Impossible Differential Cryptanalysis on Lai‐Massey Scheme. Issue 6 (1st December 2014)

• Record Type: Journal Article
• Authors: Guo, Rui; Jin, Chenhui
• Is Part Of: ETRI journal. Volume 36:Issue 6(2014)
• Page Start: 1032
• Page End: 1040
• Publication Date: 2014-12-01
• Subjects: Lai‐Massey scheme -- FOX cipher -- impossible differentials analysis; Telecommunication -- Periodicals; Electronics -- Periodicals; Electronics; Telecommunication; Periodicals; Periodicals; 621.38205
• DOI: 10.4218/etrij.14.0113.1335
• Languages: English
• ISSNs: 1225-6463

Abstract

Abstract : 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.