Cryptology ePrint Archive: Report 2018/709

Simple oblivious transfer protocols compatible with Kummer and supersingular isogenies

Vanessa Vitse

Abstract: The key exchange protocol of Diffie and Hellman, which can be defined for any group, has the special feature of using only exponentiations. In particular, it can also be instantiated in Kummer varieties, which are not groups, and in the post-quantum isogeny-based setting with the supersingular isogeny DH scheme of De Feo, Jao and Plūt (SIDH).

In this article, we propose a new simple oblivious transfer (OT) protocol, based on the Diffie-Hellman key exchange, that only uses exponentiations; we also revisit the older Wu-Zhang-Wang scheme. Both protocols can be directly instantiated on fast Kummer varieties; more importantly, they can also be transposed in the post-quantum SIDH setting. The semantic security of our proposals relies on the hardness of non-standard versions of the (supersingular) Diffie-Hellman problem, that are investigated within this article. To the best of our knowledge, these protocols are the simplest secure discrete-log based OT schemes using only exponentiations, and the first isogeny-based OT schemes.

Category / Keywords: Oblivious transfer, Diffie-Hellman key exchange, supersingular isogeny, post-quantum cryptography

Date: received 27 Jul 2018, last revised 12 Oct 2018

Contact author: vanessa vitse at univ-grenoble-alpes fr

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Version: 20181012:202637 (All versions of this report)

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