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Implementing Complete Formulas on Weierstrass Curves in Hardware

2016; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-319-49445-6_5

1611-3349

Pedro Maat C. Massolino, Joost Renes, Lejla Batina,

Algebraic Geometry and Number Theory

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 field multiplications.