Paper 2021/1097

The Hadamard square of concatenated linear codes

Ivan Chizhov and Alexandra Davletshina

Abstract

The paper is devoted to the Hadamard square of concatenated linear codes. Such codes consist of codewords that are obtained by concatenation part of the codewords from other codes. It is proved that if the sum of Hadamard squares’ dimensions of the codes used in the concatenation is slightly less than the dimension of the entire space, then the Hadamard square of the concatenated code is equal to the Cartesian product of the Hadamard square of code-components. It means that the cryptanalysis for many code-based post-quantum cryptographic mechanisms built on concatenated codes is equivalent to the cryptanalysis of these mechanisms built on code-components. So using the concatenation of codes from different classes instead of one class of codes, generally speaking, does not increase the cryptographic strength of the mechanisms.