International Association for Cryptologic Research

International Association
for Cryptologic Research


New proof systems and an OPRF from CSIDH

Robi Pedersen , COSIC, KU Leuven
Cyprien Delpech de Saint Guilhem , COSIC, KU Leuven
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Presentation: Slides
Conference: PKC 2024
Abstract: Isogeny computations in CSIDH (Asiacrypt 2018) are described using a commutative group G acting on the set of supersingular elliptic curves. The commutativity property gives CSIDH enough flexibility to allow the creation of many cryptographic primitives and protocols. Nevertheless, these operations are limited and more complex applications have not yet been proposed. When calling the composition of two group elements of G, \emph{addition}, our goal in this work is to explore exponentiation, multiplication with public elements, and multiplication between secret elements of this group. We first introduce a two-party interactive protocol for multiplication of secret group elements. Then, we explore zero-knowledge proofs of these different arithmetic operations. We present two types of approaches, using either standard sigma protocols or the MPC-in-the-Head paradigm. Most of our proofs need a trusted setup, which can be removed in the MPC-in-the-Head setting using cut-and-choose techniques. We conclude this work by presenting an oblivious pseudorandom function based on our new framework, that is competitive with current state-of-the-art designs.
  title={New proof systems and an OPRF from CSIDH},
  author={Robi Pedersen and Cyprien Delpech de Saint Guilhem},