Paper 2020/1012

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

Yi-Fu Lai and Steven D. Galbraith and Cyprien Delpech de Saint Guilhem

Abstract

Oblivious transfer (OT) is an essential tool of cryptographic protocols. It can serve as a building block for realizing all multiparty functionalities. The strongest security notion against malicious adversaries is universal composibility (UC-secure). Due to the rigorous algebraic structures and operations, achieving the specific security notion with isogenies is believed to be difficult. Hence, it is an open problem to have an efficient UC-secure OT oblivious transfer scheme based on isogenies. In this work, we propose the first isogeny-based UC-secure oblivious transfer protocol in the presence of malicious adversaries without analogues in the Diffie-Hellman setting. The simple and compact CSIDH-based scheme consists of a constant number of isogeny computations. The underlying relaxed problem is called the computational reciprocal CSIDH problem which we can prove equivalent to the computational CSIDH problem with a quantum reduction.

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