Cryptology ePrint Archive: Report 2020/032

A New Approach for the Implementation of Binary Matrices Using SLP Applications

Mahdi Sajadieh and Mohsen Mousavi

Abstract: In this paper, we propose a method for implementing binary matrices with low-cost XOR. First, using a random-iterative method, we obtain a list S from a binary matrix A. Then, based on the list S, we construct a binary matrix B. Next, we find a relation between the implementations of A and B. In other words, using the implementation of the matrix B, we get a low-cost implementation for the matrix A. Also, we show that the implementation of an MDS matrix M is associated with the form of the binary matrix used to construct the binary form of M. In addition, we propose a heuristics algorithm to implement MDS matrices. The best result of this paper is the implementation of a 8 8 involutory MDS matrix over 8-bit words with 408 XOR gates. The Paar algorithm is used as an SLP application to obtain implementations of this paper.

Category / Keywords: implementation / Shortest Straight-Line Program, MDS matrix, Heuristics algorithm for SLP

Date: received 12 Jan 2020

Contact author: m mousavi at mut-es ac ir

Available format(s): PDF | BibTeX Citation

Version: 20200113:102957 (All versions of this report)

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