Lightweight MDS Serial-type Matrices with Minimal Fixed XOR Count (Full version)

Dylan Toh; Jacob Teo; Khoongming Khoo; Siang Meng Sim

Paper 2017/1084

Lightweight MDS Serial-type Matrices with Minimal Fixed XOR Count (Full version)

Dylan Toh, Jacob Teo, Khoongming Khoo, and Siang Meng Sim

Abstract

Many block ciphers and hash functions require the diffusion property of Maximum Distance Separable (MDS) matrices. Serial matrices with the MDS property obtain a trade-off between area requirement and clock cycle performance to meet the needs of lightweight cryptography. In this paper, we propose a new class of serial-type matrices called Diagonal-Serial Invertible (DSI) matrices with the sparse property. These matrices have a fixed XOR count (contributed by the connecting XORs) which is half that of existing matrices. We prove that for matrices of order 4, our construction gives the matrix with the lowest possible fixed XOR cost. We also introduce the Reversible Implementation (RI) property, which allows the inverse matrix to be implemented using the similar hardware resource as the forward matrix, even when the two matrices have different finite field entries. This allows us to search for serial-type matrices which are lightweight in both directions by just focusing on the forward direction. We obtain MDS matrices which outperform existing lightweight (involutory) matrices.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Minor revision. AFRICACRYPT 2018
Keywords: MDS matrix Serial matrix lightweight cryptography XOR count
Contact author(s): ssim011 @ e ntu edu sg
History: 2018-02-27: revised; 2017-11-10: received; See all versions
Short URL: https://ia.cr/2017/1084
License: CC BY

BibTeX

@misc{cryptoeprint:2017/1084,
      author = {Dylan Toh and Jacob Teo and Khoongming Khoo and Siang Meng Sim},
      title = {Lightweight {MDS} Serial-type Matrices with Minimal Fixed {XOR} Count (Full version)},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/1084},
      year = {2017},
      url = {https://eprint.iacr.org/2017/1084}
}