2019年4月1日月曜日

開発環境

Programming Bitcoin: Learn How to Program Bitcoin from Scratch (Jimmy Song(著)、O'Reilly Media)のChapter 2(Elliptic Curves)、Point Addition for When x1≠x2、Exercises 5(36)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))

    def test_add_identity(self):
        p1 = Point(0, 0, 0, 0)
        p2 = Point(1, -1, 0, 0)
        inf = Point(None, None, 0, 0)
        self.assertEqual(p1, p1 + inf)
        self.assertEqual(p1, inf + p1)
        self.assertEqual(p2, p2 + inf)
        self.assertEqual(p2, inf + p2)

    def test_add_inverses(self):
        p1 = Point(1, 1, 0, 0)
        p2 = Point(1, -1, 0, 0)
        inf = Point(None, None, 0, 0)
        self.assertEqual(inf, p1 + p2)

    def test_add_when_x_not_equal_to(self):
        p1 = Point(2, 5, 5, 7)
        p2 = Point(-1, -1, 5, 7)
        self.assertEqual(Point(3, -7, 5, 7), p1 + p2)


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):
        self.a = a
        self.b = b
        self.x = x
        self.y = y
        if self.x is None and self.y is None:
            return
        if y ** 2 != x ** 3 + a * x + b:
            raise ValueError(f'({x}, {y}) is not on the curve')

    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
                self.b == other.b)

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

    def __add__(self, other):
        if self.a != other.a or self.b != other.b:
            raise TypeError(f'Points {self}, {other} are no on the same curve')
        if self.x is None:
            return other
        if other.x is None:
            return self
        if self.x == other.x and self.y != other.y:
            return self.__class__(None, None, self.a, self.b)
        if self.x != other.x:
            s = (other.y - self.y) / (other.x - self.x)
            x = s ** 2 - self.x - other.x
            y = s * (self.x - x) - self.y
            return self.__class__(x, y, self.a, self.b)

        raise NotImplementedError('Point.__add__')


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 divide 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 ecc_test.py
..........E...
======================================================================
ERROR: test_add_when_x_not_equal_to (__main__.PointTest)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "ecc_test.py", line 45, in test_add_when_x_not_equal_to
    self.assertEqual(Point(3, -7, 5, 7), p1 + p2)
  File "...\Programming Bitcoin\ch2\ecc.py", line 39, in __add__
    raise NotImplementedError('Point.__add__')
NotImplementedError: Point.__add__

----------------------------------------------------------------------
Ran 14 tests in 0.001s

FAILED (errors=1)

C:\Users\...>py ecc_test.py
..........E...
======================================================================
ERROR: test_add_when_x_not_equal_to (__main__.PointTest)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "ecc_test.py", line 45, in test_add_when_x_not_equal_to
    self.assertEqual(Point(3, -7, 5, 7), p1 + p2)
  File "...\Programming Bitcoin\ch2\ecc.py", line 34, in __add__
    s = (other.y - self.y) / (other.x - other.y)
ZeroDivisionError: division by zero

----------------------------------------------------------------------
Ran 14 tests in 0.001s

FAILED (errors=1)

C:\Users\...>py ecc_test.py
..............
----------------------------------------------------------------------
Ran 14 tests in 0.001s

OK

C:\Users\...>

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