Pseudorandom Permutation Families over Abelian Groups

  • Louis Granboulan
  • Éric Levieil
  • Gilles Piret
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4047)


We propose a general framework for differential and linear cryptanalysis of block ciphers when the block is not a bitstring. We prove piling-up lemmas for the generalized differential probability and the linear potential, and we study their lower bounds and average value, in particular in the case of permutations of \({\mathbb{F}_p}\). Using this framework, we describe a toy cipher, that operates on blocks of 32 decimal digits, and study its security against common attacks.


block cipher arbitrary domain differential and linear cryptanalysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Louis Granboulan
    • 1
  • Éric Levieil
    • 1
  • Gilles Piret
    • 1
  1. 1.École Normale Supérieure 

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