International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Impossible Differential Cryptanalysis of SPN Ciphers

Ruilin Li
Bing Sun
Chao Li
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Abstract: Impossible differential cryptanalysis is a very popular tool for analyzing the security of modern block ciphers and the core of such attack is based on the existence of impossible differentials. Currently, most methods for finding impossible differentials are based on the miss-in-the-middle technique and they are very ad-hoc. In this paper, we concentrate SPN ciphers and propose several criteria on the linear transformation $P$ and its inversion $P^{-1}$ to characterize the existence of $3/4$-round impossible differentials. We further discuss the possibility to extend these methods to analyze $5/6$-round impossible differentials. Using these criteria, impossible differentials for reduced-round Rijndael are found that are consistent with the ones found before. New $4$-round impossible differentials are discovered for block cipher ARIA. And many $4$-round impossible differentials are firstly detected for a kind of SPN cipher that employs a $32\times32$ binary matrix proposed at ICISC 2006 as its diffusion layer.
  title={Impossible Differential Cryptanalysis of SPN Ciphers},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / block ciphers, SPN, Rijndael, ARIA, linear transformation, impossible differential},
  note={ 14760 received 23 May 2010, last revised 31 May 2010},
  author={Ruilin Li and Bing Sun and Chao Li},