On Hermitian LCD codes from cyclic codes and their applications to orthogonal direct sum masking

TL;DR

This paper constructs cyclic Hermitian LCD codes over finite fields, analyzes their parameters, and applies them to develop a Hermitian orthogonal direct sum masking scheme for fault injection attack protection.

Contribution

It introduces new cyclic Hermitian LCD codes with analyzed parameters and demonstrates their application in a novel masking scheme for enhanced security.

Findings

Constructed cyclic Hermitian LCD codes with known dimensions

Established lower bounds on minimum distances of these codes

Proposed a Hermitian orthogonal direct sum masking scheme for fault protection

Abstract

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. It was proved that asymptotically good Hermitian LCD codes exist. The objective of this paper is to construct some cyclic Hermitian LCD codes over finite fields and analyse their parameters. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented. Most Hermitian LCD codes presented in this paper are not BCH codes. In addition, we employ Hermitian LCD codes to propose a Hermitian orthogonal direct sum masking scheme that achieves protection against fault injection attacks. It is shown that the codes with great minimum distances are desired to improve the resistance.