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A survey of elliptic curves for proof systems

Diego Aranha 1 Youssef El Housni 2, 3 Aurore Guillevic 1, 4
3 GRACE - Geometry, arithmetic, algorithms, codes and encryption
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
4 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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.
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https://hal.inria.fr/hal-03667798
Contributor : Aurore Guillevic Connect in order to contact the contributor
Submitted on : Friday, May 13, 2022 - 4:03:10 PM
Last modification on : Monday, May 16, 2022 - 3:54:44 PM

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  • HAL Id : hal-03667798, version 1

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Diego Aranha, Youssef El Housni, Aurore Guillevic. A survey of elliptic curves for proof systems. 2022. ⟨hal-03667798⟩

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