Paper 2024/084

Efficient Instances of Docked Double Decker With AES, and Application to Authenticated Encryption

Abstract

A tweakable wide blockcipher is a construction which behaves in the same way as a tweakable blockcipher, with the difference that the actual block size is flexible. Due to this feature, a tweakable wide blockcipher can be directly used as a strong encryption scheme that provides full diffusion when encrypting plaintexts to ciphertexts and vice versa. Furthermore, it can be the basis of authenticated encryption schemes fulfilling the strongest security notions. In this paper, we present two instantiations of the docked double decker tweakable wide blockcipher: $\mathit{ddd}\text{-}\mathit{AES}$ and $\mathit{bbb}\text{-}\mathit{ddd}\text{-}\mathit{AES}$. Both instances exclusively use similar building blocks as AES-GCM (AES and finite field multiplication), are designed for maximal parallelism, and hence, can make efficient use of existing hardware accelerators. Moreover, $\mathit{bbb}\text{-}\mathit{ddd}\text{-}\mathit{AES}$ builds upon a novel beyond birthday bound secure pseudorandom function, a tweakable variant of the XOR of permutations, facilitating in the need to include a tweak in the AES evaluations without sacrificing flexibility in docked double decker. We furthermore introduce an authenticated encryption mode $\mathit{aaa}$ specifically tailored to be instantiated with $\mathit{ddd}\text{-}\mathit{AES}$ and $\mathit{bbb}\text{-}\mathit{ddd}\text{-}\mathit{AES}$, where special attentions is given to how the nonce and associated data can be processed. We prove that this mode is secure both in the nonce-respecting setting as well as in the setting where random nonces are used.