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NEON-SIDH: Efficient Implementation of Supersingular Isogeny Diffie-Hellman Key Exchange Protocol on ARM

Part of the Lecture Notes in Computer Science book series (LNSC,volume 10052)


We investigate the efficiency of implementing the Jao and De Feo isogeny-based post-quantum key exchange protocol (from PQCrypto 2011) on ARM-powered embedded platforms. In this work we propose new primes to speed up constant-time finite field arithmetic and perform isogenies quickly. Montgomery multiplication and reduction are employed to produce a speedup of 3 over the GNU Multiprecision Library. We analyze the recent projective isogeny formulas presented in Costello et al. (Crypto 2016) and conclude that affine isogeny formulas are much faster in ARM devices. We provide fast affine SIDH libraries over 512, 768, and 1024-bit primes. We provide timing results for emerging embedded ARM platforms using the ARMv7A architecture for the 85-, 128-, and 170-bit quantum security levels. Our assembly-optimized arithmetic cuts the computation time for the protocol by 50 % in comparison to our portable C implementation and performs approximately 3 times faster than the only other ARMv7 results found in the literature. The goal of this paper is to show that isogeny-based cryptosystems can be implemented further and be used as an alternative to classical cryptosystems on embedded devices.


  • Elliptic curve cryptography
  • Post-quantum cryptography
  • Isogeny-based cryptosystems
  • ARM embedded processors
  • Finite-field arithmetic
  • Assembly implementation

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  1. 1.

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  1. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), pp. 124–134 (1994)

    Google Scholar 

  2. Güneysu, T., Lyubashevsky, V., Pöppelmann, T.: Practical lattice-based cryptography: a signature scheme for embedded systems. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 530–547. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33027-8_31

    CrossRef  Google Scholar 

  3. Heyse, S.: Implementation of Mceliece based on quasi-dyadic goppa codes for embedded devices. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 143–162. Springer, Heidelberg (2011). doi:10.1007/978-3-642-25405-5_10

    CrossRef  Google Scholar 

  4. Heyse, S., Maurich, I., Güneysu, T.: Smaller keys for code-based cryptography: QC-MDPC McEliece implementations on embedded devices. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 273–292. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40349-1_16

    CrossRef  Google Scholar 

  5. Jao, D., 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). doi:10.1007/978-3-642-25405-5_2

    CrossRef  Google Scholar 

  6. De Feo, L., Jao, D., Plut, J.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. J. Math. Cryptology 8(3), 209–247 (2014)

    MathSciNet  MATH  Google Scholar 

  7. 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). doi:10.1007/978-3-662-53018-4_21

    CrossRef  Google Scholar 

  8. Chen, L., Jordan, S.: Report on post-quantum cryptography, NIST IR 8105 (2016)

    Google Scholar 

  9. Azarderakhsh, R., Jao, D., Kalach, K., Koziel, B., Leonardi, C.: Key compression for isogeny-based cryptosystems. In: Proceedings of the 3rd ACM International Workshop on ASIA Public-Key Cryptography, AsiaPKC 2016, pp. 1–10. ACM, New York (2016)

    Google Scholar 

  10. Azarderakhsh, R., Fishbein, D., Jao, D.: Efficient implementations of a quantum-resistant key-exchange protocol on embedded systems. Technical report, University of Waterloo (2014)

    Google Scholar 

  11. Silverman, J.H.: The Arithmetic of Elliptic Curves. GTM, vol. 106. Springer, New York (1992)

    Google Scholar 

  12. Mestre, J.F.: La méthode des graphes. Exemples et applications. In: Proceedings of the International Conference on Class Numbers and Fundamental Units of Algebraic Number Fields (Katata, 1986), pp. 217–242. Nagoya Univ., Nagoya (1986)

    Google Scholar 

  13. Montgomery, P.: Speeding the pollard and elliptic curve methods of factorization. Math. Comput. 48, 243–264 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Bernstein, D.J., Lange, T.: Explicit-formulas database (2007).

  15. Bernstein, D.J.: Differential addition chains. Technical report (2006).

  16. Azarderakhsh, R., Karabina, K.: A new double point multiplication algorithm and its application to binary elliptic curves with endomorphisms. IEEE Trans. Comput. 63(10), 2614–2619 (2014)

    CrossRef  MathSciNet  Google Scholar 

  17. Gueron, S., Krasnov, V.: Fast prime field elliptic-curve cryptography with 256-bit primes. J. Cryptograph. Eng. 5(2), 141–151 (2014)

    CrossRef  Google Scholar 

  18. Montgomery, P.L.: Modular multiplication without trial division. Math. Comput. 44(170), 519–521 (1985)

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Seo, H., Liu, Z., Grobschadl, J., Kim, H.: Efficient arithmetic on ARM-NEON and its application for high-speed RSA implementation. Cryptology ePrint Archive, Report 2015/465 (2015)

    Google Scholar 

  20. Kaliski, B.S.: The montgomery inverse and its applications. IEEE Trans. Comput. 44(8), 1064–1065 (1995)

    CrossRef  MATH  Google Scholar 

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The authors would like to thank the reviewers for their constructive comments. This material is based upon work supported by the National Science Foundation under grant No. CNS-1464118 awarded to Reza Azarderakhsh.

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Correspondence to Brian Koziel .

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Koziel, B., Jalali, A., Azarderakhsh, R., Jao, D., Mozaffari-Kermani, M. (2016). NEON-SIDH: Efficient Implementation of Supersingular Isogeny Diffie-Hellman Key Exchange Protocol on ARM. In: Foresti, S., Persiano, G. (eds) Cryptology and Network Security. CANS 2016. Lecture Notes in Computer Science(), vol 10052. Springer, Cham.

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