Differential cryptanalysis of Feistel ciphers and differentially uniform mappings
INRIA, projet CODES
78153 Le Chesnay Cedex, France
Selected Areas on Cryptography, SAC'97 , pages 172-184, 1997.
In this paper we study the round permutations (or S-boxes) which
provide to Feistel ciphers the best resistance against differential
cryptanalysis. We prove that a Feistel cipher with any round keys and
with at least 5 rounds resists any differential attack if its round
permutation is differentially d-uniform for a
small d. This improves an earlier result due to Nyberg and
Knudsen which only held for independent and uniformly random round
keys. We also give some necessary conditions for a mapping to be
almost perfect nonlinear (i.e differentially 2-uniform).