MDS Matrices Over Rings For Designing Lightweight Block Cİpher

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2021-9-30

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Yetişer, Gökçe

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The primary intention of this thesis is to generate lightened Maximum Distance Separable (MDS) matrices so as not to have a high implementation cost while providing solid diffusion to a cipher. In this direction, lightweight cryptography along with the current capabilities of devices and some design principles and permutation layer is given briefly. Next, the diffusion property of block cipher design is studied, where the permutation layer is generally an invertible linear transformation, and they are generally represented as matrices. In this thesis, we mainly focus on the design of MDS matrices over rings for efficient block ciphers; in particular, the matrices resulting in better implementation costs are considered. To generate MDS matrices with lower XOR gate number and depth, we advance the technique given by Li et. al. and expand the search space and reach better implementation results. For the implementation cost, we count the number of XOR gates and the depth by benefiting a modified version of Boyar’s SLP heuristic algorithm, with depth awareness, given in the same article. In particular, we tabulate some matrices with good implementation costs. The best involutory MDS matrix, with branch number 5, found in this study has only 64 XOR gates with depth 3, which is a new record. The matrices found could be used in any cipher to provide diffusion, as long as the input size of the one-time multiplication operation is set to be 32 bits. In addition, it also provides a strong permutation with optimal cost.

Subject Keywords

MDS matrices, Block ciphers, Lightweight cryptography

URI

https://hdl.handle.net/11511/93027

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

G. Yetişer, “MDS Matrices Over Rings For Designing Lightweight Block Cİpher,” M.S. - Master of Science, Middle East Technical University, 2021.