Twisted Edwards elliptic curves for zero-knowledge circuits

Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from. The most efficient circuit-based zero-knowledge proofs use a pairing-friendly elliptic curve to generate and val...

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Detalles Bibliográficos
Autores: Bellés-Muñoz, Marta, Whitehat, Barry, Baylina, Jordi, Daza, Vanesa, Muñoz-Tapia, José L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universitat Pompeu Fabra
Repositorio:Repositorio Digital de la UPF
OAI Identifier:oai:repositori.upf.edu:10230/53624
Acceso en línea:http://hdl.handle.net/10230/53624
http://doi.org/10.3390/math9233022
Access Level:acceso abierto
Palabra clave:zero-knowledge proof
elliptic curve
blockchain
privacy
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spelling Twisted Edwards elliptic curves for zero-knowledge circuitsBellés-Muñoz, MartaWhitehat, BarryBaylina, JordiDaza, VanesaMuñoz-Tapia, José L.zero-knowledge proofelliptic curveblockchainprivacyCircuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from. The most efficient circuit-based zero-knowledge proofs use a pairing-friendly elliptic curve to generate and validate proofs. In particular, the circuits are built connecting wires that carry elements from a large prime field, whose order is determined by the number of elements of the pairing-friendly elliptic curve. In this context, it is important to generate an inner curve using this field, because it allows to create circuits that can verify public-key cryptography primitives, such as digital signatures and encryption schemes. To this purpose, in this article, we present a deterministic algorithm for generating twisted Edwards elliptic curves defined over a given prime field. We also provide an algorithm for checking the resilience of this type of curve against most common security attacks. Additionally, we use our algorithms to generate Baby Jubjub, a curve that can be used to implement elliptic-curve cryptography in circuits that can be validated in the Ethereum blockchain.This research has been partially funded by the projects Project RTI2018-102112-B-100 (AEI/FEDER, UE), i3Market (H2020-ICT-2019-2 grant number 871754) and TCO-RISEBLOCK (PID2019- 110224RB-I00).MDPI202220222021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/53624http://doi.org/10.3390/math9233022reponame:Repositorio Digital de la UPFinstname:Universitat Pompeu FabraInglésinfo:eu-repo/grantAgreement/EC/H2020/871754© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositori.upf.edu:10230/536242026-06-12T07:21:37Z
dc.title.none.fl_str_mv Twisted Edwards elliptic curves for zero-knowledge circuits
title Twisted Edwards elliptic curves for zero-knowledge circuits
spellingShingle Twisted Edwards elliptic curves for zero-knowledge circuits
Bellés-Muñoz, Marta
zero-knowledge proof
elliptic curve
blockchain
privacy
title_short Twisted Edwards elliptic curves for zero-knowledge circuits
title_full Twisted Edwards elliptic curves for zero-knowledge circuits
title_fullStr Twisted Edwards elliptic curves for zero-knowledge circuits
title_full_unstemmed Twisted Edwards elliptic curves for zero-knowledge circuits
title_sort Twisted Edwards elliptic curves for zero-knowledge circuits
dc.creator.none.fl_str_mv Bellés-Muñoz, Marta
Whitehat, Barry
Baylina, Jordi
Daza, Vanesa
Muñoz-Tapia, José L.
author Bellés-Muñoz, Marta
author_facet Bellés-Muñoz, Marta
Whitehat, Barry
Baylina, Jordi
Daza, Vanesa
Muñoz-Tapia, José L.
author_role author
author2 Whitehat, Barry
Baylina, Jordi
Daza, Vanesa
Muñoz-Tapia, José L.
author2_role author
author
author
author
dc.subject.none.fl_str_mv zero-knowledge proof
elliptic curve
blockchain
privacy
topic zero-knowledge proof
elliptic curve
blockchain
privacy
description Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from. The most efficient circuit-based zero-knowledge proofs use a pairing-friendly elliptic curve to generate and validate proofs. In particular, the circuits are built connecting wires that carry elements from a large prime field, whose order is determined by the number of elements of the pairing-friendly elliptic curve. In this context, it is important to generate an inner curve using this field, because it allows to create circuits that can verify public-key cryptography primitives, such as digital signatures and encryption schemes. To this purpose, in this article, we present a deterministic algorithm for generating twisted Edwards elliptic curves defined over a given prime field. We also provide an algorithm for checking the resilience of this type of curve against most common security attacks. Additionally, we use our algorithms to generate Baby Jubjub, a curve that can be used to implement elliptic-curve cryptography in circuits that can be validated in the Ethereum blockchain.
publishDate 2021
dc.date.none.fl_str_mv 2021
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/53624
http://doi.org/10.3390/math9233022
url http://hdl.handle.net/10230/53624
http://doi.org/10.3390/math9233022
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/EC/H2020/871754
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositorio Digital de la UPF
instname:Universitat Pompeu Fabra
instname_str Universitat Pompeu Fabra
reponame_str Repositorio Digital de la UPF
collection Repositorio Digital de la UPF
repository.name.fl_str_mv
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