Breaking Cryptosystems

Given a Cryptosystem , , , with functions and . Eve may know and , as well as probability distributions of and we consider three possible levels of attack:

1. Eve knows some piece of ciphertext
2. Eve knows a considerable length of plaintext and the corresponding ciphertext but not the key
3. Eve can acquire the ciphertext for any plaintext message

Both Substitution cipher and Vigenere Cipher for an English text fail at level 1 for sufficiently long messages because we can just perform a frequency analysis Even for suitably random plaintext, both of them fail at level 2