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Generalization of Matsui’s Algorithm 1 to linear hull for key-alternating block ciphers

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Abstract

We consider linear approximations of an iterated block cipher in the presence of several strong linear approximation trails. While the effect of such trails in Matsui’s Algorithm 2, also called the linear hull effect, has been previously studied by a number of authors, their effect on Matsui’s Algorithm 1 has not been investigated until now. The goal of this paper is to fill this gap and examine how to generalize Matsui’s Algorithm 1 to work also on linear hulls. We restrict to key-alternating ciphers and develop a mathematical framework for this kind of attacks. The complexity of the attack increases with the number of linear trails that have significant contribution to the correlation. We show how to reduce the number of trails and thus the complexity using related keys. Further, we illustrate our theory by experimental results on a reduced round version of the block cipher PRESENT.

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Authors and Affiliations

  1. Department of Information and Computer Science, Aalto University School of Science, P.O. Box 15400, 00076, Aalto, Finland

    Andrea Röck & Kaisa Nyberg

  2. Nokia Research Center, P.O. Box 407, 00045, Nokia Group, Finland

    Kaisa Nyberg

Authors
  1. Andrea Röck
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  2. Kaisa Nyberg
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Correspondence to Andrea Röck.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

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Röck, A., Nyberg, K. Generalization of Matsui’s Algorithm 1 to linear hull for key-alternating block ciphers. Des. Codes Cryptogr. 66, 175–193 (2013). https://doi.org/10.1007/s10623-012-9679-1

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  • DOI: https://doi.org/10.1007/s10623-012-9679-1

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