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

  • Nicolas Guillermin
Conference paper

DOI: 10.1007/978-3-642-15031-9_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6225)
Cite this paper as:
Guillermin N. (2010) A High Speed Coprocessor for Elliptic Curve Scalar Multiplications over \(\mathbb{F}_p\). In: Mangard S., Standaert FX. (eds) Cryptographic Hardware and Embedded Systems, CHES 2010. CHES 2010. Lecture Notes in Computer Science, vol 6225. Springer, Berlin, Heidelberg


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.


elliptic curve high speed RNS prime field FPGA 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nicolas Guillermin
    • 1
    • 2
  1. 1.DGA Information SuperiorityBruzFrance
  2. 2.IRMARUniversité Rennes 1France

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