Lightweight MDS Generalized Circulant Matrices

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• 关键词：Lightweight cryptography ; Diffusion layer ; MDS ; Circulant matrices
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9783
• 期：1
• 页码：101-120
• 全文大小：485 KB
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• 作者单位：Meicheng Liu (14) (15)
  Siang Meng Sim (14)
  
  14. Nanyang Technological University, Singapore, Singapore
  15. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, People’s Republic of China
  
• 丛书名：Fast Software Encryption
• ISBN：978-3-662-52993-5
• 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
• 卷排序：9783

文摘

In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circulant matrices, we greatly reduce the search space for finding lightweight maximum distance separable (MDS) circulant matrices. We also generalize the circulant structure and propose a new class of matrices, called cyclic matrices, which preserve the benefits of circulant matrices and, in addition, have the potential of being self-invertible. In this new class of matrices, we obtain not only the MDS matrices with the least XOR gates requirement for dimensions from \(3 \times 3\) to \(8 \times 8\) in \({\text {GF}}(2^4)\) and \({\text {GF}}(2^8)\), but also involutory MDS matrices which was proven to be non-existence in the class of circulant matrices. To the best of our knowledge, the latter matrices are the first of its kind, which have a similar matrix structure as circulant matrices and are involutory and MDS simultaneously. Compared to the existing best known lightweight matrices, our new candidates either outperform or match them in terms of XOR gates required for a hardware implementation. Notably, our work is generic and independent of the metric for lightweight. Hence, our work is applicable for improving the search for efficient circulant matrices under other metrics besides XOR gates.