Compact, Efficient and UC-Secure Isogeny-Based Oblivious Transfer

Oblivious transfer (OT) is an essential cryptographic tool that can serve as a building block for almost all secure multiparty functionalities. The strongest security notion against malicious adversaries is universal composability (UC-secure). An important goal is to have post-quantum OT protocols. One area of interest for post-quantum cryptography is isogeny-based crypto. Isogeny-based cryptography has some similarities to Diffie-Hellman, but lacks some algebraic properties that are needed for discrete-log-based OT protocols. Hence it is not always possible to directly adapt existing protocols to the isogeny setting.

We propose the first practical isogeny-based UC-secure oblivious transfer protocol in the presence of malicious adversaries. Our scheme uses the CSIDH framework and does not have an analogue in the Diffie-Hellman setting. The scheme consists of a constant number of isogeny computations. The underlying computational assumption is a problem that we call the computational reciprocal CSIDH problem, and that we prove polynomial-time equivalent to the computational CSIDH problem.