Cryptology ePrint Archive: Report 2015/116

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

Riadh Brinci and Walid Khmiri and Mefteh Mbarek and 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-

Category / Keywords: implementation / Pairing based Cryptography, FPGA, Modular integer polynomial Multiplication, Non-Standard Splitting, Pairing-Friendly Curves, BN curve, optimal pairing

Date: received 15 Feb 2015

Contact author: br riadh at gmail com

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Version: 20150224:024050 (All versions of this report)

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