Twisted Edwards Elliptic Curves for Zero-Knowledge Circuits

Marta Bellés-Muñoz, Barry Whitehat, Jordi Baylina, Vanesa Daza and Jose Luis Muñoz-Tapia
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Marta Bellés-Muñoz: Department of Information and Communications Technology, Pompeu Fabra University, Tànger Building, 08018 Barcelona, Spain
Barry Whitehat: Independent Researcher, 6300 Zug, Switzerland
Jordi Baylina: 0KIMS, Eschenring 11, 6300 Zug, Switzerland
Vanesa Daza: Department of Information and Communications Technology, Pompeu Fabra University, Tànger Building, 08018 Barcelona, Spain
Jose Luis Muñoz-Tapia: Department of Network Engineering, Campus Nord, Polytechnic University of Catalonia, 08034 Barcelona, Spain

Mathematics, 2021, vol. 9, issue 23, 1-21

Abstract: 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.

Keywords: zero-knowledge proof; elliptic curve; blockchain; privacy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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