Topic: 🖤 (Read 205 times)

#!/usr/bin/env python3

import collections
import hashlib

# ...

def point_add(point1, point2):
    if point1 is None:
        return point2
    if point2 is None:
        return point1

    x1, y1 = point1
    x2, y2 = point2

    if x1 == x2 and y1 != y2:
        return None

    if point1 == point2:
        m = (3 * x1 * x1 + curve.a) * pow(2 * y1, -1, curve.p)
    else:
        m = (y2 - y1) * pow(x2 - x1, -1, curve.p)

    x3 = (m * m - x1 - x2) % curve.p
    y3 = (m * (x1 - x3) - y1) % curve.p

    return (x3, y3)

# ... (Rest of your code remains the same)


EllipticCurve = collections.namedtuple('EllipticCurve', 'name p a b g n h')

curve = EllipticCurve(
    'secp256k1',
    # Field characteristic.
    p=0x7027,
    # Curve coefficients.
    a=0,
    b=7,
    # Base point.
    g=(0x1,
       0x2),
    # Subgroup order.
    n=0x6997,
    # Subgroup cofactor.
    h=1,
)

# Functions that work on curve points #

def is_on_curve(point):
    """Returns True if the given point lies on the elliptic curve."""
    if point is None:
        # None represents the point at infinity.
        return True

    x, y = point

    return (y * y - x * x * x - curve.a * x - curve.b) % curve.p == 0

def scalar_mult(k, point):
    """Returns k * point computed using the double and point_add algorithm."""

    if k % curve.n == 0 or point is None:
        return None

    if k < 0:
        # k * point = -k * (-point)
        return scalar_mult(-k, point_neg(point))

    result = None
    addend = point

    while k:
        if k & 1:
            # Add.
            result = point_add(result, addend)

        # Double.
        addend = point_add(addend, addend)

        k >>= 1


    return result

# Private key
private_key = 3

# Generate public key from the private key
public_key = scalar_mult(private_key, curve.g)

print('Curve: ', curve.name)
print('Generator point:\n(0x{:x},\n 0x{:x})'.format(*curve.g))
print('\n\n')
print('Private key:\n', private_key)
print('\n')
print('Public key:\n(0x{:x},\n 0x{:x})'.format(*public_key))

import random
import math

def is_prime(n, k=10000):
    """Test if a number is prime using Miller-Rabin test."""
    if n < 2:
        return False
    # Check for small primes
    for p in (2, 3, 5, 7, 11, 13, 17, 19, 23, 29):
        if n % p == 0:
            return n == p
    # Perform Miller-Rabin test
    s, d = 0, n-1
    while d % 2 == 0:
        s, d = s+1, d//2
    for _ in range(k):
        a = random.randint(2, n-2)
        x = pow(a, d, n)
        if x == 1 or x == n-1:
            continue
        for _ in range(s-1):
            x = pow(x, 2, n)
            if x == n-1:
                break
        else:
            return False
    return True

def generate_prime(n):
    """Generate a random n-bit prime using Miller-Rabin test."""
    while True:
        p = random.getrandbits(n)
        # Set the MSB and LSB to 1 to ensure n bits and odd number
        p |= (1 << n-1) | 1
        if is_prime(p):
            return p

# Generate any bit prime
p = generate_prime(256)
print("Generated prime:", p)