چالش Times¶

Curve:  y^2 = x**3 + 13x + 245 % 335135809459196851603485825030548860907
Point:  (14592775108451646097, 237729200841118959448447480561827799984)
{'ciphertext': b'SllGMo5gxalFG9g8j4KO0cIbXeub0CM2VAWzXo3nbIxMqy1Hl4f+dGwhM9sm793NikYA0EjxvFyRMcU2tKj54Q==', 'iv': b'MWkMvRmhFy2vAO9Be9Depw=='}

import hashlib
from Crypto.Cipher import AES 
from Crypto.Util.Padding import pad, unpad
from ellipticcurve import * # I'll use my own library for this
from base64 import b64encode
import os
from Crypto.Util.number import getPrime

def encrypt_flag(shared_secret: int, plaintext: str):
    iv = os.urandom(AES.block_size)

    #get AES key from shared secret
    sha1 = hashlib.sha1()
    sha1.update(str(shared_secret).encode('ascii'))
    key = sha1.digest()[:16]

    #encrypt flag
    plaintext = pad(plaintext.encode('ascii'), AES.block_size)
    cipher = AES.new(key, AES.MODE_CBC, iv)
    ciphertext = cipher.encrypt(plaintext)

    return { "ciphertext" : b64encode(ciphertext), "iv" : b64encode(iv) }

def main():
    the_curve = EllipticCurve(13, 245, getPrime(128))
    start_point = None
    while start_point is None:
        x = getPrime(64)
        start_point = the_curve.point(x)
    print("Curve: ", the_curve)
    print("Point: ", start_point)
    new_point = start_point * 1337

    flag = "byuctf{REDACTED}"
    print(encrypt_flag(new_point.x, flag))

if __name__ == "__main__":
    main()

from Crypto.Util.number import *
P=(14592775108451646097, 237729200841118959448447480561827799984)
p=335135809459196851603485825030548860907
a=13
def point_addition(P, Q, p, a):
    if P == (0,0):
        return Q
    elif Q == (0,0):
        return P
    elif P[0] == Q[0] & P[1] == -Q[1]:
        return (0,0)
    elif P != Q:
        landa = (((Q[1] - P[1]) % p) * inverse( ((Q[0] - P[0]) % p), p)) % p
    elif P == Q:
        landa = ( (((3*((P[0]**2) % p) % p) + a) % p) * inverse( ((2 * P[1]) % p), p)) % p
    x = (((landa**2) % p) - P[0] - Q[0]) % p
    y = (((landa*((P[0] - x) % p)) % p) - P[1]) % p
    return (x, y)

def scalar_multiplication(P, n, p, a):
    Q = P
    R = (0,0)
    while n > 0:
        if n % 2 == 1:
            R = point_addition(R, Q, p, a)
        Q = point_addition(Q, Q, p, a)
        n = math.floor(n/2)
    return R

scalar_multiplication(P, 1337, p, a)

from Crypto.Cipher import AES
from base64 import b64decode
from Crypto.Util.Padding import unpad


def decrypt_flag(shared_secret: int, ciphertext_dict: dict):

  # Derive AES key from shared secret (same as encryption)
  sha1 = hashlib.sha1()
  sha1.update(str(shared_secret).encode('ascii'))
  key = sha1.digest()[:16]

  # Retrieve ciphertext and IV from dictionary
  ciphertext = b64decode(ciphertext_dict["ciphertext"])
  iv = b64decode(ciphertext_dict["iv"])

  # Decrypt the ciphertext
  cipher = AES.new(key, AES.MODE_CBC, iv)
  plaintext = unpad(cipher.decrypt(ciphertext), AES.block_size)

  # Return the decrypted string
  return plaintext.decode('ascii')


shared_secret = 130102914376597655583988556541378621904

ciphertext_dict = {'ciphertext': b'SllGMo5gxalFG9g8j4KO0cIbXeub0CM2VAWzXo3nbIxMqy1Hl4f+dGwhM9sm793NikYA0EjxvFyRMcU2tKj54Q==', 'iv': b'MWkMvRmhFy2vAO9Be9Depw=='}


decrypt_flag(shared_secret, ciphertext_dict)