What is the effective key length for a block cipher: an attack on every practical block cipher

Abstract

Recently, several important block ciphers are considered to be broken by the brute-force-like cryptanalysis, with a time complexity faster than the exhaustive key search by going over the entire key space but performing less than a full encryption for each possible key. Motivated by this observation, we describe a meetin-the-middle attack that can always be successfully mounted against any practical block ciphers with success probability one. The data complexity of this attack is the smallest according to the unicity distance. The time complexity can be written as 2 k (1 − ∈), where ∈ > 0 for all practical block ciphers. Previously, the security bound that is commonly accepted is the length k of the given master key. From our result we point out that actually this k-bit security is always overestimated and can never be reached because of the inevitable loss of the key bits. No amount of clever design can prevent it, but increments of the number of rounds can reduce this key loss as much as possible. We give more insight into the problem of the upper bound of effective key bits in block ciphers, and show a more accurate bound. A suggestion about the relationship between the key size and block size is given. That is, when the number of rounds is fixed, it is better to take a key size equal to the block size. Also, effective key bits of many well-known block ciphers are calculated and analyzed, which also confirms their lower security margins than thought before. The results in this article motivate us to reconsider the real complexity that a valid attack should compare to.