LCD codes and almost optimally extendable codes from self-orthogonal codes

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2024-05-17 DOI:10.1007/s10623-024-01420-y

Xinran Wang, Ziling Heng, Fengwei Li, Qin Yue

引用次数: 0

Abstract

LCD codes and (almost) optimally extendable codes can be used to safeguard against fault injection attacks (FIA) and side-channel attacks (SCA) in the implementations of block ciphers. The first objective of this paper is to use a family of binary self-orthogonal codes given by Ding and Tang (Cryptogr Commun 12:1011–1033, 2020) to construct a family of binary LCD codes with new parameters. The parameters of the binary LCD codes and their duals are explicitly determined. It turns out that the codes by Ding and Tang are almost optimally extendable codes. The second objective is to prove that two families of known q-ary linear codes given by Heng et al. (IEEE Trans Inf Theory 66(11):6872–6883, 2020) are self-orthogonal. Using these two families of self-orthogonal codes, we construct another two families of q-ary LCD codes. The parameters of the LCD codes are determined and many optimal codes are produced. Besides, the two known families of q-ary linear codes are also proved to be almost optimally extendable codes.

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液晶编码和自正交编码的几乎最佳扩展编码

液晶编码和（几乎）可优化扩展的编码可用于防范块密码实现中的故障注入攻击（FIA）和侧信道攻击（SCA）。本文的第一个目标是利用丁和唐（Cryptogr Commun 12:1011-1033, 2020）给出的二进制自正交码族构建具有新参数的二进制 LCD 码族。二进制 LCD 码及其对偶码的参数是明确确定的。结果表明，丁和唐的编码几乎是可优化扩展的编码。第二个目标是证明恒等人（IEEE Trans Inf Theory 66(11):6872-6883, 2020）给出的两个已知 q-ary 线性编码族是自正交的。利用这两个自正交码族，我们构建了另外两个 q-ary LCD 码族。我们确定了液晶编码的参数，并产生了许多最优编码。此外，我们还证明了已知的两个 q-ary 线性码族几乎是可优化扩展的码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.