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Automatic Search of Truncated Impossible Differentials for Word-Oriented Block Ciphers

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Progress in Cryptology - INDOCRYPT 2012 (INDOCRYPT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7668))

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Abstract

Impossible differential cryptanalysis is a powerful technique to recover the secret key of block ciphers by exploiting the fact that in block ciphers specific input and output differences are not compatible. This paper introduces a novel tool to search truncated impossible differentials for word-oriented block ciphers with bijective Sboxes. Our tool generalizes the earlier \(\mathcal{U}\)-method and the UID-method. It allows to reduce the gap between the best impossible differentials found by these methods and the best known differentials found by ad hoc methods that rely on cryptanalytic insights. The time and space complexities of our tool in judging an r-round truncated impossible differential are about O(c·l 4·r 4) and O(c′·l 2·r 2) respectively, where l is the number of words in the plaintext and c, c′ are constants depending on the machine and the block cipher. In order to demonstrate the strength of our tool, we show that it does not only allow to automatically rediscover the longest truncated impossible differentials of many word-oriented block ciphers, but also finds new results. It independently rediscovers all 72 known truncated impossible differentials on 9-round CLEFIA. In addition, it finds new truncated impossible differentials for AES, ARIA, Camellia without FL and FL− 1 layers, E2, LBlock, MIBS and Piccolo. Although our tool does not improve the lengths of impossible differentials for existing block ciphers, it helps to close the gap between the best known results of previous tools and those of manual cryptanalysis.

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Author information

Authors and Affiliations

  1. Institute of Software, Chinese Academy of Sciences, Beijing, 100190, PO Box 8718, China

    Shengbao Wu

  2. Graduate School of Chinese Academy of Sciences, Beijing, 100190, China

    Shengbao Wu

  3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Mingsheng Wang

Authors
  1. Shengbao Wu
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  2. Mingsheng Wang
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Editors and Affiliations

  1. Department of Mathematics, University of Auckland, Private Bag 92019, 1142, Auckland, New Zealand

    Steven Galbraith

  2. Indian Statistical Institute, Applied Statistics Unit, 203 B.T. Road, 700108, Kolkata, West Bengal, India

    Mridul Nandi

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Wu, S., Wang, M. (2012). Automatic Search of Truncated Impossible Differentials for Word-Oriented Block Ciphers. In: Galbraith, S., Nandi, M. (eds) Progress in Cryptology - INDOCRYPT 2012. INDOCRYPT 2012. Lecture Notes in Computer Science, vol 7668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34931-7_17

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  • DOI: https://doi.org/10.1007/978-3-642-34931-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34930-0

  • Online ISBN: 978-3-642-34931-7

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