New Classes of Efficient MDS Transformations

Yubo LI  Kangquan LI  Longjiang QU  Chao LI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.11   pp.1504-1511
Publication Date: 2019/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1504
Type of Manuscript: PAPER
Category: Cryptography and Information Security
block cipher,  recursive diffusion layer,  MDS transformation,  XOR gates,  lightweight linear function,  

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MDS transformation plays an important role in resisting against differential cryptanalysis (DC) and linear cryptanalysis (LC). Recently, M. Sajadieh, et al.[15] designed an efficient recursive diffusion layer with Feistel-like structures. Moreover, they obtained an MDS transformation which is related to a linear function and the inverse is as lightweight as itself. Based on this work, we consider one specific form of linear functions to get the diffusion layer with low XOR gates for the hardware implementation by using temporary registers. We give two criteria to reduce the construction space and obtain six new classes of lightweight MDS transformations. Some of our constructions with one bundle-based LFSRs have as low XOR gates as previous best known results. We expect that these results may supply more choices for the design of MDS transformations in the (lightweight) block cipher algorithm.