CryptoDB
Jorge Jiménez Urroz
Publications
Year
Venue
Title
2023
CRYPTO
Revisiting cycles of pairing-friendly elliptic curves
Abstract
A recent area of interest in cryptography is recursive composition of proof systems. One of the approaches to make recursive composition efficient involves cycles of pairing-friendly elliptic curves of prime order. However, known constructions have very low embedding degrees. This entails large parameter sizes, which makes the overall system inefficient. In this paper, we explore 2-cycles composed of curves from families parameterized by polynomials, and show that such cycles do not exist unless a strong condition holds. As a consequence, we prove that no 2-cycles can arise from the known families, except for those cycles already known. Additionally, we show some general properties about cycles, and provide a detailed computation on the density of pairing-friendly cycles among all cycles.
2005
CRYPTO
Coauthors
- Marta Bellés Muñoz (1)
- Ronald Cramer (1)
- Vanesa Daza (1)
- Ignacio Gracia (1)
- Gregor Leander (1)
- Jaume Martí-Farré (1)
- Carles Padró (1)
- Javier Silva (1)
- Jorge Jiménez Urroz (2)