High-performance area-efficient polynomial ring processor for CRYSTALS-Kyber on FPGAs

The quantum-resistant attribute is a new design criterion for cryptography algorithms in the era of quantum supremacy. Lattice-based cryptography is proved to be secure against quantum computing. CRYSTALS-Kyber is a lattice-based promising candidate in the post-quantum cryptography standardization p...

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Vydáno v:	Integration (Amsterdam) Ročník 78; s. 25 - 35
Hlavní autoři:	Chen, Zhaohui, Ma, Yuan, Chen, Tianyu, Lin, Jingqiang, Jing, Jiwu
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.05.2021 Elsevier BV
Témata:	Algorithms Cryptography Crystal lattices CRYSTALS-Kyber Design criteria Field programmable gate arrays Finite state machines FPGA Microprocessors Multiplication Number-Theoretic Transform Performance evaluation Polynomial ring Polynomials Post-quantum cryptography Quantum computing Quantum cryptography Quantum physics Rings (mathematics) Standardization Post-quantum cryptography Number-Theoretic Transform Polynomial ring FPGA CRYSTALS-Kyber
ISSN:	0167-9260, 1872-7522
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Abstract	The quantum-resistant attribute is a new design criterion for cryptography algorithms in the era of quantum supremacy. Lattice-based cryptography is proved to be secure against quantum computing. CRYSTALS-Kyber is a lattice-based promising candidate in the post-quantum cryptography standardization process. This paper proposes a high-performance polynomial ring processor for the CRYSTALS-Kyber algorithm. The processor executes optimized polynomial ring arithmetic, which cuts off over 20%/50% on the times of modular multiplication/addition compared with the straightforward implementations. Besides, the forward and inverse Number Theoretic Transform (NTT) reuse the control logic with the help of an efficient configurable butterfly unit to minimize the area of the finite state machine. Further, the underlying dual-column sequential storage scheme breaks the bottleneck of memory accessing. To evaluate the performance, a fully pipelined architecture is implemented on a low-cost FPGA platform. Benefiting from these optimizations, the Kyber1024processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1 μs, and it achieves speedup by a factor of 2.1 compared with the state-of-the-art implementation. •Kyber1024 processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1μs on a low-cost FPGA.•Saving more than 20% on the times of modular multiplication operations in polynomial ring arithmetic.•Optimized NTT signal flow reuses the loop control logic to save nearly 50% of the resource.•Dual-column sequential storage improves memory bandwidth.•Configurable butterfly unit supports Cooley–Tukey butterfly-based forward NTT, Gentlemen–Sande butterfly-based inverse NTT, and other meta operations.
AbstractList	The quantum-resistant attribute is a new design criterion for cryptography algorithms in the era of quantum supremacy. Lattice-based cryptography is proved to be secure against quantum computing. CRYSTALS-Kyber is a lattice-based promising candidate in the post-quantum cryptography standardization process. This paper proposes a high-performance polynomial ring processor for the CRYSTALS-Kyber algorithm. The processor executes optimized polynomial ring arithmetic, which cuts off over 20%/50% on the times of modular multiplication/addition compared with the straightforward implementations. Besides, the forward and inverse Number Theoretic Transform (NTT) reuse the control logic with the help of an efficient configurable butterfly unit to minimize the area of the finite state machine. Further, the underlying dual-column sequential storage scheme breaks the bottleneck of memory accessing. To evaluate the performance, a fully pipelined architecture is implemented on a low-cost FPGA platform. Benefiting from these optimizations, the Kyber1024processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1μs, and it achieves speedup by a factor of 2.1 compared with the state-of-the-art implementation. The quantum-resistant attribute is a new design criterion for cryptography algorithms in the era of quantum supremacy. Lattice-based cryptography is proved to be secure against quantum computing. CRYSTALS-Kyber is a lattice-based promising candidate in the post-quantum cryptography standardization process. This paper proposes a high-performance polynomial ring processor for the CRYSTALS-Kyber algorithm. The processor executes optimized polynomial ring arithmetic, which cuts off over 20%/50% on the times of modular multiplication/addition compared with the straightforward implementations. Besides, the forward and inverse Number Theoretic Transform (NTT) reuse the control logic with the help of an efficient configurable butterfly unit to minimize the area of the finite state machine. Further, the underlying dual-column sequential storage scheme breaks the bottleneck of memory accessing. To evaluate the performance, a fully pipelined architecture is implemented on a low-cost FPGA platform. Benefiting from these optimizations, the Kyber1024processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1 μs, and it achieves speedup by a factor of 2.1 compared with the state-of-the-art implementation. The quantum-resistant attribute is a new design criterion for cryptography algorithms in the era of quantum supremacy. Lattice-based cryptography is proved to be secure against quantum computing. CRYSTALS-Kyber is a lattice-based promising candidate in the post-quantum cryptography standardization process. This paper proposes a high-performance polynomial ring processor for the CRYSTALS-Kyber algorithm. The processor executes optimized polynomial ring arithmetic, which cuts off over 20%/50% on the times of modular multiplication/addition compared with the straightforward implementations. Besides, the forward and inverse Number Theoretic Transform (NTT) reuse the control logic with the help of an efficient configurable butterfly unit to minimize the area of the finite state machine. Further, the underlying dual-column sequential storage scheme breaks the bottleneck of memory accessing. To evaluate the performance, a fully pipelined architecture is implemented on a low-cost FPGA platform. Benefiting from these optimizations, the Kyber1024processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1 μs, and it achieves speedup by a factor of 2.1 compared with the state-of-the-art implementation. •Kyber1024 processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1μs on a low-cost FPGA.•Saving more than 20% on the times of modular multiplication operations in polynomial ring arithmetic.•Optimized NTT signal flow reuses the loop control logic to save nearly 50% of the resource.•Dual-column sequential storage improves memory bandwidth.•Configurable butterfly unit supports Cooley–Tukey butterfly-based forward NTT, Gentlemen–Sande butterfly-based inverse NTT, and other meta operations.
Author	Lin, Jingqiang Ma, Yuan Jing, Jiwu Chen, Zhaohui Chen, Tianyu
Author_xml	– sequence: 1 givenname: Zhaohui surname: Chen fullname: Chen, Zhaohui email: chenzhaohui17@mails.ucas.ac.cn organization: School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, China – sequence: 2 givenname: Yuan surname: Ma fullname: Ma, Yuan email: mayuan@iie.ac.cn organization: State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing, 100093, China – sequence: 3 givenname: Tianyu surname: Chen fullname: Chen, Tianyu email: chentianyu@iie.ac.cn organization: State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing, 100093, China – sequence: 4 givenname: Jingqiang surname: Lin fullname: Lin, Jingqiang email: linjq@ustc.edu.cn organization: School of Cyber Security, University of Science and Technology of China, Hefei, Anhui, 230027, China – sequence: 5 givenname: Jiwu surname: Jing fullname: Jing, Jiwu email: jwjing@ucas.ac.cn organization: School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, China
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Cites_doi	10.1109/TIT.1976.1055638 10.1145/3292548 10.1137/S0097539795293172 10.46586/tches.v2020.i2.49-72 10.1109/TCSI.2019.2956651 10.1007/s10623-014-9938-4 10.46586/tches.v2019.i4.17-61 10.1109/TVLSI.2019.2922999
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Keywords	Post-quantum cryptography Number-Theoretic Transform Polynomial ring FPGA CRYSTALS-Kyber
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Snippet	The quantum-resistant attribute is a new design criterion for cryptography algorithms in the era of quantum supremacy. Lattice-based cryptography is proved to...
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SubjectTerms	Algorithms Cryptography Crystal lattices CRYSTALS-Kyber Design criteria Field programmable gate arrays Finite state machines FPGA Microprocessors Multiplication Number-Theoretic Transform Performance evaluation Polynomial ring Polynomials Post-quantum cryptography Quantum computing Quantum cryptography Quantum physics Rings (mathematics) Standardization
Title	High-performance area-efficient polynomial ring processor for CRYSTALS-Kyber on FPGAs
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