Cryptology ePrint Archive: Report 2016/1133

Implementing Complete Formulas on Weierstrass Curves in Hardware

Pedro Maat C. Massolino and Joost Renes and Lejla Batina

Abstract: This work revisits the recent complete addition formulas for prime order elliptic curves of Renes, Costello and Batina in light of parallelization. We introduce the first hardware implementation of the new formulas on an FPGA based on three arithmetic units performing Montgomery multiplication. Our results are competitive with current literature and show the potential of the new complete formulas in hardware design. Furthermore, we present algorithms to compute the formulas using anywhere between two and six processors, using the minimum number of parallel field multiplications.

Category / Keywords: implementation / Elliptic curve cryptography, FPGA, Weierstrass curves, Complete Addition Formulas

Original Publication (with minor differences): Security, Privacy, and Applied Cryptography Engineering (SPACE 2016)

Date: received 5 Dec 2016

Contact author: P Massolino at cs ru nl

Available format(s): PDF | BibTeX Citation

Version: 20161208:165332 (All versions of this report)

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