Title: Dynamic MDS diffusion layers with efficient software implementation

Authors: Mohammad Reza Mirzaee Shamsabad; Seyed Mojtaba Dehnavi

Addresses: Faculty of Mathematics, Shahid Beheshti University, Iran ' Department of Mathematical and Computer Sciences, University of Kharazmi, Iran

Abstract: Maximum distance separable (MDS) matrices play a crucial role in symmetric ciphers as diffusion layers. Dynamic diffusion layers for software applications are less considered up to now. Dynamic (randomised) components could make symmetric ciphers more resistant against statistical and algebraic attacks. In this paper, after some theoretical investigation we present a family of parametric n × n, binary matrices A_α, n = 4t, such that for 4^t many α ∈ Fⁿ₂ the matrices A_α, A³_α ⊕ I and A⁷_α ⊕ I are non-singular. With the aid of the proposed family of matrices, some well-known diffusion layers including the cyclic AES-like matrices and some recursive MDS diffusion layers could be made dynamic, at little extra cost in software. Then, we provide new families of MDS matrices which could be used as dynamic diffusion layers, using the proposed family of matrices. The implementation cost of every member in the presented families of MDS diffusion layers (except one cyclic family) is equal to its inverse. The proposed diffusion layers have a suitable implementation cost on a variety of modern processors.

Keywords: MDS matrix; symmetric cipher; dynamic diffusion layer; branch number; software implementation.

DOI: 10.1504/IJACT.2020.107164

International Journal of Applied Cryptography, 2020 Vol.4 No.1, pp.36 - 44

Received: 28 Jul 2018
Accepted: 01 May 2019
Published online: 06 May 2020 *

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