Open Access
Impossible Differential Cryptanalysis on Lai‐Massey Scheme
Author(s) -
Guo Rui,
Jin Chenhui
Publication year - 2014
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.14.0113.1335
Subject(s) - block cipher , differential cryptanalysis , impossible differential cryptanalysis , linear cryptanalysis , mathematics , boomerang attack , key schedule , higher order differential cryptanalysis , differential (mechanical device) , permutation (music) , cipher , algorithm , encryption , cryptography , computer science , computer security , physics , acoustics , thermodynamics
The Lai‐Massey scheme, proposed by Vaudenay, is a modified structure in the International Data Encryption Algorithm cipher. A family of block ciphers, named FOX, were built on the Lai‐Massey scheme. Impossible differential cryptanalysis is a powerful technique used to recover the secret key of block ciphers. This paper studies the impossible differential cryptanalysis of the Lai‐Massey scheme with affine orthomorphism for the first time. Firstly, we prove that there always exist 4‐round impossible differentials of a Lai‐Massey cipher having a bijective F‐function. Such 4‐round impossible differentials can be used to help find 4‐round impossible differentials of FOX64 and FOX128. Moreover, we give some sufficient conditions to characterize the existence of 5‐, 6‐, and 7‐round impossible differentials of Lai‐Massey ciphers having a substitution‐permutation (SP) F‐function, and we observe that if Lai‐Massey ciphers having an SP F‐function use the same diffusion layer and orthomorphism as a FOX64, then there are indeed 5‐ and 6‐round impossible differentials. These results indicate that both the diffusion layer and orthomorphism should be chosen carefully so as to make the Lai‐Massey cipher secure against impossible differential cryptanalysis.