Pseudorandom permutation families over abelian groups

  • Authors:
  • Louis Granboulan;Éric Levieil;Gilles Piret

  • Affiliations:
  • École Normale Supérieure;École Normale Supérieure;École Normale Supérieure

  • Venue:
  • FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
  • Year:
  • 2006

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Abstract

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.