《区块链编程》-第二章

《区块链编程》第二章

椭圆曲线

练习1

p32

代码实现

def onCurve(x, y):
    return y**2 == x**3 + 5 * x + 7


if __name__ == '__main__':
    print(onCurve(2, 4))
    print(onCurve(-1, -1))
    print(onCurve(18, 77))
    print(onCurve(5, 7))

测试

False
True
True
False
[Finished in 237ms]

练习2

p32

代码实现

class Point():
    def __init__(self, x, y, a, b):
        self.x = x
        self.y = y
        self.a = a
        self.b = b
        if self.y ** 2 != self.x ** 3 + a * x + b:
            raise ValueError('({},{}) is not on the curve'.format(x, y))

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y \
            and self.a == other.a and self.b == other.b

    def __ne__(self, other):
        # this is my answer,but it is error. oh no, I am a rookie
        # oh, I found my error, the function __eq__() requires only one parameter
        # but I give it two. "==" and self.__eq__(..) is equivalent.
        # return not self.__eq__(self, other)
        return not (self == other)

if __name__ == '__main__':
    a = Point(-1, -1, 5, 7)
    b = Point(-1, -2, 5, 7)
    print(a != b)

测试

-1，-2 不在曲线上， 报错。

Traceback (most recent call last):
  File "temp.py", line 31, in <module>
    b = Point(-1, -2, 5, 7)
  File "temp.py", line 15, in __init__
    raise ValueError('({},{}) is not on the curve'.format(x, y))
ValueError: (-1,-2) is not on the curve
[Finished in 237ms]

实现加法恒等元的点加法运算

p37

代码实现

# -*- coding: utf-8 -*-
# @Author: 从化北(喵星人)
# @Date:   2021-12-20 21:31:48
# @Last Modified by:   从化北
# @Last Modified time: 2021-12-20 23:06:44


class Point():
    def __init__(self, x, y, a, b):
        self.x = x
        self.y = y
        self.a = a
        self.b = b
        # if the point is infinity point , return null
        if self.x is None and self.y is None:
            return
        if self.y ** 2 != self.x ** 3 + a * x + b:
            raise ValueError('({},{}) is not on the curve'.format(x, y))

    def __repr__(self):
        if self.x == None:
            return "Point(infinity)"
        return "Point({}, {})_{}_{}".format(self.x, self.y, self.a, self.b)

    def __add__(self, other):
        if self.a != other.a or self.b != other.b:
            raise TypeError('Points {}, {} are not on the same curve.'.format(self, other))
        # if self.x is None, then the self point is infinity point.
        if self.x is None:
            return other
        if other.x is None:
            return self
        # add this sentence for a straight line that can't reach zero point.
        # this is temp programme
        return self.__class__(None, None, self.a, self.b)

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y \
            and self.a == other.a and self.b == other.b

    def __ne__(self, other):
        # this is my answer,but it is error. oh no, I am a rookie
        # oh, I found my error, the function __eq__() requires only one parameter
        # but I give it two. "==" and self.__eq__(..) is equivalent.
        # return not self.__eq__(self, other)
        return not (self == other)


def onCurve(x, y):
    return y**2 == x**3 + 5 * x + 7


if __name__ == '__main__':
    a = Point(-1, -1, 5, 7)
    b = Point(-1, 1, 5, 7)
    inf = Point(None, None, 5, 7)
    print(a + inf)
    print(a + b)

测试

Point(-1, -1)_5_7
Point(infinity)
[Finished in 406ms]

练习3

p38

代码实现

class Point():
...
        if self.x == other.x and self.y != other.y:
            return self.__class__(None, None, self.a, self.b)

练习4

p40

代码实现

if __name__ == '__main__':
    x1, y1 = 2, 5
    x2, y2 = -1, -1
    s = (y2 - y1) / (x2 - x1)
    x3 = s ** 2 - x1 - x2
    y3 = s * (x1 - x3) - y1
    print("({}, {})".format(x3, y3))

运行结果

(3.0, -7.0)
[Finished in 250ms]

练习5

p40
实现x1 ！= x2 时的点加法

代码实现

class Point():
	...
	def __add__(self, other):
	...
        if self.x != other.x:
            s = (other.y - self.y) / (other.x - self.x)
            x3 = s**2 - self.x - other.x
            y3 = s * (self.x - x3) - self.y
            return self.__class__(x3, y3, self.a, self.b)
if __name__ == '__main__':
    a = Point(x=3, y=7, a=5, b=7)
    b = Point(x=-1, y=-1, a=5, b=7)
    print(a + b, Point(x=2, y=-5, a=5, b=7))

运行结果

Point(2.0, -5.0)_5_7 Point(2, -5)_5_7
[Finished in 270ms]

练习6

p42
注意： 书中这里给的点是（-1，-1）

代码实现

if __name__ == '__main__':
    a, b = 5, 7
    x1, y1 = -1, -1
    s = (3 * x1**2 + a) / (2 * y1)
    x3 = s ** 2 - 2 * x1
    y3 = s * (x1 - x3) - y1
    print("({}, {})".format(x3, y3))

运行结果

(18.0, 77.0)
[Finished in 259ms]

练习7

p42
实现p1 = p2 时的点加法

代码实现

class Point():
	...
	def __add__(self, other):
	...
        # this is for P1 = P2
        if self.x == other.x and self.y == other.y:
            s = (3 * self.x**2 + self.a) / (2 * self.y)
            x3 = s ** 2 - 2 * self.x
            y3 = s * (self.x - x3) - self.y
            return self.__class__(x3, y3, self.a, self.b)
if __name__ == '__main__':
    a = Point(x=-1, y=-1, a=5, b=7)
    b = Point(x=-1, y=-1, a=5, b=7)
    print(a + b)

运行结果

Point(18.0, 77.0)_5_7
[Finished in 251ms]

本章完整代码

这里为了将所有代码都放在一个文件中， 所以相比参考答案做了一点修改

# -*- coding: utf-8 -*-
# @Author: 从化北(喵星人)
# @Date:   2021-12-20 21:31:48
# @Last Modified by:   从化北
# @Last Modified time: 2021-12-21 11:21:59
from unittest import TestSuite, TextTestRunner, TestCase


def run(test):
    suite = TestSuite()
    suite.addTest(test)
    TextTestRunner().run(suite)


class Point():
    def __init__(self, x, y, a, b):
        self.x = x
        self.y = y
        self.a = a
        self.b = b
        # if the point is infinity point , return null
        if self.x is None and self.y is None:
            return
        if self.y ** 2 != self.x ** 3 + a * x + b:
            raise ValueError('({},{}) is not on the curve'.format(x, y))

    def __repr__(self):
        if self.x == None:
            return "Point(infinity)"
        return "Point({}, {})_{}_{}".format(self.x, self.y, self.a, self.b)

    def __add__(self, other):
        # premise verification
        if self.a != other.a or self.b != other.b:
            raise TypeError('Points {}, {} are not on the same curve.'.format(self, other))

        # drop this notes： if self.x is None, then the self point is infinity point.
        # this is in order to have an infinity point situation
        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)

        # this is for P1 = P2
        if self.x == other.x and self.y == other.y:
            s = (3 * self.x**2 + self.a) / (2 * self.y)
            x3 = s ** 2 - 2 * self.x
            y3 = s * (self.x - x3) - self.y
            return self.__class__(x3, y3, self.a, self.b)
        # this is to deal with a special case that is P1 = P2 and there y coordinate is 0
        if self == other and self.y == 0 * self.x:
            return self.__class__(None, None, self.a, self.b)
        # this is for x1 ！= x2
        if self.x != other.x:
            s = (other.y - self.y) / (other.x - self.x)
            x3 = s**2 - self.x - other.x
            y3 = s * (self.x - x3) - self.y
            return self.__class__(x3, y3, self.a, self.b)

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y \
            and self.a == other.a and self.b == other.b

    def __ne__(self, other):
        # this is my answer,but it is error. oh no, I am a rookie
        # oh, I found my error, the function __eq__() requires only one parameter
        # but I give it two. "==" and self.__eq__(..) is equivalent.
        # return not self.__eq__(self, other)
        return not (self == other)


class PointTest(TestCase):

    def test_ne(self):
        a = Point(x=3, y=-7, a=5, b=7)
        b = Point(x=18, y=77, a=5, b=7)
        self.assertTrue(a != b)
        self.assertFalse(a != a)

    def test_add0(self):
        a = Point(x=None, y=None, a=5, b=7)
        b = Point(x=2, y=5, a=5, b=7)
        c = Point(x=2, y=-5, a=5, b=7)
        self.assertEqual(a + b, b)
        self.assertEqual(b + a, b)
        self.assertEqual(b + c, a)

    def test_add1(self):
        a = Point(x=3, y=7, a=5, b=7)
        b = Point(x=-1, y=-1, a=5, b=7)
        self.assertEqual(a + b, Point(x=2, y=-5, a=5, b=7))

    def test_add2(self):
        a = Point(x=-1, y=-1, a=5, b=7)
        self.assertEqual(a + a, Point(x=18, y=77, a=5, b=7))


def onCurve(x, y):
    return y**2 == x**3 + 5 * x + 7


if __name__ == '__main__':
    run(PointTest("test_ne"))
    run(PointTest("test_add0"))
    run(PointTest("test_add1"))
    run(PointTest("test_add2"))

测试结果

.
----------------------------------------------------------------------
Ran 1 test in 0.000s

OK
.
----------------------------------------------------------------------
Ran 1 test in 0.000s

OK
.
----------------------------------------------------------------------
Ran 1 test in 0.000s

OK
.
----------------------------------------------------------------------
Ran 1 test in 0.000s

OK
[Finished in 287ms]