On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form

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KURT PEHLİVANOĞLU M., BÜYÜKSARAÇOĞLU SAKALLI F., Akleylek S., Sakalli M. T.

IEEE ACCESS, vol.11, pp.32708-32715, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11
  • Publication Date: 2023
  • Doi Number: 10.1109/access.2023.3262924
  • Journal Name: IEEE ACCESS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
  • Page Numbers: pp.32708-32715
  • Keywords: Ciphers, Optimization, Measurement, Costs, Codes, Matrices, Logic gates, Cryptography, Diffusion layers, generalized subfield construction, global optimization, lightweight cryptography, MDS matrices, DIFFUSION LAYERS, GENERATE
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Maximum Distance Separable (MDS) matrices are used as the main component of diffusion layers in block ciphers. MDS matrices have the optimal diffusion properties and the maximum branch number, which is a criterion to measure diffusion rate and security against linear and differential crypt analysis. However, it is a challenging problem to construct hardware-friendly MDS matrices with optimal or close to optimal circuits, especially for involutory ones. In this paper, we consider the generalized subfield construction method from the global optimization perspective and then give new 4 x 4 involutory MDS matrices over F-2(3) and F-2(5). After that, we present 1,176 (= 28 x 42) new 4 x 4 involutory and MDS diffusion matrices by 33 XORs and depth 3. This new record also improves the previously best-known cost of 38 XOR gates.