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

Mahdi Sajadieh; Mohsen Mousavi

Paper 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.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Keywords: Shortest Straight-Line Program MDS matrix Heuristics algorithm for SLP
Contact author(s): m mousavi @ mut-es ac ir
History: 2020-01-13: received
Short URL: https://ia.cr/2020/032
License: CC BY

BibTeX

@misc{cryptoeprint:2020/032,
      author = {Mahdi Sajadieh and Mohsen Mousavi},
      title = {A New Approach for the Implementation of Binary Matrices Using {SLP} Applications},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/032},
      year = {2020},
      url = {https://eprint.iacr.org/2020/032}
}