Security and Cryptography in Python - One Time Pad

XOR Example

def xor(x, s):
    print(x, 'xor', s, '=', x^s)

def xorb(x, s):
    print(bin(x), 'xor', bin(s), '=', bin(x^s))

xor(4, 8)
xorb(4, 8)
xor(4, 4)
xorb(4, 4)
xor(255, 1)
xorb(255, 1)
xor(255, 128)
xorb(255, 128)

Running Result:

What is One Time Pad?

Encryption: message^key(random) = cipher

Decryption: cipher^key(random) = message

import random

def generate_key_stream(n):
    return bytes(random.randrange(0, 256) for i in range(n))

def xor_bytes(key_stream, message):
    length = min(len(key_stream), len(message))
    return bytes([key_stream[i]^ message[i] for i in range(length)])

message = "YOU ARE AWESOME"
message = message.encode()
key_stream = generate_key_stream(len(message))
cipher = xor_bytes(key_stream, message)
print(key_stream)
print(cipher)
print(xor_bytes(key_stream, cipher))

Running Result:

One Time Pad - Security

The One Time Pad is unbreakable

Requirements:

• Key stream only used once
• Key stream only know by sender and receiver
• Key stream is generated by true randomness

Why can't One Time Pad be Broken?

You can decrypted to any plaintext available in the universe with that length.

import random

def generate_key_stream(n):
    return bytes(random.randrange(0, 256) for i in range(n))

def xor_bytes(key_stream, message):
    length = min(len(key_stream), len(message))
    return bytes([key_stream[i]^ message[i] for i in range(length)])

# this is done by your enemy
message = "DO ATTACK"
message = message.encode()
key_stream = generate_key_stream(len(message))
cipher = xor_bytes(key_stream, message)

# this is us trying to break it
print(cipher)
message = "NO ATTACK"
message = message.encode()
guess_key_stream = xor_bytes(message, cipher)
print(xor_bytes(guess_key_stream, cipher))

Running Result: