A Long Tweak Goes a Long Way: High Multi-user Security Authenticated Encryption from Tweakable Block Ciphers

Abstract

We analyze the multi-user (mu) security of a family of nonce-based authentication encryption (nAE) schemes based on a tweakable block cipher (TBC). The starting point of our work is an analysis of the mu security of the SCT-II mode which underlies the nAE scheme Deoxys-II, winner of the CAESAR competition for the defense-in-depth category. We extend this analysis in two directions, as we detail now. First, we investigate the mu security of several TBC-based variants of the counter encryption mode (including CTRT, the encryption mode used within SCT-II) that differ by the way a nonce, a random value, and a counter are combined as tweak and plaintext inputs to the TBC to produce the keystream blocks that will mask the plaintext blocks. Then, we consider the authentication part of SCT-II and study the mu security of the nonce-based MAC Nonce-as-Tweak (NaT) built from a TBC and an almost universal (AU) hash function. We also observe that the standard construction of an AU hash function from a (T)BC can be proven secure under the assumption that the underlying TBC is unpredictable rather than pseudorandom, allowing much better conjectures on the concrete AU advantage. This allows us to derive the mu security of the family of nAE modes obtained by combining these encryption/MAC building blocks through the NSIV composition method. Some of these modes require an underlying TBC with a larger tweak length than what is usually available for existing ones. We then show the practicality of our modes by instantiating them with two new TBC constructions, Deoxys-TBC-512 and Deoxys-TBC-640, which can be seen as natural extensions of the Deoxys-TBC family to larger tweak input sizes. Designing such TBCs with unusually large tweaks is prone to pitfalls: Indeed, we show that a large-tweak proposal for SKINNY published at EUROCRYPT 2020 presents an inherent construction flaw. We therefore provide a sound design strategy to construct large-tweak TBCs within the Superposition Tweakey (STK) framework, leading to new Deoxys-TBC and SKINNY variants. We provide software benchmarks indicating that while ensuring a very high security level, the performances of our proposals remain very competitive.