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On Constructions of Circulant MDS Matrices for Lightweight Cryptography

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Book cover Information Security Practice and Experience (ISPEC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8434))

Abstract

Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In this paper we study and construct efficient d ×d circulant MDS matrices for d up to 8 and consider their inverses, which are essential for SPN networks. We explore some interesting and useful properties of circulant matrices which are prevalent in many parts of mathematics and computer science. We prove that circulant MDS matrix can not be involutory. We also prove that 2d ×2d circulant matrix can not be both orthogonal and MDS.

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Author information

Authors and Affiliations

  1. Applied Statistics Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108, India

    Kishan Chand Gupta & Indranil Ghosh Ray

Authors
  1. Kishan Chand Gupta
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  2. Indranil Ghosh Ray
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Editors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, No. 32 Shangsan Road, 350007, Fuzhou, China

    Xinyi Huang

  2. Infocom Security Department, Institute for Infocomm Research, 1 Fusionopolis Way, #21-01 Connexis, South Tower, 138632, Singapore, Singapore

    Jianying Zhou

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Chand Gupta, K., Ghosh Ray, I. (2014). On Constructions of Circulant MDS Matrices for Lightweight Cryptography. In: Huang, X., Zhou, J. (eds) Information Security Practice and Experience. ISPEC 2014. Lecture Notes in Computer Science, vol 8434. Springer, Cham. https://doi.org/10.1007/978-3-319-06320-1_41

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  • DOI: https://doi.org/10.1007/978-3-319-06320-1_41

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06319-5

  • Online ISBN: 978-3-319-06320-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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