计算机工程与科学2025，Vol.47Issue(12)：2139-2149,11.DOI:10.3969/j.issn.1007-130X.2025.12.006
基于MDS码和NMDS码的(几乎)最优可扩展码构造
Several constructions of(almost)optimally extendable linear codes from MDS codes and NMDS codes
摘要
Abstract
In the implementation of block ciphers,side channel attacks(SCAs)and fault injection attacks(FIAs)are crucial cryptanalysis methods.Let be a linear code over Fq with a generator matrix G,and'be a linear code over Fq with a generator matrix G'=[G:Ik],where Ik is the identity matrix of order k.If d('⊥)=d(⊥),then is said to be an optimally extendable linear code;if d('⊥)=d(⊥)-1,then is said to be an almost optimally extendable linear code.Optimally or almost opti-mally extendable linear codes effectively protect not only sensitive data stored in registers from SCAs and FIAs but also the entire algorithm.A class of almost optimally extendable linear codes with dimen-sion 5 is constructed by special generator matrices,and its parameters and weight enumerators are obtained.In addition,it is proved that another 4 classes of NMDS(near maximum distance separable)codes with dimension 5 and 2 classes of NMDS codes with dimension 4 are optimally extendable linear codes.In particular,the parameters of the(almost)optimally extendable linear codes are different from those of known(almost)optimally extendable linear codes,and the constructed codes have potential applications in direct sum masking.关键词
线性码/可扩展码/重量计数器Key words
linear code/extendable code/weight enumerator分类
数理科学引用本文复制引用
LI Wenting,HENG Ziling,LI Xiaoru..基于MDS码和NMDS码的(几乎)最优可扩展码构造[J].计算机工程与科学,2025,47(12):2139-2149,11.基金项目
国家自然科学基金(12271059) （12271059）
东南大学移动通信全国重点实验室开放研究基金(2024D10) （2024D10）
