### A survey of elliptic curves for proof systems

Diego F. Aranha, Youssef El Housni, and Aurore Guillevic

##### Abstract

Elliptic curves have become key ingredients for instantiating zero-knowledge proofs and more generally proof systems. Recently, there have been many tailored constructions of these curves that aim at efficiently implementing different kinds of proof systems. In this survey we provide the reader with a comprehensive view on existing work and revisit the contributions in terms of efficiency and security. We present an overview at three stages of the process: curves to instantiate a SNARK, curves to instantiate a recursive SNARK, and also curves to express an elliptic-curve related statement. We provide new constructions of curves for SNARKs and generalize the state-of-the-art constructions for recursive SNARKs. We also exhaustively document the existing work and open-source implementations.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
elliptic curvesproof systemsSNARKspairings
Contact author(s)
youssef el-housni @ inria fr
aurore guillevic @ inria fr
History
Short URL
https://ia.cr/2022/586

CC BY

BibTeX

@misc{cryptoeprint:2022/586,
author = {Diego F.  Aranha and Youssef El Housni and Aurore Guillevic},
title = {A survey of elliptic curves for proof systems},
howpublished = {Cryptology ePrint Archive, Paper 2022/586},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/586}},
url = {https://eprint.iacr.org/2022/586}
}

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