New software speed records for cryptographic pairings

Authors:
Michael Naehrig;Ruben Niederhagen;Peter Schwabe
Affiliations:
Microsoft Research, One Microsoft Way, Redmond, WA;Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan and Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, Netherlands;Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, Netherlands
Venue:
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Year:
2010

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Abstract

This paper presents new software speed records for the computation of cryptographic pairings. More specifically, we present details of an implementation which computes the optimal ate pairing on a 257- bit Barreto-Naehrig curve in only 4,470,408 cycles on one core of an Intel Core 2 Quad Q6600 processor. This speed is achieved by combining 1.) state-of-the-art high-level optimization techniques, 2.) a new representation of elements in the underlying finite fields which makes use of the special modulus arising from the Barreto-Naehrig curve construction, and 3.) implementing arithmetic in this representation using the double-precision floating-point SIMD instructions of the AMD64 architecture.