A New Family of Pairing-Friendly elliptic curves

Michael Scott 1 Aurore Guillevic 2
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : There have been recent advances in solving the finite extension field discrete logarithm problem as it arises in the context of pairing-friendly elliptic curves. This has lead to the abandonment of approaches based on supersingular curves of small characteristic, and to the reconsideration of the field sizes required for implementation based on non-supersingular curves of large characteristic. This has resulted in a revision of recommendations for suitable curves, particularly at a higher level of security. Indeed for a security level of 256 bits, the BLS48 curves have been suggested, and demonstrated to be superior to other candidates. These curves have an embedding degree of 48. The well known taxonomy of Freeman, Scott and Teske only considered curves with embedding degrees up to 50. Given some uncertainty around the constants that apply to the best discrete logarithm algorithm, it would seem to be prudent to push a little beyond 50. In this note we announce the discovery of a new family of pairing friendly elliptic curves which includes a new construction for a curve with an embedding degree of 54.
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download

https://hal.inria.fr/hal-01875361
Contributor : Aurore Guillevic <>
Submitted on : Monday, September 17, 2018 - 11:49:04 AM
Last modification on : Thursday, February 7, 2019 - 3:45:07 PM
Long-term archiving on : Tuesday, December 18, 2018 - 1:06:45 PM

File

18_ScottGuillevic.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Michael Scott, Aurore Guillevic. A New Family of Pairing-Friendly elliptic curves. International Workshop on the Arithmetic of Finite Fields - WAIFI, Lilya Budaghyan and Tor Helleseth, Jun 2018, Bergen, Norway. pp.43-57, ⟨10.1007/978-3-030-05153-2_2⟩. ⟨hal-01875361⟩

Share

Metrics

Record views

134

Files downloads

99