A Generalization of Linear Cryptanalysis and the Applicability of Matsui’s Piling-up Lemma

Abstract

. Matsui’s linear cryptanalysis for iterated block ciphers is generalized by replacing his linear expressions with 1/ 0 sums. For a single round, an 1/0 sum is the XOR of a balanced binary-valued function of the round input and a balanced binary-valued function of the round output. The basic attack is described and conditions for it to be successful are given. A procedure for finding effective 1/ 0 sums, i.e., 1/0 sums yielding successful attacks, is given. A cipher contrived to be secure against linear cryptanalysis but vulncrable to this generalization of linear cryptanalysis is given. Finally, it is argued that the ciphers IDEA and SAFER K-64 are secure against this generalization.