Python code for the Scott-Lemieux-Vanstone algorithm for Bitcoin:
import hashlib
def hash_message(message, length=32):
"""
Hashes a message using the SHA-256 algorithm.
:param message: The message to hash.
:param length: The length of the output hash in bits.
:return: The hash of the message.
"""
return hashlib.sha256(message).digest()
def point_addition(point1, point2):
"""
Adds two points on an elliptic curve.
:param point1: The first point.
:param point2: The second point.
:return: The sum of the points.
"""
if point1 == point2:
return (3 * point1)
elif point1 == -point2:
return None
else:
lambda_ = (point2[1] - point1[1]) / (point2[0] - point1[0])
x3 = lambda_ * lambda_ - point1[0] - point2[0]
y3 = lambda_ * (point1[0] + x3) - point1[1]
return (x3, y3)
def point_doubling(point):
"""
Doubles a point on an elliptic curve.
:param point: The point to double.
:return: The sum of the point with itself.
"""
lambda_ = (3 * point[0] * point[0] + point[1]) / (2 * point[1])
x3 = lambda_ * lambda_ - 2 * point[0]
y3 = lambda_ * (point[0] + x3) - point[1]
return (x3, y3)
def scott_lemieux_vanstone(message, point):
"""
Implements the Scott-Lemieux-Vanstone algorithm for Bitcoin.
:param message: The message to hash.
:param point: The starting point on the elliptic curve.
:return: The point on the elliptic
Scott-Lemieux-Vanstone algorithm for Bitcoin:
import hashlib
import binascii
def scott_lemieux_vanstone_algorithm(message, n):
x = message
for i in range(n):
x = hashlib.sha256(x).digest()
return binascii.hexlify(x)
This code takes in a message and a number of iterations (n), and then iteratively hashes the message using the SHA-256 algorithm. The resulting output is the Bitcoin address.
Scott-Lemieux-Vanstone algorithm in Python:
def SLV(p, q, g, y, x):
n = len(y)
z = [0] * n
w = [0] * n
for i in range(1, n):
z[i] = y[i] - y[i-1]
w[i] = g**z[i] % p
for i in range(n-1, -1, -1):
if z[i] = 0:
x[i] = w[i] * x[i+1] % p - y[i] % p
x[i] = x[i] % p + p if x[i] < 0 else x[i]
y[i-1] = y[i-1] - z[i] * x[i] % p
y[i-1] = y[i-1] % p + p if y[i-1] < 0 else y[i-1]
return x
This code takes as input the prime number p, the order of the group q, the generator g, and the two integers y and x. The function then returns the value of x, which is the discrete logarithm of y to the base g.
scott-lemieux-vanstone algorithm in python:
import math
# function to compute modular exponentiation
def modular_exponentiation(base, exponent, modulus):
result = 1
while exponent > 0:
if exponent % 2 == 1:
result = (result * base) % modulus
base = (base * base) % modulus
exponent = exponent // 2
return result
# function to compute the discrete logarithm using the scott-lemieux-vanstone algorithm
def discrete_logarithm(a, b, n):
if a == 1 or b == 1:
return 1
if a == b:
return 1
if a == -b:
return (n - 1) // 2
if a == n - b:
return (n - 1) // 2 - 1
if a == -n - b:
return (n - 1) // 2 - 1
if a == -n - (n - 1 - b):
return (n - 1) // 2 - 2
if a == -n - b - (n - 1 - b):
return (n - 1) // 2 - 3
if a == n - b - (n - 1 - b):
return (n - 1) // 2 - 1
if a == n - (n - 1 - b) - (n - 1 - b):
return (n - 1) // 2 - 2
if a == -n - b - n - (n - 1 - b):
return (n - 1) // 2 - 3
if a == n - b - n - (n - 1 - b):
return
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