New Software Speed Records for Cryptographic Pairings

  • Michael Naehrig
  • Ruben Niederhagen
  • Peter Schwabe
Conference paper

DOI: 10.1007/978-3-642-14712-8_7

Volume 6212 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Naehrig M., Niederhagen R., Schwabe P. (2010) New Software Speed Records for Cryptographic Pairings. In: Abdalla M., Barreto P.S.L.M. (eds) Progress in Cryptology – LATINCRYPT 2010. LATINCRYPT 2010. Lecture Notes in Computer Science, vol 6212. Springer, Berlin, Heidelberg

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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Michael Naehrig
    • 1
  • Ruben Niederhagen
    • 2
    • 3
  • Peter Schwabe
    • 3
  1. 1.Microsoft ResearchOne Microsoft WayRedmondUSA
  2. 2.Department of Electrical EngineeringNational Taiwan UniversityTaipeiTaiwan
  3. 3.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenNetherlands