The multi-user security of double encryption

Abstract

It is widely known that double encryption does not substantially increase the security of a block cipher. Indeed, the classical meet-in-the middle attack recovers the 2k-bit secret key at the cost of roughly 2k off-line enciphering operations, in addition to very few known plaintext-ciphertext pairs. Thus, essentially as efficiently as for the underlying cipher with a k-bit key. This paper revisits double encryption under the lens of multi-user security. We prove that its security degrades only very mildly with an increasing number of users, as opposed to single encryption, where security drops linearly. More concretely, we give a tight bound for the multiuser security of double encryption as a pseudorandom permutation in the ideal-cipher model, and describe matching attacks. Our contribution is also conceptual: To prove our result, we enhance and generalize the generic technique recently proposed by Hoang and Tessaro for lifting single-user to multi-user security. We believe this technique to be broadly applicable.