New Software Speed Records for Cryptographic Pairings

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 256-bit Barreto-Naehrig curve in only 4,379,912 cycles on one core of an Intel Core 2 Quad Q9550 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.