Twist Attack

BY KEYHUNTER 21.02.2024
Twist Attack

Python script that implements the twist attack on aes encryption:

  1. import the necessary libraries, such as numpy, cryptography, and scipy.
  2. define the key and ciphertext that you want to attack.
  3. create a function that generates the twist matrix based on the key.
  4. use the twist matrix to create a set of equations that relate the ciphertext to the plaintext.
  5. solve the equations using a numerical method, such as lstsq or lsq_linear.
  6. extract the plaintext from the solution.

here is a sample code snippet that shows how to generate the twist matrix:

from numpy import matrix

# define the key
key = [0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68]

# create the twist matrix
twist_matrix = matrix([[0, 0, 0, 0, 0, 0, 0, 0],
                        [0, 1, 0, 0, 0, 0, 0, 0],
                        [0, 0, 2, 0, 0, 0, 0, 0],
                        [0, 0, 0, 3, 0, 0, 0, 0],
                        [0, 0, 0, 0, 4, 0, 0, 0],
                        [0, 0, 0, 0, 0, 5, 0, 0],
                        [0, 0, 0, 0, 0, 0, 6, 0],
                        [0, 0, 0, 0, 0, 0, 0, 7]])

this creates a 8×8 matrix where each row corresponds to a byte of the key. the first column contains the powers of 2, and the remaining columns are filled with zeros.

 Twisted Edwards curve attack is a side-channel attack on elliptic curve cryptography (ECC) systems that use the Twisted Edwards curve. The attack exploits the leakage of information through the timing and power consumption of the device during ECC operations. The attacker can use this information to recover the secret key used in the ECC system.

To prevent this attack, it is recommended to use ECC systems that are resistant to side-channel attacks, such as those based on the Montgomery curve or the Edwards curve with complete addition laws. Additionally, it is important to implement countermeasures against side-channel attacks, such as masking or blinding techniques, and to use secure hardware platforms for ECC operations.

A twist attack is a type of side-channel attack on cryptographic algorithms that exploits the fact that the execution time of the algorithm depends on the secret key. In other words, by measuring the time it takes to execute the algorithm, an attacker can deduce information about the key. This attack was first proposed in the paper “Twist-Based Cryptanalysis of Block Ciphers” by Gauravaram, Gangadhar, and Kiran.

writing a python script based on the article you shared. here are the steps:

  1. read the article carefully and understand the twist attack and how it works.
  2. decide on the programming language you want to use (in this case, python).
  3. choose a cryptography library to work with (e.g., cryptography or pycrypto).
  4. import the necessary libraries and modules into your python script.
  5. define the functions and variables needed for the twist attack implementation.
  6. implement the twist attack algorithm in python code.
  7. test your code by running it with sample input data.
  8. analyze the output and make any necessary adjustments to the code.

keep in mind that the implementation of the twist attack in python is a complex task that requires advanced knowledge of cryptography and programming. if you are not familiar with these topics, it is recommended to seek the help of a professional cryptographer or programmer.

Python script for the twist attack could look like.

First, you would need to import the necessary libraries, such as numpy and scipy. Then, you would define a function to generate the twist matrix, which is a matrix that twists the signal in the time-frequency domain.

Next, you would define a function to perform the twist attack on the signal, using the twist matrix you just generated. This function would take in the original signal as input, and output the modified signal.

Finally, you would define a function to recover the original signal from the modified signal, using the inverse of the twist matrix.

Here’s a rough outline of what the code might look like:

import numpy as np
import scipy.io.wavfile as wav

# Define function to generate twist matrix
def generate_twist_matrix(fs, f0, t, N):
    # Compute parameters
    n = N // 2 + 1
    k = np.arange(-n, n+1)
    w = np.exp(-1j * 2 * np.pi * k / N)
    S = np.zeros((N, N))
    for i in range(N):
        for j in range(N):
            S[i, j] = w[i] * np.exp(-1j * 2 * np.pi * f0 * t * (j - n)) / N

# Define function to perform twist attack
def perform_twist_attack(signal, fs, f0, t):
    # Generate twist matrix
    S = generate_twist_matrix(fs, f0, t, len(signal))
    # Apply twist matrix to signal
    modified_signal = np.dot(S, signal)
    return modified_signal

# Define function to recover original signal
def recover_original_signal(modified_signal, fs, f0, t):
    # Generate inverse of twist matrix
    S_inv = np.linalg.inv(generate_twist_matrix(fs, f0, t, len(modified_signal)))
    # Apply inverse twist matrix to modified signal
    recovered_signal = np.dot(S_inv, modified_signal)
    return recovered_signal

# Main function
def main():
    # Load signal from file
    fs, signal = wav.read('signal.wav')
    # Perform twist attack
    modified_signal = perform_twist_attack(signal, fs, 1000, 1)
    # Save modified signal to file
    wav.write('modified_signal.wav', fs, modified_signal)
    # Recover original signal
    recovered_signal = recover_original_signal(modified_signal, fs, 1000, 1)
    # Save recovered signal to file
    wav.write('recovered_signal.wav', fs, recovered_signal)

# Call main function
if __name__ == '__main__':
    main()

Note that this is just a rough outline and the code may need to be modified to work properly.

this script, you will need to import the hashlib library.

import hashlib

next, you will need to define the function that takes a message and a key as inputs, and returns the twist hash.

def twist_hash(message, key):
    # code to implement twist hash goes here

the first step in implementing the twist hash is to convert the message and key into byte arrays using the encode() function.

message_bytes = message.encode()
key_bytes = key.encode()

then, you will need to initialize the hash object using the hashlib.sha256() function.

hash_obj = hashlib.sha256()

next, you will need to update the hash object with the key and message bytes using the update() function.

hash_obj.update(key_bytes)
hash_obj.update(message_bytes)

finally, you will need to return the hexadecimal representation of the hash using the hexdigest() function.

return hash_obj.hexdigest()

putting it all together, here is the complete python script:

import hashlib

def twist_hash(message, key):
    message_bytes = message.encode()
    key_bytes = key.encode()
    hash_obj = hashlib.sha256()
    hash_obj.update(key_bytes)
    hash_obj.update(message_bytes)
    return hash_obj.hexdigest()

you can now call the twist_hash() function with a message and key as inputs, and it will return the twist hash in hexadecimal format.

Twist Attack is a method of cryptanalysis that targets the encryption algorithm used in WEP (Wired Equivalent Privacy) and WPA (Wi-Fi Protected Access) protocols. It works by exploiting a weakness in the RC4 cipher, which is used in both WEP and WPA. The attack involves collecting a large number of packets encrypted with the same key and then analyzing them to extract the key.

The attack is called Twist because it involves applying a mathematical transformation called a “twist” to the encrypted packets. This transformation makes it easier to find patterns in the encrypted data that can be used to recover the key. Once the key is known, an attacker can decrypt any packets that are encrypted with it.

However, it’s important to note that the Twist Attack is not effective against modern encryption protocols, such as WPA2 and WPA3, which use stronger encryption algorithms.

Python script that implements the twist attack. Here is an example:

import hashlib

def twist_attack(message, salt):
    for i in range(1000):
        for j in range(1000):
            hashed_message = hashlib.sha256(message + str(i) + str(j) + salt).hexdigest()
            if hashed_message[:8] == "00000000":
                return i, j
    return None, None

message = "this is the message"
salt = "this is the salt"

result = twist_attack(message, salt)
if result is not None:
    i, j = result
    print("Found a collision with i = {}, j = {}".format(i, j))
else:
    print("No collision found.")

In this script, the twist_attack function takes a message and a salt as inputs, and returns the values of i and j that produce a collision with the given salt. The function loops through all possible values of i and j and checks if the resulting hash value has 8 leading zeros. If a collision is found, the function returns the corresponding values of i and j. If no collision is found, the function returns None, None.

In the main part of the script, we define a message and a salt, and call the twist_attack function. If a collision is found, we print the corresponding values of i and j. Otherwise, we print a message indicating that no collision was found.

Please note that this script is for educational purposes only and should not be used for malicious activities.

here is the code:

import hashlib
import hmac

def twist_attack(message, signature):
    # extract the r and s components of the signature
    r = int.from_bytes(signature[:32], byteorder='big')
    s = int.from_bytes(signature[32:], byteorder='big')

    # compute the twist of the signature
    twisted_r = (r + (s - r) // 2) % 2**256
    twisted_s = (s - (r - s) // 2) % 2**256

    # recompute the signature with the twisted values
    twisted_signature = hmac.new(b'message', bytes([0]*32) + twisted_r.to_bytes(32, byteorder='big') + twisted_s.to_bytes(32, byteorder='big'), hashlib.sha256).digest()

    # check if the twisted signature is valid
    if hmac.compare_digest(twisted_signature, signature):
        print('twist attack succeeded!')
    else:
        print('twist attack failed.')

# example usage
message = b'hello, world!'
signature = hashlib.sha256(message).digest()
twist_attack(message, signature)

this code implements the twist attack on a given message and signature. it first extracts the r and s components of the signature, then computes the twist of the signature by adding or subtracting 2**256/2 to r and s, respectively. it then recomputes the signature with the twisted values and checks if the twisted signature is valid by comparing it to the original signature.

note that this code is for educational purposes only and should not be used to attack real-world cryptographic systems.

python code that would implement the twist attack as described in the article. here it is:

import hashlib

def twist_attack(hash_value, salt):
    """
    this function implements the twist attack on a given hash value and salt.
    """
    # convert the hash value to a list of bytes
    hash_bytes = hashlib.sha256(hash_value.encode()).digest()
    # create a new list with the salt and the original hash value
    salted_hash = salt + hash_bytes
    # apply the twist function to the salted hash
    twisted_hash = hashlib.sha256(salted_hash).digest()
    # apply the twist function again to the twisted hash
    double_twisted_hash = hashlib.sha256(twisted_hash).digest()
    # compare the double-twisted hash with the original hash value
    if double_twisted_hash == hash_bytes:
        return true
    else:
        return false

this function takes two arguments: hash_value, which is the hash value you want to attack, and salt, which is the salt used to generate the hash value. it first converts the hash value to a list of bytes using the hashlib library. it then creates a new list with the salt and the original hash value, and applies the hashlib.sha256 function twice to the salted hash, creating a twisted_hash and a double_twisted_hash. finally, it compares the double_twisted_hash with the original hash_value to see if the twist attack was successful.

to use this function, you would call it with the hash value and salt you want to attack, like this:

hash_value = b'my_password'
salt = b'my_salt'
if twist_attack(hash_value, salt):
    print('attack successful!')
else:
    print('attack failed.')

note that this code is provided for educational purposes only, and should not be used for malicious purposes.

To write a Python script that implements the Twist attack, you need to have a good understanding of the mathematics and cryptography involved in the attack. You also need to have experience in Python programming, particularly in using cryptographic libraries and implementing algorithms.

Here are some general steps that you can follow to write the Python script:

  1. Import the necessary cryptographic libraries, such as Crypto.
  2. Define the encryption function that uses the Twist cipher. You can use the Crypto library to implement the encryption function.
  3. Define the decryption function that uses the Twist cipher. You can use the Crypto library to implement the decryption function.
  4. Implement the Twist attack by modifying the encryption function to use a different key. You can use the Crypto library to modify the encryption function.
  5. Test the Twist attack by encrypting a message using the modified encryption function and decrypting it using the decryption function.
  6. Print the results of the attack, including the original message, the encrypted message, and the decrypted message.
  7. Save the Python script with an appropriate name and extension.

Note that this is a high-level overview of how to write the Python script. You will need to have a deep understanding of the Twist attack and cryptography to implement it correctly.

Useful information for enthusiasts:

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