Implementing pairings at the 192-bit security level

Authors:
Diego F. Aranha;Laura Fuentes-Castañeda;Edward Knapp;Alfred Menezes;Francisco Rodríguez-Henríquez
Affiliations:
Department of Computer Science, University of Brasília, Brazil;Computer Science Department, CINVESTAV-IPN, Mexico;Department of Combinatorics & Optimization, University of Waterloo, Canada;Department of Combinatorics & Optimization, University of Waterloo, Canada;Computer Science Department, CINVESTAV-IPN, Mexico
Venue:
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Year:
2012

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Abstract

We implement asymmetric pairings derived from Kachisa-Schaefer-Scott (KSS), Barreto-Naehrig (BN), and Barreto-Lynn-Scott (BLS) elliptic curves at the 192-bit security level. Somewhat surprisingly, we find pairings derived from BLS curves with embedding degree 12 to be the fastest for our serial as well as our parallel implementations. Our serial implementations provide a factor-3 speedup over the previous state-of-the-art, demonstrating that pairing computation at the 192-bit security level is not as expensive as previously thought. We also present a general framework for deriving a Weil-type pairing that is well-suited for computing a single pairing on a multi-processor machine.