Abstract
Public-key cryptography, including conventional cryptosystems and post-quantum cryptography, involves computation-intensive workloads. With noticing the extraordinary computing power of AI accelerators, in this paper, we further explore the feasibility to introduce AI accelerators into high-performance cryptographic computing. Since AI accelerators are dedicated to machine learning or neural networks, the biggest challenge is how to transform cryptographic workloads into their operations, while ensuring the correctness of the results and bringing convincing performance gains.
After investigating and analysing the workload of NVIDIA AI accelerator, Tensor Core, we choose to utilize it to accelerate the polynomial multiplication, usually the most time-consuming part in lattice-based cryptography. We take measures to accommodate the matrix-multiply-and-add mode of Tensor Core and make a trade-off between precision and performance, to leverage it as a high-performance NTT box performing NTT/INTT through CUDA C++ WMMA APIs. Meanwhile, we take CRYSTALS-Kyber, the candidate to be standardized by NIST, as a case study on RTX 3080 with the Ampere Tensor Core. The empirical results show that the customized NTT of polynomial vector (\(n=256,k=4\)) with our NTT box obtains a speedup around 6.47x that of the state-of-the-art implementation on the same GPU platform. Compared with the AVX2 implementation submitted to NIST, our Kyber-1024 can achieve a speedup of 26x, 36x, and 35x for each phase.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ajtai, M.: Generating hard instances of lattice problems. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 99–108 (1996)
Alkım, E., Bilgin, Y.A., Cenk, M.: Compact and simple RLWE based key encapsulation mechanism. In: Schwabe, P., Thériault, N. (eds.) LATINCRYPT 2019. LNCS, vol. 11774, pp. 237–256. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30530-7_12
Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 719–737. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_42
Barrett, P.: Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 311–323. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_24
Bos, J., et al.: CRYSTALS-Kyber: a CCA-secure module-lattice-based KEM. In: 2018 IEEE European Symposium on Security and Privacy (EuroS &P), pp. 353–367. IEEE (2018)
Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theor. (TOCT) 6(3), 1–36 (2014)
Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_26
Cloud, G.: Cloud TPU. https://cloud.google.com/tpu/. Accessed 19 May 2021
Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex fourier series. Math. Comput. 19(90), 297–301 (1965)
Gao, Y., Xu, J., Wang, H.: cuNH: efficient GPU implementations of post-quantum KEM NewHope. IEEE Trans. Parallel Distrib. Syst. 33(3), 551–568 (2021)
Greconici, D.O., Kannwischer, M.J., Sprenkels, D.: Compact dilithium implementations on Cortex-M3 and Cortex-M4. In: IACR Transactions on Cryptographic Hardware and Embedded Systems, pp. 1–24 (2021)
Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC acceleration using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Trans. Parallel Distrib. Syst. 32(3), 575–586 (2020)
Inc, A.: Apple unleashes M1. www.apple.com/newsroom/2020/11/apple-unleashes-m1/. Accessed 19 May 2021
Inc, N.: NVIDIA tensor cores-unprecedented acceleration for HPC and AI. www.nvidia.com/en-us/data-center/tensor-cores/. Accessed 19 May 2021
Karatsuba, A.: Multiplication of multidigit numbers on automata. In: Soviet Physics Doklady, vol. 7, pp. 595–596 (1963)
Langlois, A., Stehlé, D.: Worst-case to average-case reductions for module lattices. Des. Codes Crypt. 75(3), 565–599 (2014). https://doi.org/10.1007/s10623-014-9938-4
Lu, X., et al.: Lac: Practical ring-LWE based public-key encryption with byte-level modulus. Cryptology ePrint Archive (2018)
Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_1
Lyubashevsky, V., Seiler, G.: NTTRU: truly fast NTRU using NTT. In: IACR Transactions on Cryptographic Hardware and Embedded Systems, pp. 180–201 (2019)
Matthias, K., Peter, S., Douglas, S.: Wiggers: The pqclean project. https://github.com/PQClean/PQClean. Accessed 8 Apr 2022
Montgomery, P.L.: Modular multiplication without trial division. Math. Comput. 44(170), 519–521 (1985)
Moody, D.: Status report on the third round of the NIST post-quantum cryptography standardization process. Tech. rep, Gaithersburg, MD (2022)
Nakai, T., Suzuki, D., Fujino, T.: Timing black-box attacks: Crafting adversarial examples through timing leaks against DNNs on embedded devices. In: IACR Transactions on Cryptographic Hardware and Embedded Systems, pp. 149–175 (2021)
NIST: Post-quantum cryptography, call for proposals. https://csrc.nist.gov/Projects/post-quantum-cryptography/post-quantum-cryptography-standardization/Call-for-Proposals. Accessed 31 Mar 2022
NIST: Post-quantum cryptography, selected algorithms 2022. https://csrc.nist.gov/projects/post-quantum-cryptography/selected-algorithms-2022. Accessed 22 Apr 2022
Prouff, E., Rivain, M.: Masking against side-channel attacks: a formal security proof. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 142–159. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_9
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56(6), 1–40 (2009)
Sanal, P., Karagoz, E., Seo, H., Azarderakhsh, R., Mozaffari-Kermani, M.: Kyber on ARM64: compact implementations of Kyber on 64-Bit ARM cortex-a processors. In: Garcia-Alfaro, J., Li, S., Poovendran, R., Debar, H., Yung, M. (eds.) SecureComm 2021. LNICST, vol. 399, pp. 424–440. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90022-9_23
Schwabe, P.: Crystals-cryptographic suite for algebraic lattices. https://pq-crystals.org/kyber/index.shtml. Accessed 18 May 2021
Seiler, G.: Faster AVX2 optimized NTT multiplication for Ring-LWE lattice cryptography. IACR Cryptol. ePrint Arch. 2018, 39 (2018)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)
Toom, A.L.: The complexity of a scheme of functional elements realizing the multiplication of integers. In: Soviet Mathematics Doklady, vol. 3, pp. 714–716 (1963)
Wan, L., Zheng, F., Lin, J.: TESLAC: accelerating lattice-based cryptography with AI accelerator. In: Garcia-Alfaro, J., Li, S., Poovendran, R., Debar, H., Yung, M. (eds.) SecureComm 2021. LNICST, vol. 398, pp. 249–269. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90019-9_13
Xing, Y., Li, S.: A compact hardware implementation of CCA-secure key exchange mechanism CRYSTALS-KYBER on FPGA. In: IACR Transactions on Cryptographic Hardware and Embedded Systems, pp. 328–356 (2021)
Acknowledgements
We would like to thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. We are grateful to Massimiliano Albanese for helping us to improve our paper. This work is supported in part by National Key RD Plan of China under Grant No. 2020YFB1005803, the National Natural Science Foundation of China No. 61902392, CCF-Tencent Open Fund under Grant No. RAGR20210131 and CCF-Huawei Populus euphratica Fund.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Wan, L. et al. (2022). A Novel High-Performance Implementation of CRYSTALS-Kyber with AI Accelerator. In: Atluri, V., Di Pietro, R., Jensen, C.D., Meng, W. (eds) Computer Security – ESORICS 2022. ESORICS 2022. Lecture Notes in Computer Science, vol 13556. Springer, Cham. https://doi.org/10.1007/978-3-031-17143-7_25
Download citation
DOI: https://doi.org/10.1007/978-3-031-17143-7_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-17142-0
Online ISBN: 978-3-031-17143-7
eBook Packages: Computer ScienceComputer Science (R0)