Twisted edwards curve algorithm for Bitcoin

BY KEYHUNTER 03.03.2024
Twisted edwards curve algorithm for Bitcoin

Python code for the twisted Edwards curve algorithm used in Bitcoin:

def x_to_y(x):
    y_squared = (x**3 + 3) / (2 * x**2)
    y = (y_squared**2 - 1) / (2 * x)
    return y

def y_to_x(y):
    y_squared = (y**2 - 1) / (2 * y)
    x = (y_squared**2 - 3) / (2 * y_squared)
    return x

def add_points(x1, y1, x2, y2):
    lambda_inv = (y2 - y1) / (x2 - x1)
    x3 = lambda_inv**2 - x1 - x2
    y3 = lambda_inv * (x3 - x1) - y1
    return x3, y3

def multiply_point(x, y, scalar):
    lambda_inv = (3 * x**2 + a) / (2 * y)
    x3 = lambda_inv**2 - 2 * x
    y3 = lambda_inv * (x3 - x) - y
    return x3, y3

In this code, x and y represent the coordinates of a point on the twisted Edwards curve, a is a constant equal to -1, and scalar is a number used to multiply the point by. The add_points function adds two points on the curve, while the multiply_point function multiplies a point on the curve by a scalar.

It is an algorithm used in cryptography, which is used in Bitcoin. It is a type of elliptic curve cryptography (ECC) that is used to generate public and private keys for digital signatures. The algorithm is used to create a twisted Edwards curve, which is a type of elliptic curve. The curve is defined by an equation of the form -x^2 + y^2 = 1 + dx^2y^2, where d is a constant. The algorithm uses a finite field arithmetic to perform calculations on the curve.

twisted edwards curve algorithm for Bitcoin in Python:

import hashlib
from Crypto.Util.number import long_to_bytes, bytes_to_long

def hash_to_point(hash_hex):
    hash = hashlib.sha256(hash_hex).digest()
    x = int.from_bytes(hash, "big") % 2**256
    y = ((x**3 + 7) % 2**256)
    x = (x**2 - y**2) % 2**256
    y = (x**2 + y**2 * 121665) % 2**256
    y = (y - 121665) % 2**256
    return (x, y)

def point_addition(x1, y1, x2, y2):
    z1 = (x1**2 - y1**2) % 2**256
    z2 = (x2**2 - y2**2) % 2**256
    z3 = (z1 - z2) % 2**256
    x3 = ((z3 - x1) * (z3 + x2)) % 2**256
    y3 = ((z3 - y1) * (z3 + y2)) % 2**256
    return (x3, y3)

def point_multiplication(x, y, scalar):
    x_sq = x ** 2
    y_sq = y ** 2
    y_sq_x = y_sq * x
    y_sq_x_sq = y_sq_x ** 2
    y_sq_x_sq_sq = y_sq_x_sq ** 2
    x_sq_sq = x_sq ** 2
    x_sq_sq_y = x_sq_sq * y
    x_sq_sq_y_sq = x_sq_sq_y ** 2

Python code for the Twisted Edwards curve algorithm used in Bitcoin. Here’s the code:

import hashlib

def F(x):
    if x == 0:
        return 1
    else:
        return x + 1

def G(x):
    if x == 0:
        return 1
    else:
        return x + 1

def x(y):
    return (y ** 2 - 1) // (y ** 2 + 1)

def y(x):
    return (x ** 3 + 3) // (x ** 2 + 1)

def add(x, y):
    if x == y:
        return x
    elif x == -y:
        return 0
    else:
        if x < 0:
            x = x + 1
        if y < 0:
            y = y + 1
        if x > y:
            x = x - y
            if x == -y:
                x = x + 1
        return x

def double(x):
    return 2 * x // (x ** 2 + 1)

def negate(x):
    if x == 0:
        return 0
    else:
        return (x ** 2 + 1) // (2 * x)

def scalar_mult(x, y, n):
    if n == 0:
        return 0
    elif n == 1:
        return x
    else:
        return scalar_mult(y, double(x), n // 2) + x
        if n % 2 == 1:
            return add(scalar_mult(y, double(x), n // 2), x)

the twisted edwards curve is a type of elliptic curve that is used in cryptography, particularly in bitcoin. it is a specific type of curve that is defined by the equation y^2 = x^3 + ax^2 + x, where a is a constant that is defined for each specific curve.

to generate a public key from a private key using the twisted edwards curve algorithm, you first generate a random private key, which is simply a random integer. then, you multiply the private key by a generator point on the curve to get the public key. the generator point is a fixed point on the curve that is defined for each specific curve.

to generate a public key from a private key using the twisted edwards curve algorithm, you first generate a random private key, which is simply a random integer. then, you multiply the private key by a generator point on the curve to get the public key. the generator point is a fixed point on the curve that is defined for each specific curve.

to generate a bitcoin address from a public key, you first convert the public key to a compressed form, which is simply a shorter representation of the same point on the curve. then, you hash the compressed public key using the sha256 algorithm, and then hash the resulting hash using the ripemd-160 algorithm. finally, you append a checksum to the resulting hash to get the bitcoin address.

code snippet in python to perform twisted edwards curve algorithm. however, i cannot guarantee that the code will work as expected or that it will solve the discrete logarithm problem. here is an example:

from cryptography.hazmat.primitives.asymmetric.ed25519 import (
    ed25519privatekey, ed25519publickey, ed25519signature
)

private_key = ed25519privatekey.generate()
public_key = private_key.public_key()
message = b"hello, world!"
signature = private_key.sign(message)

verified = public_key.verify(signature, message)
print(verified)

in this example, we use the cryptography library to generate a private key, public key, and sign a message using the twisted edwards curve algorithm. the verify method is used to check if the signature is valid.

twisted edwards curve algorithm in python. however, i must remind you that this algorithm is used for cryptographic purposes, and it should be used responsibly and ethically. here’s the code:

from cryptography.hazmat.primitives.asymmetric import eddsa
from cryptography.hazmat.primitives.asymmetric.ed25519 import (
    eddsa_public_key, eddsa_private_key
)
from cryptography.hazmat.primitives.asymmetric.ed25519 import (
    eddsa_signature, eddsa_verify
)

# generate a key pair
private_key = eddsa_private_key.generate()
public_key = private_key.public_key()

# generate a message
message = b'hello world!'

# sign the message with the private key
signature = private_key.sign(message)

# verify the signature with the public key
public_key.verify(signature, message)

this code uses the cryptography library to generate a key pair, sign a message, and verify the signature. the eddsa algorithm is used for the signature scheme.

Useful information for enthusiasts:

Contact me via Telegram: @ExploitDarlenePRO