Abstract
In this work, we present the first highly-optimized implementation of Supersingular Isogeny Key Encapsulation (SIKE) submitted to NIST’s second round of post quantum standardization process, on 64-bit ARMv8 processors. To the best of our knowledge, this work is the first optimized implementation of SIKE round 2 on 64-bit ARM over SIKEp434 and SIKEp610. The proposed library is explicitly optimized for these two security levels and provides constant-time implementation of the SIKE mechanism on ARMv8-powered embedded devices. We adapt different optimization techniques to reduce the total number of underlying arithmetic operations on the filed level. In particular, the benchmark results on embedded processors equipped with ARM Cortex-A53@1.536 GHz show that the entire SIKE round 2 key encapsulation mechanism takes only 84 ms at NIST’s security level 1. Considering SIKE’s extremely small key size in comparison to other candidates, our result implies that SIKE is one of the promising candidates for key encapsulation mechanism on embedded devices in the quantum era.
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
Notes
- 1.
The value of t is defined by the implementation parameters.
References
Adj, G., Cervantes-Vázquez, D., Chi-Domínguez, J., Menezes, A., Rodríguez-Henríquez, F.: On the cost of computing isogenies between supersingular elliptic curves. In: Cid, C., Jacobson Jr., M. (eds.) SAC 2018. LNCS, vol. 11349, pp. 322–343. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-10970-7_15
ARM Limited. ARM architecture reference manual ARMv8, for ARMv8-A architecture profile (2013–2017). https://static.docs.arm.com/ddi0487/ca/DDI0487C_a_armv8_arm.pdf
Azarderakhsh, R., et al.: Supersingular Isogeny Key Encapsulation - Submission to the NIST’s post-quantum cryptography standardization process, round 2 (2019). https://csrc.nist.gov/projects/post-quantum-cryptography/round-2-submissions/SIKE.zip
Azarderakhsh, R., et al.: Supersingular Isogeny Key Encapsulation - Submission to the NIST’s post-quantum cryptography standardization process (2017). https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/round-1/submissions/SIKE.zip
Bos, J.W., Friedberger, S.: Fast arithmetic modulo \(2^{x}p^{y}\pm 1\). In: IEEE Symposium on Computer Arithmetic (ARITH 2017), pp. 148–155. IEEE (2017)
Charles, D.X., Lauter, K.E., Goren, E.Z.: Cryptographic hash functions from expander graphs. J. Cryptol. 22(1), 93–113 (2009)
Chen, L., et al.: Report on post-quantum cryptography. US Department of Commerce, National Institute of Standards and Technology (2016)
Comba, P.G.: Exponentiation cryptosystems on the IBM PC. IBM Syst. J. 29(4), 526–538 (1990)
Costello, C., Longa, P., Naehrig, M.: Efficient algorithms for supersingular isogeny Diffie-Hellman. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 572–601. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_21
Galbraith, S.D., Petit, C., Shani, B., Ti, Y.B.: On the security of supersingular isogeny cryptosystems. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 63–91. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_3
Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 341–371. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_12
Jalali, A., Azarderakhsh, R., Kermani, M.M., Jao, D.: Supersingular isogeny Diffie-Hellman key exchange on 64-bit ARM. IEEE Trans. Dependable Secure Comput. PP, 1 (2017)
Jalali, A., Azarderakhsh, R., Mozaffari-Kermani, M.: Efficient post-quantum undeniable signature on 64-Bit ARM. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 281–298. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72565-9_14
Jao, D., De Feo, L.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 19–34. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25405-5_2
Montgomery, P.L.: Five, six, and seven-term Karatsuba-like formulae. IEEE Trans. Comput. 54(3), 362–369 (2005)
Seo, H., Liu, Z., Longa, P., Hu, Z.: SIDH on ARM: faster modular multiplications for faster post-quantum supersingular isogeny key exchange. IACR Trans. Cryptogr. Hardware Embedded Syst. 1–20 (2018)
The National Institute of Standards and Technology (NIST). Post-quantum cryptography standardization (2017–2018). https://csrc.nist.gov/projects/post-quantum-cryptography/post-quantum-cryptography-standardization
Acknowledgement
This work of Hwajeong Seo was supported by Institute for Information communications Technology Planning Evaluation (IITP) grant funded by the Korea government(MSIT) (\({<}\)Q|Crypton\({>}\), No. 2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity).
This work of Reza Azarderakhsh and Amir Jalali is supported in parts by NSF CNS-1801341 and NIST-60NANB16D246.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Seo, H., Jalali, A., Azarderakhsh, R. (2020). Optimized SIKE Round 2 on 64-bit ARM. In: You, I. (eds) Information Security Applications. WISA 2019. Lecture Notes in Computer Science(), vol 11897. Springer, Cham. https://doi.org/10.1007/978-3-030-39303-8_26
Download citation
DOI: https://doi.org/10.1007/978-3-030-39303-8_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39302-1
Online ISBN: 978-3-030-39303-8
eBook Packages: Computer ScienceComputer Science (R0)