A Unified Method for Finding Impossible Differentials of Block Cipher Structures

Yiyuan Luo; Zhongming Wu; Xuejia Lai; Guang Gong

Paper 2009/627

A Unified Method for Finding Impossible Differentials of Block Cipher Structures

Yiyuan Luo, Zhongming Wu, Xuejia Lai, and Guang Gong

Abstract

In this paper, we propose a systematic method for finding impossible differentials for block cipher structures, better than the $\mathcal{U}$-method introduced by Kim \textit{et al}~\cite{Kim03}. It is referred as a unified impossible differential finding method (UID-method). We apply the UID-method to some popular block ciphers such as {\sf Gen-Skipjack}, {\sf Gen-CAST256}, {\sf Gen-MARS}, {\sf Gen-RC6}, {\sf Four-Cell}, {\sf SMS4} and give the detailed impossible differentials. By the UID-method, we find a 16-round impossible differential on {\sf Gen-Skipjack} and a 19-round impossible differential on {\sf Gen-CAST256}. Thus we disprove the \textsl{Conjecture 2} proposed in \textsl{Asiacrypt'00}~\cite{Sung00} and the theorem in \textsl{FSE'09} rump session presentation~\cite{Pudovkina09}. On {\sf Gen-MARS} and {\sf SMS4}, the impossible differentials find by the UID-method are much longer than that found by the $\mathcal{U}$-method. On the {\sf Four-Cell} block cipher, our result is the same as the best result previously obtained by case-by-case treatment.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: secret-key cryptography block ciphers impossible Differential
Contact author(s): luoyiyuan @ gmail com
History: 2010-09-07: revised; 2009-12-26: received; See all versions
Short URL: https://ia.cr/2009/627
License: CC BY

BibTeX

@misc{cryptoeprint:2009/627,
      author = {Yiyuan Luo and Zhongming Wu and Xuejia Lai and Guang Gong},
      title = {A Unified Method for Finding Impossible Differentials of Block Cipher Structures},
      howpublished = {Cryptology ePrint Archive, Paper 2009/627},
      year = {2009},
      note = {\url{https://eprint.iacr.org/2009/627}},
      url = {https://eprint.iacr.org/2009/627}
}