Abstract
We present the first general-purpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is an application of Unruh’s construction of non-interactive zero-knowledge proofs to an interactive zero-knowledge proof proposed by De Feo, Jao, and Plût. We implement our proposed scheme on an x86-64 PC platform as well as an ARM-powered device. We exploit the state-of-the-art techniques to speed up the computations for general C and assembly. Finally, we provide timing results for real world applications.
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Notes
- 1.
Source code is available at https://github.com/yhyoo93/isogenysignature.
References
Ambainis, A., Rosmanis, A., Unruh, D.: Quantum attacks on classical proof systems: the hardness of quantum rewinding. In: 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, 18–21 October 2014, pp. 474–483 (2014)
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)
Barreto, P.S.L.M., Longa, P., Naehrig, M., Ricardini, J.E., Zanon, G.: Sharper ring-LWE signatures. Cryptology ePrint Archive, report 2016/1026 (2016)
Bernstein, D.J., Hopwood, D., Hülsing, A., Lange, T., Niederhagen, R., Papachristodoulou, L., Schneider, M., Schwabe, P., Wilcox-O’Hearn, Z.: SPHINCS: practical stateless hash-based signatures. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 368–397. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_15
Bernstein, D.J., Lange, T., Peters, C.: Attacking and defending the McEliece cryptosystem. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 31–46. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88403-3_3
Boneh, D., Zhandry, M.: Secure signatures and chosen ciphertext security in a quantum computing world. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 361–379. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_21
Costello, C., Jao, D., Longa, P., Naehrig, M., Renes, J., Urbanik, D.: Efficient compression of SIDH public keys. Cryptology ePrint Archive, report 2016/963 (2016)
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
Courtois, N.T., Finiasz, M., Sendrier, N.: How to achieve a McEliece-based digital signature scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_10
Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005). https://doi.org/10.1007/11496137_12
Ducas, L., Durmus, A., Lepoint, T., Lyubashevsky, V.: Lattice signatures and bimodal Gaussians. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 40–56. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_3
Feo, L.D., Jao, D., Plût, J.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. J. Math. Cryptol. 8(3), 209–247 (2014)
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12
Galbraith, S.D., Petit, C., Silva, J.: Signature schemes based on supersingular isogeny problems. Cryptology ePrint Archive, report 2016/1154 (2016)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC 1996, pp. 212–219. ACM, New York (1996)
Jao, D., Soukharev, V.: Isogeny-based quantum-resistant undeniable signatures. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 160–179. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11659-4_10
Koziel, B., Jalali, A., Azarderakhsh, R., Jao, D., Kermani, M.M.: NEON-SIDH: Efficient implementation of supersingular isogeny Diffe-Hellman key exchange protocol on ARM. In: Cryptology and Network Security - 15th International Conference, CANS 2016, Milan, Italy, 14–16 November 2016, Proceedings, pp. 88–103 (2016)
Petzoldt, A., Bulygin, S., Buchmann, J.: Selecting parameters for the rainbow signature scheme. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 218–240. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12929-2_16
Seshadri, S.M., Chandrasekaran, V.: Isogeny-based quantum-resistant undeniable blind signature scheme. Cryptology ePrint Archive, Report 2016/148 (2016)
Sun, X., Tian, H., Wang, Y.: Toward quantum-resistant strong designated verifier signature from isogenies. In: 2012 Fourth International Conference on Intelligent Networking and Collaborative Systems (2012)
Tani, S.: Claw finding algorithms using quantum walk. Theor. Comput. Sci. 410(50), 5285–5297 (2009)
Tate, J.: Endomorphisms of Abelian varieties over finite fields. Inventiones Mathematicae 2(2), 134–144 (1966)
Unruh, D.: Quantum proofs of knowledge. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 135–152. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_10
Unruh, D.: Non-interactive zero-knowledge proofs in the quantum random Oracle model. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 755–784. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_25
Watrous, J.: Zero-knowledge against quantum attacks. SIAM J. Comput. 39(1), 25–58 (2009)
Zhang, S.: Promised and distributed quantum search. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 430–439. Springer, Heidelberg (2005). https://doi.org/10.1007/11533719_44
Acknowledgments
We thank Steven Galbraith for helpful comments on an earlier version of this paper, and the anonymous reviewers for their constructive feedback. This work was partially supported by NSF grant no. CNS-1464118, NIST award 60NANB16D246, the CryptoWorks21 NSERC CREATE Training Program in Building a Workforce for the Cryptographic Infrastructure of the 21st Century, and InfoSec Global, Inc.
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Yoo, Y., Azarderakhsh, R., Jalali, A., Jao, D., Soukharev, V. (2017). A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies. In: Kiayias, A. (eds) Financial Cryptography and Data Security. FC 2017. Lecture Notes in Computer Science(), vol 10322. Springer, Cham. https://doi.org/10.1007/978-3-319-70972-7_9
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