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.
Category / Keywords: implementation / Pairings, Barreto-Naehrig curves, ate pairing, amd64 architecture, modular arithmetic, SIMD floating-point instructions Date: received 6 Apr 2010, last revised 14 Jul 2010 Contact author: michael at cryptojedi org, ruben@polycephaly org, peter@cryptojedi org Available formats: PDF | BibTeX Citation Version: 20100714:135917 (All versions of this report) Discussion forum: Show discussion | Start new discussion