CrownOTP.py

import random
import time
import json

from decimal import Decimal, getcontext


#########################################################
#                        Alice                          #
#########################################################

def crown_npsn_rng() -> int:
    """This mocks the Crown RNG that generates non-perfect square numbers."""
    return random.choice([2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26])


def int_to_bytes(x: int) -> bytes:
    return x.to_bytes((x.bit_length() + 7) // 8, 'big')


def generate_otp(seed: int, length: int, offset: int) -> bytes:
    getcontext().prec = 5 * (length + offset)
    square_root       = Decimal(seed).sqrt()

    decimal_expansion = str(square_root).split('.')[1]
    keystream_integer = int(decimal_expansion[offset:])
    one_time_pad      = int_to_bytes(keystream_integer)[:length]
    return one_time_pad


def xor_bytestrings(var: bytes, key: bytes) -> bytes:
    assert len(var) == len(key)
    return bytes(a ^ b for a, b in zip(var, key))


#########################################################
#                   Eve (Eavesdropper)                  #
#########################################################

def crack_crown_otp(ciphertext: bytes) -> str:
    """Crack the OTP ciphertext.

    Crown Sterling's claim is their OTP has perfect secrecy.
    Therefore brute force attack like the one below should
    not be possible.
    """

    for seed in range(1, 30):
        for offset in range(1, 30):

            try:
                pad_candidate = generate_otp(seed=seed, length=len(ciphertext), offset=offset)
            except IndexError:
                continue

            try:
                decryption_candidate = xor_bytestrings(ciphertext, pad_candidate).decode()
                data_structure       = json.loads(decryption_candidate)
                return 'Successful decryption: ' + data_structure['message']
            except UnicodeDecodeError:
                continue

    return 'Error: Decryption failed'


#########################################################
#                         Main                          #
#########################################################

def main():

    message = 'Attack at dusk'

    packet_data_structure = {'message': message, 'send_unix_timestamp': time.time()}
    plaintext_packet      = json.dumps(packet_data_structure, default=(lambda o: {k: packet_data_structure[k] for k in packet_data_structure}), indent=0).encode()

    # Alice
    one_time_pad = generate_otp(seed=crown_npsn_rng(),
                                length=len(plaintext_packet),
                                offset=random.randint(1, 10))
    ciphertext   = xor_bytestrings(plaintext_packet, one_time_pad)

    # Eve
    decryption = crack_crown_otp(ciphertext=ciphertext)
    print(decryption)


if __name__ == '__main__':
    main()