Efficient Hardware Design for Computing Pairings Using Few FPGA In-built DSPs

Riadh Brinci; Walid Khmiri; Mefteh Mbarek; Abdellatif Ben Rabâa; Ammar Bouallègue

Paper 2015/116

Efficient Hardware Design for Computing Pairings Using Few FPGA In-built DSPs

Riadh Brinci, Walid Khmiri, Mefteh Mbarek, Abdellatif Ben Rabâa, and Ammar Bouallègue

Abstract

This paper is devoted to the design of a 258-bit multiplier for computing pairings over Barreto-Naehrig (BN) curves at 128-bit security level. The proposed design is optimized for Xilinx ﬁeld programmable gate array (FPGA). Each 258-bit integer is represented as a polynomial with ﬁve, 65 bit signed integer, coefficients. Exploiting this splitting we designed a pipelined 65-bit multiplier based on new Karatsuba- Ofman variant using non-standard splitting to ﬁt to the Xilinx embedded digital signal processor (DSP) blocks. We prototype the coprocessor in two architectures pipelined and serial on a Xilinx Virtex-6 FPGA using around 17000 slices and 11 DSPs in the pipelined design and 7 DSPs in the serial. The pipelined 128-bit pairing is computed in 1. 8 ms running at 225MHz and the serial is performed in 2.2 ms running at 185MHz. To the best of our knowledge, this implementation outperforms all reported hardware designs in term of DSP use. Keywords-

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
Keywords: Pairing based Cryptography FPGA Modular integer polynomial Multiplication Non-Standard Splitting Pairing-Friendly Curves BN curve optimal pairing
Contact author(s): br riadh @ gmail com
History: 2015-02-24: received
Short URL: https://ia.cr/2015/116
License: CC BY

BibTeX

@misc{cryptoeprint:2015/116,
      author = {Riadh Brinci and Walid Khmiri and Mefteh Mbarek and Abdellatif Ben Rabâa and Ammar Bouallègue},
      title = {Efficient Hardware Design for Computing Pairings Using Few {FPGA} In-built {DSPs}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/116},
      year = {2015},
      url = {https://eprint.iacr.org/2015/116}
}