On the Construction of Low-latency 32 × 32 Binary MDS Matrices from GHadamard Matrices

Year 2021, Volume: 10 Issue: 4, 111 - 118, 31.12.2021

Meltem Kurt Pehlivanoğlu , Fatma Büyüksaraçoğlu Sakallı Muharrem Tolga Sakallı

Abstract

In this paper, we generate new hardware efficient involutory 32 × 32 binary Maximum Distance Separable (MDS) diffusion layers with branch number 5. In our construction method, the idea used in Generalised Hadamard (GHadamard) matrix form is applied when generating these diffusion layers. We construct lightweight circuits by applying Boyar’s global optimization heuristic (BP) to these diffusion layers. Hence, new 32 × 32 binary involutory MDS matrices with the best-known implementation cost (78 XORs) and depth 4 are generated. The obtained result is the same with the previous result given in [1], and we show that the diffusion layer given in [1] can also be obtained directly by using our construction method. As a result, we give thirteen more new involutory 32 × 32 binary MDS matrices with the best-known result.

Keywords

GHadamard matrix form, 32 × 32 binary MDS matrix, Global optimization, Involutory matrix

Supporting Institution

Scientific Research Project Department of Kocaeli University

Project Number

FHD- 2020-2272

Thanks

Meltem Kurt Pehlivanoğlu is partially supported by the Scientific Research Project Department of Kocaeli University under the Project No: FHD-2020-2272.

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