ecc.py

from binascii import hexlify, unhexlify
from io import BytesIO
from random import randint
from unittest import TestCase

from helper import double_sha256, encode_base58, encode_base58_checksum, hash160, decode_base58_checksum, big_endian_to_int


class FieldElement:

    def __init__(self, num, prime):
        self.num = num
        self.prime = prime
        if self.num >= self.prime or self.num < 0:
            error = 'Num {} not in field range 0 to {}'.format(
                self.num, self.prime-1)
            raise RuntimeError(error)

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

    def __ne__(self, other):
        if other is None:
            return True
        return self.num != other.num or self.prime != other.prime

    def __repr__(self):
        return 'FieldElement_{}({})'.format(self.prime, self.num)

    def __add__(self, other):
        if self.prime != other.prime:
            raise RuntimeError('Primes must be the same')
        # self.num and other.num are the actual values
        num = (self.num + other.num) % self.prime
        # self.prime is what you'll need to mod against
        prime = self.prime
        # You need to return an element of the same class
        # use: self.__class__(num, prime)
        return self.__class__(num, prime)

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

    def __sub__(self, other):
        if self.prime != other.prime:
            raise RuntimeError('Primes must be the same')
        # self.num and other.num are the actual values
        num = (self.num - other.num) % self.prime
        # self.prime is what you'll need to mod against
        prime = self.prime
        # You need to return an element of the same class
        # use: self.__class__(num, prime)
        return self.__class__(num, prime)

    def __mul__(self, other):
        if self.prime != other.prime:
            raise RuntimeError('Primes must be the same')
        # self.num and other.num are the actual values
        num = (self.num * other.num) % self.prime
        # self.prime is what you'll need to mod against
        prime = self.prime
        # You need to return an element of the same class
        # use: self.__class__(num, prime)
        return self.__class__(num, prime)

    def __rmul__(self, coefficient):
        num = (self.num * coefficient) % self.prime
        return self.__class__(num=num, prime=self.prime)

    def __pow__(self, n):
        # remember fermat's little theorem:
        # self.num**(p-1) % p == 1
        # you might want to use % operator on n
        prime = self.prime
        num = pow(self.num, n % (prime-1), prime)
        return self.__class__(num, prime)

    def __truediv__(self, other):
        if self.prime != other.prime:
            raise RuntimeError('Primes must be the same')
        # self.num and other.num are the actual values
        num = (self.num * pow(other.num, self.prime - 2, self.prime)) % self.prime
        # self.prime is what you'll need to mod against
        prime = self.prime
        # use fermat's little theorem:
        # self.num**(p-1) % p == 1
        # this means:
        # 1/n == pow(n, p-2, p)
        # You need to return an element of the same class
        # use: self.__class__(num, prime)
        return self.__class__(num, prime)



class FieldElementTest(TestCase):

    def test_add(self):
        a = FieldElement(2, 31)
        b = FieldElement(15, 31)
        self.assertEqual(a+b, FieldElement(17, 31))
        a = FieldElement(17, 31)
        b = FieldElement(21, 31)
        self.assertEqual(a+b, FieldElement(7, 31))

    def test_neg(self):
        a = FieldElement(2, 31)
        b = -a
        self.assertEqual(a+b, FieldElement(0, 31))

    def test_sub(self):
        a = FieldElement(29, 31)
        b = FieldElement(4, 31)
        self.assertEqual(a-b, FieldElement(25, 31))
        a = FieldElement(15, 31)
        b = FieldElement(30, 31)
        self.assertEqual(a-b, FieldElement(16, 31))

    def test_mul(self):
        a = FieldElement(24, 31)
        b = FieldElement(19, 31)
        self.assertEqual(a*b, FieldElement(22, 31))

    def test_rmul(self):
        a = FieldElement(24, 31)
        b = 2
        self.assertEqual(b*a, a+a)

    def test_pow(self):
        a = FieldElement(17, 31)
        self.assertEqual(a**3, FieldElement(15, 31))
        a = FieldElement(5, 31)
        b = FieldElement(18, 31)
        self.assertEqual(a**5 * b, FieldElement(16, 31))

    def test_div(self):
        a = FieldElement(3, 31)
        b = FieldElement(24, 31)
        self.assertEqual(a/b, FieldElement(4, 31))
        a = FieldElement(17, 31)
        self.assertEqual(a**-3, FieldElement(29, 31))
        a = FieldElement(4, 31)
        b = FieldElement(11, 31)
        self.assertEqual(a**-4*b, FieldElement(13, 31))



class Point:

    def __init__(self, x, y, a, b):
        self.a = a
        self.b = b
        self.x = x
        self.y = y
        # x being None and y being None represents the point at infinity
        # Check for that here since the equation below won't make sense
        # with None values for both.
        if self.x is None and self.y is None:
            return
        # make sure that the elliptic curve equation is satisfied
        # y**2 == x**3 + a*x + b
        if self.y**2 != self.x**3 + a*x + b:
        # if not, throw a RuntimeError
            raise RuntimeError('({}, {}) is not on the curve'.format(self.x, self.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):
        return self.x != other.x or self.y != other.y \
            or self.a != other.a or self.b != other.b

    def __sub__(self, other):
        return self + (-other)

    def __neg__(self):
        return self.__class__(None, None, self.a, self.b) if self.x is None else self.__class__(self.x, -self.y, self.a, self.b)

    def __repr__(self):
        if self.x is None:
            return 'Point(infinity)'
        else:
            return 'Point({},{})'.format(self.x, self.y)

    def __add__(self, other):
        if self.a != other.a or self.b != other.b:
            raise RuntimeError('Points {}, {} are not on the same curve'.format(self, other))
        # Case 0.0: self is the point at infinity, return other
        if self.x is None:
            return other
        # Case 0.1: other is the point at infinity, return self
        if other.x is None:
            return self

        # Case 1: self.x == other.x, self.y != other.y
        # Result is point at infinity
        if self.x == other.x and self.y != other.y:
        # Remember to return an instance of this class:
        # self.__class__(x, y, a, b)
            return self.__class__(None, None, self.a, self.b)
 
        # Case 2: self.x != other.x
        if self.x != other.x:
        # Formula (x3,y3)==(x1,y1)+(x2,y2)
        # s=(y2-y1)/(x2-x1)
            s = (other.y - self.y) / (other.x - self.x)
        # x3=s**2-x1-x2
            x = s**2 - self.x - other.x
        # y3=s*(x1-x3)-y1
            y = s*(self.x-x) - self.y
        # Remember to return an instance of this class:
        # self.__class__(x, y, a, b)
            return self.__class__(x, y, self.a, self.b)

        # Case 3: self.x == other.x, self.y == other.y
        else:
        # Formula (x3,y3)=(x1,y1)+(x1,y1)
        # s=(3*x1**2+a)/(2*y1)
            s = (3*self.x**2 + self.a) / (2*self.y)
        # x3=s**2-2*x1
            x = s**2 - 2*self.x
        # y3=s*(x1-x3)-y1
            y = s*(self.x-x) - self.y
        # Remember to return an instance of this class:
        # self.__class__(x, y, a, b)
            return self.__class__(x, y, self.a, self.b)

    def __rmul__(self, coefficient):
        # rmul calculates coefficient * self
        # implement the naive way:
        # start product from 0 (point at infinity)
        # use: self.__class__(None, None, a, b)
        product = self.__class__(None, None, self.a, self.b)
        # loop coefficient times
        # use: for _ in range(coefficient):
        for _ in range(coefficient):
            # keep adding self over and over
            product += self
        # return the product
        return product
        # Extra Credit:
        # a more advanced technique uses point doubling
        # find the binary representation of coefficient
        # keep doubling the point and if the bit is there for coefficient
        # add the current.
        # remember to return an instance of the class


class PointTest(TestCase):

    def test_on_curve(self):
        with self.assertRaises(RuntimeError):
            Point(x=-2, y=4, a=5, b=7)
        # these should not raise an error
        Point(x=3, y=-7, a=5, b=7)
        Point(x=18, y=77, a=5, b=7)

    def test_neg(self):
        p = Point(x=3, y=-7, a=5, b=7)
        q = -p
        self.assertEqual(p+q, Point(None,None,5,7))

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


class ECCTest(TestCase):

    def test_on_curve(self):
        # tests the following points whether they are on the curve or not
        # on curve y^2=x^3-7 over F_223:
        # (192,105) (17,56) (200,119) (1,193) (42,99)
        # the ones that aren't should raise a RuntimeError
        prime = 223
        a = FieldElement(0, prime)
        b = FieldElement(7, prime)
        
        valid_points = ((192,105), (17,56), (1,193))
        invalid_points = ((200,119), (42,99))
        
        # iterate over valid points
        for x_raw, y_raw in valid_points:
            # Initialize points this way:
            # x = FieldElement(192, prime)
            # y = FieldElement(105, prime)
            # Point(x, y, a, b)
            x = FieldElement(x_raw, prime)
            y = FieldElement(y_raw, prime)
            # Creating the point should not result in an error
            Point(x, y, a, b)

        # iterate over invalid points
        for x_raw, y_raw in invalid_points:
            # Initialize points this way:
            # x = FieldElement(192, prime)
            # y = FieldElement(105, prime)
            # Point(x, y, a, b)
            x = FieldElement(x_raw, prime)
            y = FieldElement(y_raw, prime)
            # check that creating the point results in a RuntimeError
            # with self.assertRaises(RuntimeError):
            #     Point(x, y, a, b)
            with self.assertRaises(RuntimeError):
                Point(x, y, a, b)

    def test_add1(self):
        # tests the following additions on curve y^2=x^3-7 over F_223:
        # (192,105) + (17,56)
        # (47,71) + (117,141)
        # (143,98) + (76,66)
        prime = 223
        a = FieldElement(0, prime)
        b = FieldElement(7, prime)

        additions = (
            # (x1, y1, x2, y2, x3, y3)         
            (192, 105, 17, 56, 170, 142),
            (47, 71, 117, 141, 60, 139),
            (143, 98, 76, 66, 47, 71),
        )
        # iterate over the additions
        for x1_raw, y1_raw, x2_raw, y2_raw, x3_raw, y3_raw in additions:
            # Initialize points this way:
            # x = FieldElement(192, prime)
            # y = FieldElement(105, prime)
            # p1 = Point(x, y, a, b)
            x1 = FieldElement(x1_raw, prime)
            y1 = FieldElement(y1_raw, prime)
            p1 = Point(x1, y1, a, b)
            x2 = FieldElement(x2_raw, prime)
            y2 = FieldElement(y2_raw, prime)
            p2 = Point(x2, y2, a, b)
            x3 = FieldElement(x3_raw, prime)
            y3 = FieldElement(y3_raw, prime)
            p3 = Point(x3, y3, a, b)
            # check that p1 + p2 == p3
            self.assertEqual(p1+p2, p3)

    def test_rmul(self):
        # tests the following scalar multiplications
        # 2*(192,105)
        # 2*(143,98)
        # 2*(47,71)
        # 4*(47,71)
        # 8*(47,71)
        # 21*(47,71)
        prime = 223
        a = FieldElement(0, prime)
        b = FieldElement(7, prime)

        multiplications = (
            # (coefficient, x1, y1, x2, y2)
            (2, 192, 105, 49, 71),
            (2, 143, 98, 64, 168),
            (2, 47, 71, 36, 111),
            (4, 47, 71, 194, 51),
            (8, 47, 71, 116, 55),
            (21, 47, 71, None, None),
        )

        # iterate over the multiplications
        for s, x1_raw, y1_raw, x2_raw, y2_raw in multiplications:
            # Initialize points this way:
            # x = FieldElement(192, prime)
            # y = FieldElement(105, prime)
            # p = Point(x, y, a, b)
            x1 = FieldElement(x1_raw, prime)
            y1 = FieldElement(y1_raw, prime)
            p1 = Point(x1, y1, a, b)
            # initialize the second point based on whether it's the point at infinity
            if x2_raw is None:
                p2 = Point(None, None, a, b)
            else:
                x2 = FieldElement(x2_raw, prime)
                y2 = FieldElement(y2_raw, prime)
                p2 = Point(x2, y2, a, b)
        
            # check that the product is equal to the expected point
            self.assertEqual(s*p1, p2)        


A = 0
B = 7
P = 2**256 - 2**32 - 977
N = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141


class S256Field(FieldElement):

    def __init__(self, num, prime=None):
        super().__init__(num=num, prime=P)

    def hex(self):
        return '{:x}'.format(self.num).zfill(64)

    def __repr__(self):
        return self.hex()

    def sqrt(self):
        return self**((P+1)//4)


class S256Point(Point):
    bits = 256


    def __init__(self, x, y, a=None, b=None):
        a, b = S256Field(A), S256Field(B)
        if x is None:
            super().__init__(x=None, y=None, a=a, b=b)
        elif type(x) == int:
            super().__init__(x=S256Field(x), y=S256Field(y), a=a, b=b)
        else:
            super().__init__(x=x, y=y, a=a, b=b)

    def __repr__(self):
        if self.x is None:
            return 'Point(infinity)'
        else:
            return 'Point({},{})'.format(self.x, self.y)

    def __rmul__(self, coefficient):
        coefficient %= N
        # current will undergo binary expansion
        current = self
        # result is what we return, starts at 0
        result = S256Point(None, None)
        # we double 256 times and add where there is a 1 in the binary
        # representation of coefficient
        for i in range(coefficient.bit_length()):
            if coefficient & 1:
                result += current
            current += current
            # we shift the coefficient to the right
            coefficient >>= 1
        return result

    def sec(self, compressed=True):
        # returns the binary version of the sec format, NOT hex
        # if compressed, starts with b'\x02' if self.y.num is even, b'\x03' if self.y is odd
        # then self.x.num
        # remember, you have to convert self.x.num/self.y.num to binary (some_integer.to_bytes(32, 'big'))
        if compressed:
            if self.y.num % 2 == 0:
                return b'\x02' + self.x.num.to_bytes(32, 'big')
            else:
                return b'\x03' + self.x.num.to_bytes(32, 'big')
        else:
        # if non-compressed, starts with b'\x04' followod by self.x and then self.y
            return b'\x04' + self.x.num.to_bytes(32, 'big') + self.y.num.to_bytes(32, 'big')

    def address(self, compressed=True, testnet=False):
        '''Returns the address string'''
        # get the sec
        sec = self.sec(compressed)
        # hash160 the sec
        h160 = hash160(sec)
        # raw is hash 160 prepended w/ b'\x00' for mainnet, b'\x6f' for testnet
        if testnet:
            prefix = b'\x6f'
        else:
            prefix = b'\x00'
        raw = prefix + h160
        # checksum is first 4 bytes of double_sha256 of raw
        checksum = double_sha256(raw)[:4]
        # encode_base58 the raw + checksum
        address = encode_base58(raw+checksum)
        # return as a string, you can use .decode('ascii') to do this.
        return address.decode('ascii')

    def verify(self, z, sig):
        # remember sig.r and sig.s are the main things we're checking
        # remember 1/s = pow(s, N-2, N)
        s_inv = pow(sig.s, N-2, N)
        # u = z / s
        u = z * s_inv % N
        # v = r / s
        v = sig.r * s_inv % N
        # u*G + v*P should have as the x coordinate, r
        total = u*G + v*self
        return total.x.num == sig.r

    @classmethod
    def parse(self, sec_bin):
        '''returns a Point object from a compressed sec binary (not hex)
        '''
        if sec_bin[0] == 4:
            x = int(hexlify(sec_bin[1:33]), 16)
            y = int(hexlify(sec_bin[33:65]), 16)
            return S256Point(x=x, y=y)
        is_even = sec_bin[0] == 2
        x = S256Field(int(hexlify(sec_bin[1:]), 16))
        # right side of the equation y^2 = x^3 + 7
        alpha = x**3 + S256Field(B)
        # solve for left side
        beta = alpha.sqrt()
        if beta.num % 2 == 0:
            even_beta = beta
            odd_beta = S256Field(P - beta.num)
        else:
            even_beta = S256Field(P - beta.num)
            odd_beta = beta
        if is_even:
            return S256Point(x, even_beta)
        else:
            return S256Point(x, odd_beta)

S256Point.inf = S256Point(None, None)


G = S256Point(
    0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
    0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)


class S256Test(TestCase):

    def test_order(self):
        point = N*G
        self.assertIsNone(point.x)

    def test_pubpoint(self):
        # write a test that tests the public point for the following
        points = (
            # secret, x, y
            (7, 0x5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc, 0x6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da),
            (1485, 0xc982196a7466fbbbb0e27a940b6af926c1a74d5ad07128c82824a11b5398afda, 0x7a91f9eae64438afb9ce6448a1c133db2d8fb9254e4546b6f001637d50901f55),
            (2**128, 0x8f68b9d2f63b5f339239c1ad981f162ee88c5678723ea3351b7b444c9ec4c0da, 0x662a9f2dba063986de1d90c2b6be215dbbea2cfe95510bfdf23cbf79501fff82),
            (2**240+2**31, 0x9577ff57c8234558f293df502ca4f09cbc65a6572c842b39b366f21717945116, 0x10b49c67fa9365ad7b90dab070be339a1daf9052373ec30ffae4f72d5e66d053),
        )

        # iterate over points
        for secret, x, y in points:
            # initialize the secp256k1 point (S256Point)
            point = S256Point(x, y)
            # check that the secret*G is the same as the point
            self.assertEqual(secret*G, point)

    def test_sec(self):
        coefficient = 999**3
        uncompressed = '049d5ca49670cbe4c3bfa84c96a8c87df086c6ea6a24ba6b809c9de234496808d56fa15cc7f3d38cda98dee2419f415b7513dde1301f8643cd9245aea7f3f911f9'
        compressed = '039d5ca49670cbe4c3bfa84c96a8c87df086c6ea6a24ba6b809c9de234496808d5'
        point = coefficient*G
        self.assertEqual(point.sec(compressed=False), unhexlify(uncompressed))
        self.assertEqual(point.sec(compressed=True), unhexlify(compressed))
        coefficient = 123
        uncompressed = '04a598a8030da6d86c6bc7f2f5144ea549d28211ea58faa70ebf4c1e665c1fe9b5204b5d6f84822c307e4b4a7140737aec23fc63b65b35f86a10026dbd2d864e6b'
        compressed = '03a598a8030da6d86c6bc7f2f5144ea549d28211ea58faa70ebf4c1e665c1fe9b5'
        point = coefficient*G
        self.assertEqual(point.sec(compressed=False), unhexlify(uncompressed))
        self.assertEqual(point.sec(compressed=True), unhexlify(compressed))
        coefficient = 42424242
        uncompressed = '04aee2e7d843f7430097859e2bc603abcc3274ff8169c1a469fee0f20614066f8e21ec53f40efac47ac1c5211b2123527e0e9b57ede790c4da1e72c91fb7da54a3'
        compressed = '03aee2e7d843f7430097859e2bc603abcc3274ff8169c1a469fee0f20614066f8e'
        point = coefficient*G
        self.assertEqual(point.sec(compressed=False), unhexlify(uncompressed))
        self.assertEqual(point.sec(compressed=True), unhexlify(compressed))

    def test_address(self):
        secret = 888**3
        mainnet_address = '148dY81A9BmdpMhvYEVznrM45kWN32vSCN'
        testnet_address = 'mieaqB68xDCtbUBYFoUNcmZNwk74xcBfTP'
        point = secret*G
        self.assertEqual(
            point.address(compressed=True, testnet=False), mainnet_address)
        self.assertEqual(
            point.address(compressed=True, testnet=True), testnet_address)
        secret = 321
        mainnet_address = '1S6g2xBJSED7Qr9CYZib5f4PYVhHZiVfj'
        testnet_address = 'mfx3y63A7TfTtXKkv7Y6QzsPFY6QCBCXiP'
        point = secret*G
        self.assertEqual(
            point.address(compressed=False, testnet=False), mainnet_address)
        self.assertEqual(
            point.address(compressed=False, testnet=True), testnet_address)
        secret = 4242424242
        mainnet_address = '1226JSptcStqn4Yq9aAmNXdwdc2ixuH9nb'
        testnet_address = 'mgY3bVusRUL6ZB2Ss999CSrGVbdRwVpM8s'
        point = secret*G
        self.assertEqual(
            point.address(compressed=False, testnet=False), mainnet_address)
        self.assertEqual(
            point.address(compressed=False, testnet=True), testnet_address)

    def test_verify(self):
        point = S256Point(
            0x887387e452b8eacc4acfde10d9aaf7f6d9a0f975aabb10d006e4da568744d06c,
            0x61de6d95231cd89026e286df3b6ae4a894a3378e393e93a0f45b666329a0ae34)
        z = 0xec208baa0fc1c19f708a9ca96fdeff3ac3f230bb4a7ba4aede4942ad003c0f60
        r = 0xac8d1c87e51d0d441be8b3dd5b05c8795b48875dffe00b7ffcfac23010d3a395
        s = 0x68342ceff8935ededd102dd876ffd6ba72d6a427a3edb13d26eb0781cb423c4
        self.assertTrue(point.verify(z, Signature(r, s)))
        z = 0x7c076ff316692a3d7eb3c3bb0f8b1488cf72e1afcd929e29307032997a838a3d
        r = 0xeff69ef2b1bd93a66ed5219add4fb51e11a840f404876325a1e8ffe0529a2c
        s = 0xc7207fee197d27c618aea621406f6bf5ef6fca38681d82b2f06fddbdce6feab6
        self.assertTrue(point.verify(z, Signature(r, s)))

    def test_parse(self):
        sec = unhexlify('0349fc4e631e3624a545de3f89f5d8684c7b8138bd94bdd531d2e213bf016b278a')
        point = S256Point.parse(sec)
        want = 0xa56c896489c71dfc65701ce25050f542f336893fb8cd15f4e8e5c124dbf58e47
        self.assertEqual(point.y.num, want)



class Signature:

    def __init__(self, r, s):
        self.r = r
        self.s = s

    def __repr__(self):
        return 'Signature({:x},{:x})'.format(self.r, self.s)

    def der(self):
        rbin = self.r.to_bytes(32, byteorder='big')
        # if rbin has a high bit, add a 00
        if rbin[0] > 128:
            rbin = b'\x00' + rbin
        result = bytes([2, len(rbin)]) + rbin
        sbin = self.s.to_bytes(32, byteorder='big')
        # if sbin has a high bit, add a 00
        if sbin[0] > 128:
            sbin = b'\x00' + sbin
        result += bytes([2, len(sbin)]) + sbin
        return bytes([0x30, len(result)]) + result

    @classmethod
    def parse(cls, signature_bin):
        s = BytesIO(signature_bin)
        compound = s.read(1)[0]
        if compound != 0x30:
            raise RuntimeError("Bad Signature")
        length = s.read(1)[0]
        if length + 2 != len(signature_bin):
            raise RuntimeError("Bad Signature Length")
        marker = s.read(1)[0]
        if marker != 0x02:
            raise RuntimeError("Bad Signature")
        rlength = s.read(1)[0]
        r = int(hexlify(s.read(rlength)), 16)
        marker = s.read(1)[0]
        if marker != 0x02:
            raise RuntimeError("Bad Signature")
        slength = s.read(1)[0]
        s = int(hexlify(s.read(slength)), 16)
        if len(signature_bin) != 6 + rlength + slength:
            raise RuntimeError("Signature too long")
        return cls(r, s)


class SignatureTest(TestCase):

    def test_der(self):
        testcases = (
            (1, 2),
            (randint(0, 2**256), randint(0, 2**255)),
            (randint(0, 2**256), randint(0, 2**255)),
        )
        for r, s in testcases:
            sig = Signature(r, s)
            der = sig.der()
            sig2 = Signature.parse(der)
            self.assertEqual(sig2.r, r)
            self.assertEqual(sig2.s, s)


class PrivateKey:
    def __init__(self, secret = None):
      self.secret = secret if secret is not None else randint(0, 2**256)
      self.point = self.secret*G

    def hex(self):
        return '{:x}'.format(self.secret).zfill(64)

    def sign(self, z):
        # we need a random number k: randint(0, 2**256)
        k = randint(0, 2**256)
        # r is the x coordinate of the resulting point k*G
        r = (k*G).x.num
        # remember 1/k = pow(k, N-2, N)
        k_inv = pow(k, N-2, N)
        # s = (z+r*secret) / k
        s = (z + r*self.secret) * k_inv % N
        # return an instance of Signature:
        # Signature(r, s)
        return Signature(r, s)

    def wif(self, compressed=True, testnet=False):
        # convert the secret from integer to a 32-bytes in big endian using num.to_bytes(32, 'big')
        secret_bytes = self.secret.to_bytes(32, 'big')
        # prepend b'\xef' on testnet, b'\x80' on mainnet
        if testnet:
            prefix = b'\xef'
        else:
            prefix = b'\x80'
        # append b'\x01' if compressed
        if compressed:
            suffix = b'\x01'
        else:
            suffix = b''
        # encode_base58_checksum the whole thing
        return encode_base58_checksum(prefix + secret_bytes + suffix)

    @classmethod
    def parse(cls, s, compressed=True, testnet=False):
        b = decode_base58_checksum(s)
        # prepend b'\xef' on testnet, b'\x80' on mainnet
        if testnet:
            prefix = b'\xef'
        else:
            prefix = b'\x80'

        if prefix != b[:1]:
            raise RuntimeError("bad suffix or prefix")

        # append b'\x01' if compressed
        if compressed:
            suffix = b'\x01'
            if suffix != b[-1:]:
                raise RuntimeError("bad suffix or prefix")
            secret_bytes = b[1:-1]
        else:
            secret_bytes = b[1:]
        return cls(big_endian_to_int(secret_bytes))


class PrivateKeyTest(TestCase):

    def test_sign(self):
        pk = PrivateKey(randint(0, 2**256))
        z = randint(0, 2**256)
        sig = pk.sign(z)
        self.assertTrue(pk.point.verify(z, sig))

    def test_wif(self):
        pk = PrivateKey(2**256-2**199)
        expected = 'L5oLkpV3aqBJ4BgssVAsax1iRa77G5CVYnv9adQ6Z87te7TyUdSC'
        res = pk.wif(compressed=True, testnet=False)
        self.assertEqual(res, expected)
        self.assertEqual(PrivateKey.parse(res, compressed=True, testnet=False).secret, pk.secret)

        pk = PrivateKey(2**256-2**201)
        expected = '93XfLeifX7Jx7n7ELGMAf1SUR6f9kgQs8Xke8WStMwUtrDucMzn'
        self.assertEqual(pk.wif(compressed=False, testnet=True), expected)
        pk = PrivateKey(0x0dba685b4511dbd3d368e5c4358a1277de9486447af7b3604a69b8d9d8b7889d)
        expected = '5HvLFPDVgFZRK9cd4C5jcWki5Skz6fmKqi1GQJf5ZoMofid2Dty'
        self.assertEqual(pk.wif(compressed=False, testnet=False), expected)
        pk = PrivateKey(0x1cca23de92fd1862fb5b76e5f4f50eb082165e5191e116c18ed1a6b24be6a53f)
        expected = 'cNYfWuhDpbNM1JWc3c6JTrtrFVxU4AGhUKgw5f93NP2QaBqmxKkg'
        self.assertEqual(pk.wif(compressed=True, testnet=True), expected)