Open AccessPractical and Provable Security against Differential and Linear Cryptanalysis for Substitution‐Permutation Networks
Author(s) -
Kang JuSung,
Hong Seokhie,
Lee Sangjin,
Yi Okyeon,
Park Choonsik,
Lim Jongin
Publication year - 2001
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.01.0101.0402
Subject(s) - linear cryptanalysis , permutation (music) , block cipher , provable security , mathematics , differential (mechanical device) , bounded function , cryptanalysis , differential cryptanalysis , discrete mathematics , diffusion , higher order differential cryptanalysis , combinatorics , algorithm , cryptography , mathematical analysis , physics , acoustics , thermodynamics
We examine the diffusion layers of some block ciphers referred to as substitution‐permutation networks. We investigate the practical and provable security of these diffusion layers against differential and linear cryptanalysis. First, in terms of practical security, we show that the minimum number of differentially active S‐boxes and that of linearly active S‐boxes are generally not identical and propose some special conditions in which those are identical. We also study the optimal diffusion effect for some diffusion layers according to their constraints. Second, we obtain the results that the consecutive two rounds of SPN structure provide provable security against differential and linear cryptanalysis, i.e., we prove that the probability of each differential (resp. linear hull) of the consecutive two rounds of SPN structure with a maximal diffusion layer is bounded by p n (resp. q n ) and that of each differential (resp. linear hull) of the SDS function with a semi‐maximal diffusion layer is bounded by p n‐ 1 (resp. q n‐ 1 ), where p and q are maximum differential and linear probabilities of the substitution layer, respectively.