Supersingular Isogeny Oblivious Transfer
Abstract
In this paper we present an Oblivious Transfer (OT) protocol that combines an OT scheme together with the supersingular isogeny Diffie-Hellman (SIDH) primitive. Our proposal is a candidate for post-quantum secure OT and demonstrates that SIDH naturally supports OT functionality. We consider the (cid:1)-SIOT and analyze the protocol to protocol in the simplest configuration of (cid:0)2 verify its security. 1References
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Barak, B. (2007). Oblivious transfer and private information retrieval. https://www.cs.princeton.edu/courses/archive/fall07/cos433/lec19.pdf.
Bennett, C. H., Brassard, G., Crépeau, C., and Skubiszewska, M.-H. (1992). Pratical In Feigenbaum, J., editor, Advances in Cryptology — quantum oblivious transfer.
CRYPTO '91: Proceedings, pages 351–366, Berlin, Heidelberg. Springer Berlin Hei- delberg.
Chou, T. and Orlandi, C. (2015). The simplest protocol for oblivious transfer. In Lauter, K. and Rodríguez-Henríquez, F., editors, Progress in Cryptology – LATINCRYPT 2015: 4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015, Proceedings. Springer International Publishing.
Crepeau, C. and Kilian, J. (1988). Achieving oblivious transfer using weakened security assumptions. In 29th Annual Symposium on Foundations of Computer Science, pages 42–52.
Even, S., Goldreich, O., and Lempel, A. (1985). A randomized protocol for signing contracts. ACM, 28(6):637–647.
Feo, L. D., Jao, D., and Plût, J. (2014). Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. Journal of Mathematical Cryptology, 8(3):209– 247.
Galbraith., S. D. (2012). Mathematics of public key cryptography. Cambridge University Press, Cambridge.
Hazay, C. and Lindell., Y. (2010). Efcient Secure Two - Party Protocols - Techniques and Constructions. Springer Berlin Heidelberg.
Hoffstein, J., Pipher, J., and Silverman, J. H. (2014). An introduction to mathematical cryptography. Undergraduate Texts in Mathematics. Springer, New York, second edition edition.
Kalai, Y. T. (2005). Smooth projective hashing and two-message oblivious transfer. Advances in Cryptology – EUROCRYPT 2005., 3494.
Kazmi, R. A. (2015). Cryptography from Post-quantum Assumptions. McGill theses. McGill University Libraries. Archive, Report 2005/187. Berlin and Heidelberg, 3321.
Rabin, M. O. (1981). How to exchange secrets with oblivious transfer. Cryptology ePrint Rogaway, P. (2004). On the role of denitions in and beyond cryptography. Springer and Silvermann, J. H. (2009). The arithmetic of elliptic curves, volume 106 of Graduate Texts in Mathematics. Springer, Dordrecht, second. edition.
Vitse, V. (2019). Simple oblivious transfer protocols compatible with kummer and super- singular isogenies. hal-01981552.
Wagner, D. (2016). Technical perspective: Fairness and the coin ip. Communications of the ACM., 59(4):75.
Washington., L. C. (2008). Elliptic curves - Number Theory and Cryptography. Taylor & Francis Group. LLC, second edition. edition.
Published
2019-09-02
How to Cite
BARRETO, Paulo; OLIVEIRA, Gláucio; BENITS, Waldyr; NASCIMENTO, Anderson.
Supersingular Isogeny Oblivious Transfer. In: BRAZILIAN SYMPOSIUM ON CYBERSECURITY (SBSEG), 19. , 2019, São Paulo.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2019
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p. 99-112.
DOI: https://doi.org/10.5753/sbseg.2019.13965.
