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Direct Construction of Recursive MDS Diffusion Layers using Shortened BCH Codes

Daniel Augot 1, 2 Matthieu Finiasz 3
2 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having a compact description suitable even for constrained environ- ments. However, up to now, finding recursive MDS matrices required to perform an exhaustive search on families of companion matrices, thus limiting the size of MDS matrices one could look for. In this article we propose a new direct construction based on shortened BCH codes, al- lowing to efficiently construct such matrices for whatever parameters. Unfortunately, not all recursive MDS matrices can be obtained from BCH codes, and our algorithm is not always guaranteed to find the best matrices for a given set of parameters.
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https://hal.inria.fr/hal-01044597
Contributor : Daniel Augot <>
Submitted on : Saturday, December 13, 2014 - 5:53:02 PM
Last modification on : Friday, April 30, 2021 - 9:54:22 AM
Long-term archiving on: : Saturday, March 14, 2015 - 10:25:10 AM

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Daniel Augot, Matthieu Finiasz. Direct Construction of Recursive MDS Diffusion Layers using Shortened BCH Codes. 21st International Workshop on Fast Software Encryption, FSE 2014, London, UK, March 3-5, Mar 2014, London, United Kingdom. pp.3-17, ⟨10.1007/978-3-662-46706-0_1⟩. ⟨hal-01044597v2⟩

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