import os
import hashlib
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.asymmetric import ec

private_key = ec.generate_private_key(ec.SECP256K1(), default_backend())
public_key = private_key.public_key()

for i in range(100):
    data = os.urandom(32)
    signature = private_key.sign(data, ec.ECDSA(hashes.SHA256()))

    # Extract the values of 'r', 's', 'z' from the signature
    r, s = signature
    z = int.from_bytes(hashlib.sha256(data).digest(), 'big')

    # Print the values of 'r', 's', 'z'
    print("r:", r)
    print("s:", s)
    print("z:", z)   

for i in range(100):

 

import ecdsa
import random

# Define the secp256k1 curve
curve = ecdsa.SECP256k1

# Generate 100 random private keys
private_keys = [ecdsa.SigningKey.generate(curve=curve) for i in range(100)]

# Create signatures using the private keys and random messages (z)
signatures = []
for i in range(100):
    z = random.randint(0, 2**256)
    private_key = private_keys[i]
    public_key = private_key.get_verifying_key()
    signature = private_key.sign_digest(z.to_bytes(32, 'big'), sigencode=ecdsa.util.sigencode_der)
    r, s = ecdsa.util.sigdecode_der(signature, curve.generator.order())
    signatures.append((z, r, s))

# Get the nonce (k) for each signature
nonce = []
for i in range(100):
    z, r, s = signatures[i]
    k = ecdsa. SigningKey.from_public_key(public_key, curve=curve).verifying_key.recover_session_key(z.to_bytes(32, 'big'), (r, s), hashfunc=ecdsa.util.sha256, sigdecode=ecdsa.util.sigdecode_der)
    nonce.append(k)

# The 100 signatures, Z values, and nonce values are stored in the signatures, Z, and nonce lists, respectively.

 

#This example twist attack on secp256k1 uses the Python library 'ecdsa'

import ecdsa

#Generate a random private key
priv_key = ecdsa.util.randrange(2**256)

#Generate a public key from the private key
pub_key = ecdsa.SigningKey.from_secret_exponent(priv_key, curve=ecdsa.SECP256k1).verifying_key

#Generate a random point on the curve
P = ecdsa.ellipticcurve.Point(ecdsa.SECP256k1.curve, ecdsa.util.randrange(ecdsa.SECP256k1.curve.p()), ecdsa.util.randrange(ecdsa.SECP256k1.curve.p()))

#Calculate the twist attack
Q = P + pub_key.pubkey.point

#Verify that the attack was successful
if Q.x() == pub_key.pubkey.point.x() and Q.y

The following code is an example of an ECDSA secp256k1 twist attack.

// Generate a random private key
var privateKey = crypto.randomBytes(32);

// Generate a public key from the private key
var publicKey = secp256k1.publicKeyCreate(privateKey);

// Generate a random message
var message = crypto.randomBytes(32);

// Sign the message with the private key
var signature = secp256k1.sign(message, privateKey);

// Generate a twisted public key
var twistedPublicKey = secp256k1.publicKeyTweakAdd(publicKey, crypto.randomBytes(32));

// Verify the signature with the twisted public key
var valid = secp256k1.verify(message, signature, twistedPublicKey);

// Output the result
console.log("Signature is valid: " + valid);

The mathematical formula to calculate k nonce from r,s,z signatures is:

k = (z + r*s) / s mod n 

where n is the order of the elliptic curve.

k= (z + r*s) % n

import ecdsa

z = int(input("Enter value of z: "))
r = int(input("Enter value of r: "))
k = int(input("Enter value of k: "))
s = int(input("Enter value of s: "))

private_key = (z + (r * k)) / s

print("Private Key =", private_key)

import ecdsa
import random
import libnum
import olll
import hashlib
import sys

 

order = 115792089237316195423570985008687907852837564279074904382605163141518161494337
pub = (xxx, xxx)

print ("Curve SECP256k1")
print ("Order:",order)
print ("pub:",pub)


priv = random.randrange(1,order)
 
Public_key = pub
Private_key = ecdsa.ecdsa.Private_key(Public_key, priv)
 
k1 = random.randrange(1, pow(2,127))
k2 = random.randrange(1, pow(2,127))

m1 =xxxx
m2 =xxxx
r1 =xxxx
r2 =xxxx
s1 =xxxx
s2 =xxxx

print ("k1: ",k1)
print ("k2: ",k2)

print ("Private key: ",Private_key)

s1_inv = libnum.invmod(s1, order)
s2_inv = libnum.invmod(s2, order)
 
matrix = [[order, 0, 0, 0], [0, order, 0, 0],
[r1*s1_inv, r2*s2_inv, (2**128) / order, 0],
[m1*s1_inv, m2*s2_inv, 0, 2**128]]
 
search_matrix = olll.reduction(matrix, 0.75)
r1_inv = libnum.invmod(r1, order)
 
for search_row in search_matrix:
    possible_k1 = search_row[0]
    try_private_key = (r1_inv * ((possible_k1 * s1) - m1)) % order
    print(f"try_private_key",try_private_key)

sf= sig.s + 1
hf= h +1