Algebraic Techniques in Linear Cryptanalysis

Abstract

Linear cryptanalysis is a statistical analysis method. Linear cryptanalysis constructs probabilistic patterns first and then distinguishes the cipher from a random permutation using lots of plaintext-ciphertext pairs. Linear cryptanalysis has a big data complexity. Algebraic attack attempts to exploit the algebraic structure of the cipher by expressing the encryption transformation as a set of polynomial equations and then attempts to solve the system to recover the encryption key. Algebraic attacks do not need too much data. This paper combines these two methods by using algebraic techniques in linear cryptanalysis, and proposes a new cryptanalysis method called Algebraic Techniques in Linear Cryptanalysis. This new method is used in the existing linear cryptanalysis of PRESENT. To recover 8-bit key information of 21-round PRESENT, the data complexity is2'and the time complexity is 2'.Compared with the result of linear cryptanalysis, the data complexity is obviously decreased.