NDLI: Towards a general construction of recursive MDS diffusion layers

Content Provider	Springer Nature Link
Author	Venkateswarlu, Ayineedi Pandey, Sumit Kumar Gupta, Kishan Chand
Copyright Year	2016
Abstract	MDS matrices are of great importance in the design of block ciphers and hash functions. MDS matrices are not sparse and have a large description and thus induce costly implementation in software/hardware. To overcome this problem, in particular for applications in light-weight cryptography, it was proposed by Guo et al. to use recursive MDS matrices. A recursive MDS matrix is an MDS matrix which can be expressed as a power of some companion matrix. Following the work of Guo et al., some ad-hoc search techniques are proposed to find recursive MDS matrices which are suitable for hardware/software implementation. In another direction, coding theoretic techniques are used to directly construct recursive MDS matrices: Berger technique uses Gabidulin codes and Augot et al. technique uses shortened BCH codes. In this paper, we first characterize the polynomials that yield recursive MDS matrices in a more general setting. Based on this we provide three methods for obtaining such polynomials. Moreover, the recursive MDS matrices obtained using shortened BCH codes can also be obtained with our first method. In fact we get a larger set of polynomials than the method which uses shortened BCH codes. Our other methods appear similar to the method which uses Gabidulin codes. We get a new infinite class of recursive MDS matrices from one of the proposed methods. Although we propose three methods for the direct construction of recursive MDS matrices, our characterization results pave the way for new direct constructions.
Ending Page	195
Page Count	17
Starting Page	179
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	1-2
Volume Number	82
Language	English
Publisher	Springer US
Publisher Date	2016-08-02
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Companion matrices Information and Communication, Circuits Data Encryption Algebraic coding theory; cryptography Diffusion layer MDS codes Applications to coding theory and cryptography Data Structures, Cryptology and Information Theory Discrete Mathematics in Computer Science Coding and Information Theory BCH codes Gabidulin codes Cryptography Combinatorics Cyclic codes Recursive MDS matrices
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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