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    On Lightweight 4 × 4 MDS Matrices over Binary Field Extensions
    (2020) Sakallı, Fatma Büyüksaraçoğlu; Aydın, Özlem; Tuncay, Gökhan; Pehlivanoğlu, Meltem Kurt; Güzel, Gülsüm Gözde; Sakallı, Muharrem Tolga
    Maximum Distance Separable (MDS) matrices are used as the main part of diffusion layers in block ciphers andhash functions. MDS matrices derived from MDS codes have the maximum differential and linear branch number, which provideresistance against some well-known attacks like differential and linear cryptanalysis together with the use of a nonlinear layer(e.g. S-boxes) in a round function of a block cipher. In this paper, we introduce generic methods to generate lightweight 4 × 4involutory/non-involutory MDS matrices over F2m and present the lightest involutory/non-involutory 4 × 4 MDS matrices over F24(to the best of our knowledge) by considering XOR count metric, which is defined to estimate hardware implementation cost. Also,the results are obtained by using a global optimization technique, namely Boyar-Peralta algorithm.
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    On the Construction of Low-latency 32 × 32 Binary MDS Matrices from GHadamard Matrices
    (2021) Pehlivanoğlu, Meltem Kurt; Sakallı, Fatma Büyüksaraçoğlu; Sakallı, Muharrem Tolga
    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