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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?

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