Round-Optimal Oblivious Transfer and MPC from Computational CSIDH

We present the first round-optimal and plausibly quantum-safe oblivious transfer (OT) and multi-party computation (MPC) protocols from the computational CSIDH assumption - the weakest and most widely studied assumption in the CSIDH family of isogeny-based assumptions. We obtain the following results:

- The first round-optimal maliciously secure OT and MPC protocols in the plain model that achieve (black-box) simulation-based security while relying on the computational CSIDH assumption.
	
- The first round-optimal maliciously secure OT and MPC protocols that achieves Universal Composability (UC) security in the presence of a trusted setup (common reference string plus random oracle) while relying on the computational CSIDH assumption.

Prior plausibly quantum-safe isogeny-based OT protocols (with/without setup assumptions) are either not round-optimal, or rely on potentially stronger assumptions.

We also build a 3-round maliciously-secure OT extension protocol where each base OT protocol requires only 4 isogeny computations. In comparison, the most efficient isogeny-based OT extension protocol till date due to Lai et al.~[Eurocrypt 2021] requires 12 isogeny computations and 4 rounds of communication, while relying on the same assumption as our construction, namely the reciprocal CSIDH assumption.