Codes over \(\mathcal{L}(GF(2)^m,GF(2)^m)\) , MDS Diffusion Matrices and Cryptographic Applications

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• 关键词：MDS matrices ; Diffusion layers ; Additive block codes ; Symmetric cryptography
• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：9084
• 期：1
• 页码：197-214
• 全文大小：310 KB
• 参考文献：1.Augot, D., Finiasz, M.: Exhaustive search for small dimension recursive MDS diffusion layers for block ciphers and hash functions. In: Proceedings of the 2013 IEEE International Symposium on Information Theory, Istanbul, Turkey, July 7-12, pp. 1551鈥?555. IEEE (2013)
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• 作者单位：Thierry P. Berger (17)
  Nora El Amrani (17) (18)
  
  17. XLIM (UMR CNRS 7252), University of Limoges, Limoges, France
  18. Laboratory of Mathematics, Computing and Applications, Faculty of sciences University of Mohammed V - Agdal, Rabat, Morocco
  
• 丛书名：Codes, Cryptology, and Information Security
• ISBN：978-3-319-18681-8
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

The aim of this paper is to provide a general framework in the study of binary block codes. The main objective is to present a general approach in order to explore MDS diffusion matrices used for example in the design of block ciphers with a Substitution Permutation Network design (the so-called SPN block-ciphers). In order to analyze these codes, we consider additive block codes over binary m-tuples. We are interested in the distance properties related to the block structure. To do this, we introduce a notion of \(\mathcal{L}\)-codes that are codes over the non-commutative ring of linear endomorphisms of GF(2) m . We study the main properties of these codes, especially the notion of duality in this context. We show how most of the known families of block codes can be interpreted in this context. Finally, we conclude by practical examples that allow to derive MDS diffusion matrices over GF(2) m from MDS matrices constructed over smaller blocks.