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