Welcome to the resource topic for 2017/195
Title:
Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices
Authors: Chaoyun Li, Qingju Wang
Abstract:Near-MDS matrices provide better trade-offs between security and efficiency compared to constructions based on MDS matrices, which are favored for hardware-oriented designs. We present new designs of lightweight linear diffusion layers by constructing lightweight near-MDS matrices. Firstly generic n\times n near-MDS circulant matrices are found for 5\leq n \leq 9. Secondly,, the implementation cost of instantiations of the generic near-MDS matrices is examined. Surprisingly, for n=7,8, it turns out that some proposed near-MDS circulant matrices of order n have the lowest XOR count among all near-MDS matrices of the same order. Further, for n=5,6, we present near-MDS matrices of order n having the lowest XOR count as well. The proposed matrices, together with previous construction of order less than five, lead to solutions of n\times n near-MDS matrices with the lowest XOR count over finite fields \mathbb{F}_{2^m} for 2\leq n \leq 8 and 4\leq m \leq 2048. Moreover, we present some involutory near-MDS matrices of order 8 constructed from Hadamard matrices. Lastly, the security of the proposed linear layers is studied by calculating lower bounds on the number of active S-boxes. It is shown that our linear layers with a well-chosen nonlinear layer can provide sufficient security against differential and linear cryptanalysis.
ePrint: https://eprint.iacr.org/2017/195
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