Optimally Secure Tweakable Block Ciphers with a Large Tweak from n-bit Block Ciphers

Yaobin Shen; François-Xavier Standaert

Paper 2023/790

Optimally Secure Tweakable Block Ciphers with a Large Tweak from n-bit Block Ciphers

Yaobin Shen, UCLouvain

François-Xavier Standaert, UCLouvain

Abstract

We consider the design of a tweakable block cipher from a block cipher whose inputs and outputs are of size $n$ bits. The main goal is to achieve $2^{n}$ security with a large tweak (i.e., more than $n$ bits). Previously, Mennink at FSE'15 and Wang et al. at Asiacrypt'16 proposed constructions that can achieve $2^{n}$ security. Yet, these constructions can have a tweak size up to $n$ -bit only. As evident from recent research, a tweakable block cipher with a large tweak is generally helpful as a building block for modes of operation, typical applications including MACs, authenticated encryption, leakage-resilient cryptography and full-disk encryption. We begin with how to design a tweakable block cipher with -bit tweak and -bit security from two block cipher calls. For this purpose, we do an exhaustive search for tweakable block ciphers with -bit tweaks from two block cipher calls, and show that all of them suffer from birthday-bound attacks. Next, we investigate the possibility to design a tweakable block cipher with -bit tweak and -bit security from three block cipher calls. We start with some conditions to build a such tweakable block cipher and propose a natural construction, called G1, that likely meets them. After inspection, we find a weakness on G1 which leads to a birthday-bound attack. Based on G1, we then propose another construction, called G2, that can avoid this weakness. We finally prove that G2 can achieve -bit security with -bit tweak.

Note: IACR Transactions on Symmetric Cryptology 2023(2)

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published by the IACR in TOSC 2024
Keywords: Tweakable Block Cipher Optimal (n-bit) Security Large Tweak
Contact author(s): yaobin shen @ uclouvain be
fstandae @ uclouvain be
History: 2023-06-06: approved; 2023-05-30: received; See all versions
Short URL: https://ia.cr/2023/790
License: CC BY

BibTeX

@misc{cryptoeprint:2023/790,
      author = {Yaobin Shen and François-Xavier Standaert},
      title = {Optimally Secure Tweakable Block Ciphers with a Large Tweak from n-bit Block Ciphers},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/790},
      year = {2023},
      url = {https://eprint.iacr.org/2023/790}
}