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Universal Gaussian elimination hardware for cryptographic purposes

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Abstract

In this paper, we investigate the possibility of performing Gaussian elimination for arbitrary binary matrices on hardware. In particular, we presented a generic approach for hardware-based Gaussian elimination, which is able to process both non-singular and singular matrices. Previous works on hardware-based Gaussian elimination can only process non-singular ones. However, a plethora of cryptosystems, for instance, quantum-safe key encapsulation mechanisms based on rank-metric codes, ROLLO and RQC, which are among NIST post-quantum cryptography standardization round-2 candidates, require performing Gaussian elimination for random matrices regardless of the singularity. We accordingly implemented an optimized and parameterized Gaussian eliminator for (singular) matrices over binary fields, making the intense computation of linear algebra feasible and efficient on hardware. To the best of our knowledge, this work solves for the first time eliminating a singular matrix on reconfigurable hardware and also describes the a generic hardware architecture for rank-code based cryptographic schemes. The experimental results suggest hardware-based Gaussian elimination can be done in linear time regardless of the matrix type.

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Notes

  1. The automation tools and reference implementations can be found at https://github.com/davidhoo1988/gaussian-elimination-hardware.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 62002023, in part by Guangdong Provincial Key Laboratory IRADS under Grant 2022B1212010006 and Grant R0400001-22, in part by Guangdong Province General Universities Key Field Project (New Generation Information Technology) under Grant 2023ZDZX1033, in part by UIC Research under Grant UICR04202401-21, and in part by A\(^*\)Star, Singapore under research grant SERC A19E3b0099.

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Authors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Jingwei Hu & Huaxiong Wang

  2. Yale University, New Haven, USA

    Wen Wang

  3. George Mason University, Fairfax, USA

    Kris Gaj

  4. BNU-HKBU United International College, Zhuhai, China

    Donglong Chen

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  1. Jingwei Hu
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  2. Wen Wang
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Correspondence to Donglong Chen.

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Hu, J., Wang, W., Gaj, K. et al. Universal Gaussian elimination hardware for cryptographic purposes. J Cryptogr Eng 14, 383–397 (2024). https://doi.org/10.1007/s13389-024-00355-3

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