Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices

Authors

  • Chaoyun Li imec - Computer Security and Industrial Cryptography (COSIC) research group, Department of Electrical Engineering (ESAT), KU Leuven, Leuven, Belgium
  • Qingju Wang imec - Computer Security and Industrial Cryptography (COSIC) research group, Department of Electrical Engineering (ESAT), KU Leuven, Leuven, Belgium;Department of Applied Mathematics and Computer Science (DTU Compute), Technical University of Denmark, Kongens Lyngby, Denmark; Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

DOI:

https://doi.org/10.13154/tosc.v2017.i1.129-155

Keywords:

lightweight cryptography, diffusion layer, near-MDS matrix, branch number

Abstract

Near-MDS matrices provide better trade-offs between security and efficiency compared to constructions based on MDS matrices, which are favored for hardwareoriented designs. We present new designs of lightweight linear diffusion layers by constructing lightweight near-MDS matrices. Firstly generic n×n near-MDS circulant matrices are found for 5 ≤ n ≤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×n near-MDS matrices with the lowest XOR count over finite fields F2m for 2 ≤ n ≤ 8 and 4 ≤ m ≤ 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.

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Published

2017-03-08

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Section

Articles

How to Cite

Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices. (2017). IACR Transactions on Symmetric Cryptology, 2017(1), 129-155. https://doi.org/10.13154/tosc.v2017.i1.129-155