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A survey of elliptic curves for proof systems
by
Aranha, Diego F.
, El Housni, Youssef
, Guillevic, Aurore
in
Algebraic Geometry
/ Coding and Information Theory
/ Computer Science
/ Cryptography and Security
/ Cryptology
/ Curves
/ Discrete Mathematics in Computer Science
/ Fourier transforms
/ Knowledge
/ Mathematics
/ Number Theory
/ Special Issue: Mathematics of Zero Knowledge
2023
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A survey of elliptic curves for proof systems
by
Aranha, Diego F.
, El Housni, Youssef
, Guillevic, Aurore
in
Algebraic Geometry
/ Coding and Information Theory
/ Computer Science
/ Cryptography and Security
/ Cryptology
/ Curves
/ Discrete Mathematics in Computer Science
/ Fourier transforms
/ Knowledge
/ Mathematics
/ Number Theory
/ Special Issue: Mathematics of Zero Knowledge
2023
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Do you wish to request the book?
A survey of elliptic curves for proof systems
by
Aranha, Diego F.
, El Housni, Youssef
, Guillevic, Aurore
in
Algebraic Geometry
/ Coding and Information Theory
/ Computer Science
/ Cryptography and Security
/ Cryptology
/ Curves
/ Discrete Mathematics in Computer Science
/ Fourier transforms
/ Knowledge
/ Mathematics
/ Number Theory
/ Special Issue: Mathematics of Zero Knowledge
2023
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Journal Article
A survey of elliptic curves for proof systems
2023
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Overview
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.
Publisher
Springer US,Springer Nature B.V,Springer Verlag
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