# Memory required for known plaintext attack on general block cipher

Consider a block cipher on binary strings of length $$k$$ and keys which can be any binary string of length $$n$$. With $$k2^n+k$$ memory we can store all key/ciphertext pairs for a fixed plaintext and this allows for a quick chosen plaintext attack. What is the corresponding result for a known plaintext attack. We can do this with about $$2^{n+k}$$ memory by storing all key/ciphertext pairs for all plaintext.

Without considering specific properties of the cipher, is it possible to do better?