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International Conference on Advanced Encryption Standard

AES 2004: Advanced Encryption Standard – AES pp 42–57Cite as

Refined Analysis of Bounds Related to Linear and Differential Cryptanalysis for the AES

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3373))

Abstract

The best upper bounds on the maximum expected linear probability (MELP) and the maximum expected differential probability (MEDP) for the AES, due to Park et al. [23], are 1.075 × 2− − 106 and 1.144 × 2− − 111, respectively, for T ≥ 4 rounds. These values are simply the 4th powers of the best upper bounds on the MELP and MEDP for T=2 [3,23]. In our analysis we first derive nontrivial lower bounds on the 2-round MELP and MEDP, thereby trapping each value in a small interval; this demonstrates that the best 2-round upper bounds are quite good. We then prove that these same 2-round upper bounds are not tight—and therefore neither are the corresponding upper bounds for T ≥ 4. Finally, we show how a modified version of the KMT2 algorithm (or its dual, KMT2-DC), due to Keliher et al. (see [8]), can potentially improve any existing upper bound on the MELP (or MEDP) for any SPN. We use the modified version of KMT2 to improve the upper bound on the AES MELP to 1.778 × 2− − 107,for T ≥ 8.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada

    Liam Keliher

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  1. Liam Keliher
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Editor information

Editors and Affiliations

  1. Cryptology and IT Security Research Group, Ruhr-University of Bochum Germany, P.O. Box,  

    Hans Dobbertin

  2. ESAT/COSIC, K.U. Leuven, Kasteelpark Arenberg 10, B-3001, Leuven-Heverlee, Belgium

    Vincent Rijmen

  3. Horst Görtz Institut für Sicherheit in der Informationstechnik, Ruhr-University of Bochum, Universitätsstrasse 150, 44780, Bochum, Germany

    Aleksandra Sowa

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Keliher, L. (2005). Refined Analysis of Bounds Related to Linear and Differential Cryptanalysis for the AES. In: Dobbertin, H., Rijmen, V., Sowa, A. (eds) Advanced Encryption Standard – AES. AES 2004. Lecture Notes in Computer Science, vol 3373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11506447_5

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  • DOI: https://doi.org/10.1007/11506447_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26557-3

  • Online ISBN: 978-3-540-31840-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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