Reproducible families of codes and cryptographic applications

Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively...

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Autores principales:	Santini Paolo, Persichetti Edoardo, Baldi Marco
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	linear block codes code-based cryptography post-quantum cryptography reproducible codes 11t71 94a60 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/67452fa856484ee7b2bf62d1b5ac6360
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spelling	oai:doaj.org-article:67452fa856484ee7b2bf62d1b5ac63602021-12-05T14:10:52ZReproducible families of codes and cryptographic applications1862-298410.1515/jmc-2020-0003https://doaj.org/article/67452fa856484ee7b2bf62d1b5ac63602021-09-01T00:00:00Zhttps://doi.org/10.1515/jmc-2020-0003https://doaj.org/toc/1862-2984Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively studied, without searching for possible bridges between them. In this article, we start from well known examples of this type and generalize them into a wider class of codes that we call ℱ-reproducible codes. Some families of ℱ-reproducible codes have the property that they can be entirely generated from a small number of signature vectors, and consequently admit matrices that can be described in a very compact way. We denote these codes as compactly reproducible codes and show that they encompass known families of compactly describable codes such as quasi-cyclic and quasi-dyadic codes. We then consider some cryptographic applications of codes of this type and show that their use can be advantageous for hindering some current attacks against cryptosystems relying on structured codes. This suggests that the general framework we introduce may enable future developments of code-based cryptography.Santini PaoloPersichetti EdoardoBaldi MarcoDe Gruyterarticlelinear block codescode-based cryptographypost-quantum cryptographyreproducible codes11t7194a60MathematicsQA1-939ENJournal of Mathematical Cryptology, Vol 16, Iss 1, Pp 20-48 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	linear block codes code-based cryptography post-quantum cryptography reproducible codes 11t71 94a60 Mathematics QA1-939
spellingShingle	linear block codes code-based cryptography post-quantum cryptography reproducible codes 11t71 94a60 Mathematics QA1-939 Santini Paolo Persichetti Edoardo Baldi Marco Reproducible families of codes and cryptographic applications
description	Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively studied, without searching for possible bridges between them. In this article, we start from well known examples of this type and generalize them into a wider class of codes that we call ℱ-reproducible codes. Some families of ℱ-reproducible codes have the property that they can be entirely generated from a small number of signature vectors, and consequently admit matrices that can be described in a very compact way. We denote these codes as compactly reproducible codes and show that they encompass known families of compactly describable codes such as quasi-cyclic and quasi-dyadic codes. We then consider some cryptographic applications of codes of this type and show that their use can be advantageous for hindering some current attacks against cryptosystems relying on structured codes. This suggests that the general framework we introduce may enable future developments of code-based cryptography.
format	article
author	Santini Paolo Persichetti Edoardo Baldi Marco
author_facet	Santini Paolo Persichetti Edoardo Baldi Marco
author_sort	Santini Paolo
title	Reproducible families of codes and cryptographic applications
title_short	Reproducible families of codes and cryptographic applications
title_full	Reproducible families of codes and cryptographic applications
title_fullStr	Reproducible families of codes and cryptographic applications
title_full_unstemmed	Reproducible families of codes and cryptographic applications
title_sort	reproducible families of codes and cryptographic applications
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/67452fa856484ee7b2bf62d1b5ac6360
work_keys_str_mv	AT santinipaolo reproduciblefamiliesofcodesandcryptographicapplications AT persichettiedoardo reproduciblefamiliesofcodesandcryptographicapplications AT baldimarco reproduciblefamiliesofcodesandcryptographicapplications
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Reproducible families of codes and cryptographic applications

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