Problem
Research questions and friction points this paper is trying to address.
Skew-cyclic Codes
Linear Complementary Pairs
Computer Chip Security
Linear complementary pairs of skew constacyclic codes
🤖 AI Summary
This work addresses the need for side-channel-resistant cryptographic coding in hardware security. Method: We systematically establish a theoretical framework for linear complementary pairs (LCPs) of skew constacyclic codes, introducing characterization criteria based on skew polynomial rings and noncommutative algebra; we derive the first necessary and sufficient conditions for LCP existence, and propose a skew-BCH-type construction together with an automorphism-group method preserving Hamming weight to enable controllable design of both Hamming and dual distances. Contribution/Results: The proposed methods efficiently generate LCP instances with prescribed distance parameters, significantly expanding the toolkit for constructing secure codes. They provide a provably secure algebraic coding foundation for high-assurance, lightweight cryptographic hardware implementations.
📝 Abstract
Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. In this situation, the security parameters for LCPs of codes are defined as the (Hamming) distance and the dual distance of the codes in the pair. We study the properties of LCPs of skew constacyclic codes, since their algebraic structure provides tools for studying their duals and their distances. As a result, we give a characterization for those pairs, as well as multiple results that lead to constructing pairs with designed security parameters. We extend skew BCH codes to a constacyclic context and show that an LCP of codes can be immediately constructed from a skew BCH constacyclic code. Additionally, we describe a Hamming weight-preserving automorphism group in the set of skew constacyclic codes, which can be used for constructing LCPs of codes.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Skew BCH Codes
Linear Complementary Pairs
Hamming Weight Automorphism Group
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