Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / concatenated linear codes, Hadamard square, Hadamard product, Schur product, component-wise product, McEliece public-key cryptosystem, post-quantum cryptography

Original Publication (in the same form): Presented in the main program of The 10th Workshop on Current Trends in Cryptology (CTCrypt 2021)

Date: received 25 Aug 2021, withdrawn 7 Dec 2021

Contact author: ichizhov at cs msu ru, sdav94 at rambler ru

Available format(s): (-- withdrawn --)

Version: 20211207:195632 (All versions of this report)

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