Paper 2023/1614

New proof systems and an OPRF from CSIDH

Cyprien Delpech de Saint Guilhem, KU Leuven
Robi Pedersen, KU Leuven

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 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.

Available format(s)
Cryptographic protocols
Publication info
A minor revision of an IACR publication in PKC 2024
Isogeny-based cryptographyCSIDHZero-knowledge proofsMPC-in-the-HeadCryptographic ProtocolsOPRF
Contact author(s)
cyprien delpechdesaintguilhem @ kuleuven be
robi pedersen @ esat kuleuven be
2024-01-19: revised
2023-10-18: received
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Creative Commons Attribution


      author = {Cyprien Delpech de Saint Guilhem and Robi Pedersen},
      title = {New proof systems and an {OPRF} from {CSIDH}},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1614},
      year = {2023},
      note = {\url{}},
      url = {}
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