Construction of generalized-involutory MDS matrices

Xuting Zhou; Tianshuo Cong

Paper 2022/577

Construction of generalized-involutory MDS matrices

Xuting Zhou and Tianshuo Cong

Abstract

Maximum Distance Separable (MDS) matrices are usually used to be diffusion layers in cryptographic designs. The main advantage of involutory MDS matrices lies in that both encryption and decryption share the same matrix-vector product. In this paper, we present a new type of MDS matrices called generalized-involutory MDS matrices, implementation of whose inverse matrix-vector products in decryption is the combination of the matrix-vector products in encryption plus a few extra XOR gates. For the purpose of verifying the existence of such matrices, we found 4 × 4 Hadamard generalized-involutory MDS matrix over GF(24) consuming as little as 38 XOR gates with 4 additional XOR gates for inverse matrix, while the best previous single-clock implementation in IWSEC 2019 needs 46 XOR gates with 51 XOR gates for inverse matrix. For GF(28), our results also beat the best previous records in ToSC 2017.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: MDS matrix XOR count Lightweight cryptography Involutory matrix
Contact author(s): zhouxt19 @ mails tsinghua edu cn
History: 2022-05-16: received
Short URL: https://ia.cr/2022/577
License: CC BY

BibTeX

@misc{cryptoeprint:2022/577,
      author = {Xuting Zhou and Tianshuo Cong},
      title = {Construction of generalized-involutory {MDS} matrices},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/577},
      year = {2022},
      url = {https://eprint.iacr.org/2022/577}
}