, 0, 0)
        self.assertNotEqual(p1, p2)

    def test_ne2(self):
        p1 = Point(0, 0, 0, 0)
        p2 = Point(1, -1, 0, 0)
        self.assertNotEqual(p1, p2)

    def test_ne_none(self):
        self.assertNotEqual(Point(0, 0, 0, 0), None)
        self.assertNotEqual(None, Point(0, 0, 0, 0))


class FieldElementTest(TestCase):
    def setUp(self):
        self.a = FieldElement(6, 13)
        self.b = FieldElement(7, 13)
        self.c = FieldElement(6, 17)

    def tearDown(self):
        pass

    def test_ne(self):
        self.assertNotEqual(self.a, None)
        self.assertNotEqual(self.a, self.b)
        self.assertNotEqual(self.a, self.c)

    def test_neg(self):
        self.assertEqual(-self.a, FieldElement(7, 13))

    def test_sub(self):
        self.assertEqual(self.a - self.a, FieldElement(0, 13))
        self.assertEqual(self.a - self.b, FieldElement(12, 13))
        self.assertEqual(self.b - self.a, FieldElement(1, 13))

    def test_mul(self):
        self.assertEqual(FieldElement(3, 13), self.a * self.b)

    def test_mul_exc(self):
        with self.assertRaises(TypeError):
            self.a + self.c

    def test_true_div1(self):
        prime = 31
        actual = FieldElement(3, prime) / FieldElement(24, prime)
        self.assertEqual(FieldElement(4, prime), actual)

    def test_true_div2(self):
        prime = 31
        actual = FieldElement(1, prime) / FieldElement(17, prime) ** 3
        self.assertEqual(FieldElement(29, prime), actual)

    def test_true_div3(self):
        prime = 31
        actual = (
            FieldElement(1, prime) /
            FieldElement(4, prime) ** 4 *
            FieldElement(11, prime)
        )
        self.assertEqual(FieldElement(13, prime), actual)


if __name__ == '__main__':
    main()

ecc.py

#!/usr/bin/env python3
class Point:
    def __init__(self, x, y, a, b):
        if y ** 2 != x ** 3 + a * x + b:
            raise ValueError(f'({x}, {y}) is not on the curve')
        self.a = a
        self.b = b
        self.x = x
        self.y = y

    def __eq__(self, other):
        if other is None:
            return False
        return (self.x == other.x and
                self.y == other.y and
                self.a == other.a and
                elf.b == other.b)

    def __ne__(self, other):
        return not (self == other)


class FieldElement:
    def __init__(self, num: int, prime: int):
        if num < 0 or prime <= num:
            raise ValueError(f'Num {num} not in field range 0 to {prime - 1}')
        self.num = num
        self.prime = prime

    def __repr__(self) -> str:
        return f'FieldElement_{self.prime}({self.num})'

    def __eq__(self, other) -> bool:
        if other is None:
            return False
        return self.num == other.num and self.prime == other.prime

    def __ne__(self, other) -> bool:
        if other is None:
            return True
        return not self == other

    def __neg__(self):
        return self.__class__(-self.num % self.prime, self.prime)

    def __add__(self, other):
        if self.prime != other.prime:
            raise TypeError('Cannot add two numbers in different Fields')
        return self.__class__((self.num + other.num) % self.prime, self.prime)

    def __sub__(self, other):
        if self.prime != other.prime:
            raise TypeError('Cannot subtract two numbers in different Fields')
        return self + (- other)

    def __mul__(self, other):
        if self.prime != other.prime:
            raise TypeError('Cannot multiply two numbers in different Fields')
        return self.__class__((self.num * other.num) % self.prime, self.prime)

    def __pow__(self, exponent):
        exponent %= (self.prime - 1)
        return self.__class__(pow(self.num, exponent, self.prime), self.prime)

    def __truediv__(self, other):
        if self.prime != other.prime:
            raise TypeError('Cannot  two numbers in different Fields')
        num = (self.num *
               pow(other.num, other.prime - 2, other.prime) %
               self.prime)
        prime = self.prime
        return self.__class__(num, prime)

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

C:\Users\...>py -3 ecc_test.py -v
test_mul (__main__.FieldElementTest) ... ok
test_mul_exc (__main__.FieldElementTest) ... ok
test_ne (__main__.FieldElementTest) ... ok
test_neg (__main__.FieldElementTest) ... ok
test_sub (__main__.FieldElementTest) ... ok
test_true_div1 (__main__.FieldElementTest) ... ok
test_true_div2 (__main__.FieldElementTest) ... ok
test_true_div3 (__main__.FieldElementTest) ... ok
test_ne1 (__main__.PointTest) ... ok
test_ne2 (__main__.PointTest) ... ok
test_ne_none (__main__.PointTest) ... ok

----------------------------------------------------------------------
Ran 11 tests in 0.001s

OK

C:\Users\...>