On Multidimensional Linear Cryptanalysis

  • Phuong Ha Nguyen
  • Lei Wei
  • Huaxiong Wang
  • San Ling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6168)

Abstract

Matsui’s Algorithms 1 and 2 with multiple approximations have been studied over 16 years. In CRYPTO’04, Biryukov et al. proposed a formal framework based on m statistically independent approximations. Started by Hermelin et al. in ACISP’08, a different approach was taken by studying m-dimensional combined approximations from m base approximations. Known as multidimensional linear cryptanalysis, the requirement for statistical independence is relaxed. In this paper we study the multidimensional Alg. 1 of Hermelin et al.. We derive the formula for N, the number of samples required for the attack and we improve the algorithm by reducing time complexity of the distillation phase from 2mN to 2m2m + mN, and that of the analysis phase from 22m to 3m2m. We apply the results on 4- and 9-round Serpent and show that Hermelin et al. actually provided a formal model for the hypothesis of Biryukov et al. in practice, and this model is now much more practical with our improvements.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Phuong Ha Nguyen
    • 1
  • Lei Wei
    • 1
  • Huaxiong Wang
    • 1
  • San Ling
    • 1
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore

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