Chapter

Cryptographic Hardware and Embedded Systems, CHES 2010

Volume 6225 of the series Lecture Notes in Computer Science pp 48-64

A High Speed Coprocessor for Elliptic Curve Scalar Multiplications over \(\mathbb{F}_p\)

  • Nicolas GuillerminAffiliated withDGA Information SuperiorityIRMAR, Université Rennes 1

Abstract

We present a new hardware architecture to compute scalar multiplications in the group of rational points of elliptic curves defined over a prime field. We have made an implementation on Altera FPGA family for some elliptic curves defined over randomly chosen ground fields offering classic cryptographic security level. Our implementations show that our architecture is the fastest among the public designs to compute scalar multiplication for elliptic curves defined over a general prime ground field. Our design is based upon the Residue Number System, guaranteeing carry-free arithmetic and easy parallelism. It is SPA resistant and DPA capable.

Keywords

elliptic curve high speed RNS prime field FPGA