A survey of elliptic curves for proof systems

Diego F. Aranha; Youssef El Housni; Aurore Guillevic

doi:10.1007/s10623-022-01135-y

A survey of elliptic curves for proof systems

Diego F. Aranha, Youssef El Housni, Aurore Guillevic

Department of Computer Science

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

7 Citations (Scopus)

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 overview 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.

Original language	English
Journal	Designs, Codes and Cryptography
Volume	91
Pages (from-to)	3333–3378
Number of pages	46
ISSN	0925-1022
DOIs	https://doi.org/10.1007/s10623-022-01135-y
Publication status	Published - Oct 2023

Keywords

Elliptic curves
Pairings
Proof systems
SNARKs

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10.1007/s10623-022-01135-y

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title = "A survey of elliptic curves for proof systems",

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 overview 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.",

keywords = "Elliptic curves, Pairings, Proof systems, SNARKs",

author = "Aranha, {Diego F.} and {El Housni}, Youssef and Aurore Guillevic",

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doi = "10.1007/s10623-022-01135-y",

language = "English",

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T1 - A survey of elliptic curves for proof systems

AU - Aranha, Diego F.

AU - El Housni, Youssef

AU - Guillevic, Aurore

N1 - submitted

PY - 2023/10

Y1 - 2023/10

N2 - 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 overview 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.

AB - 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 overview 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.

KW - Elliptic curves

KW - Pairings

KW - Proof systems

KW - SNARKs

U2 - 10.1007/s10623-022-01135-y

DO - 10.1007/s10623-022-01135-y

M3 - Journal article

SN - 0925-1022

VL - 91

SP - 3333

EP - 3378

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

ER -

A survey of elliptic curves for proof systems

Abstract

Keywords

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