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International Conference on Post-Quantum Cryptography

PQCrypto 2021: Post-Quantum Cryptography pp 234–254Cite as

Fast NEON-Based Multiplication for Lattice-Based NIST Post-quantum Cryptography Finalists

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12841))

Abstract

This paper focuses on high-speed NEON-based constant-time implementations of multiplication of large polynomials in the NIST PQC KEM Finalists: NTRU, Saber, and CRYSTALS-Kyber. We use the Number Theoretic Transform (NTT)-based multiplication in Kyber, the Toom-Cook algorithm in NTRU, and both types of multiplication in Saber. Following these algorithms and using Apple M1, we improve the decapsulation performance of the NTRU, Kyber, and Saber-based KEMs at the security level 3 by the factors of 8.4, 3.0, and 1.6, respectively, compared to the reference implementations. On Cortex-A72, we achieve the speed-ups by factors varying between 5.7 and 7.5\(\times \) for the Forward/Inverse NTT in Kyber, and between 6.0 and 7.8\(\times \) for Toom-Cook in NTRU, over the best existing implementations in pure C. For Saber, when using NEON instructions on Cortex-A72, the implementation based on NTT outperforms the implementation based on the Toom-Cook algorithm by \(14\%\) in the case of the MatrixVectorMul function but is slower by \(21\%\) in the case of the InnerProduct function. Taking into account that in Saber, keys are not available in the NTT domain, the overall performance of the NTT-based version is very close to the performance of the Toom-Cook version. The differences for the entire decapsulation at the three major security levels (1, 3, and 5) are \(-4\), \(-2\), and \(+2\%\), respectively. Our benchmarking results demonstrate that our NEON-based implementations run on an Apple M1 ARM processor are comparable to those obtained using the best AVX2-based implementations run on an AMD EPYC 7742 processor. Our work is the first NEON-based ARMv8 implementation of each of the three NIST PQC KEM finalists.

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Notes

  1. 1.

    https://www.tomshardware.com/news/arm-6-7-billion-chips-per-quarter.

  2. 2.

    https://godbolt.org/z/5qefG5.

  3. 3.

    https://www.anandtech.com/show/16252/mac-mini-apple-m1-tested.

  4. 4.

    https://github.com/dougallj.

  5. 5.

    https://github.com/GMUCERG/PQC_NEON/blob/main/neon/kyber/m1cycles.c.

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Authors and Affiliations

  1. George Mason University, Fairfax, VA, 22030, USA

    Duc Tri Nguyen & Kris Gaj

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  1. Duc Tri Nguyen
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  2. Kris Gaj
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Correspondence to Duc Tri Nguyen .

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Editors and Affiliations

  1. Seoul National University, Seoul, Korea (Republic of)

    Jung Hee Cheon

  2. Inria, Paris, France

    Jean-Pierre Tillich

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Nguyen, D.T., Gaj, K. (2021). Fast NEON-Based Multiplication for Lattice-Based NIST Post-quantum Cryptography Finalists. In: Cheon, J.H., Tillich, JP. (eds) Post-Quantum Cryptography. PQCrypto 2021. Lecture Notes in Computer Science(), vol 12841. Springer, Cham. https://doi.org/10.1007/978-3-030-81293-5_13

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  • DOI: https://doi.org/10.1007/978-3-030-81293-5_13

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