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. Keywords: Pairings, Barreto-Naehrig curves, ate pairing, AMD64 architecture, modular arithmetic, SIMD floating-point instructions.
|Title of host publication||Progress in Cryptology - LATINCRYPT 2010 (First International Conference on Cryptology and Information Security in Latin America, Puebla, Mexico, August 8-11, 2010. Proceedings)|
|Editors||M. Abdalla, P.S.L.M. Barretto|
|Place of Publication||Berlin|
|Publication status||Published - 2010|
|Name||Lecture Notes in Computer Science|
Naehrig, M., Niederhagen, R. F., & Schwabe, P. (2010). New software speed records for cryptographic pairings. In M. Abdalla, & P. S. L. M. Barretto (Eds.), Progress in Cryptology - LATINCRYPT 2010 (First International Conference on Cryptology and Information Security in Latin America, Puebla, Mexico, August 8-11, 2010. Proceedings) (pp. 109-123). (Lecture Notes in Computer Science; Vol. 6212). Springer. https://doi.org/10.1007/978-3-642-14712-8_7