Chapter

Cryptographic Algorithms on Reconfigurable Hardware

Part of the series Signals and Communication Technology pp 291-328

Elliptic Curve Cryptography

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Abstract

In this chapter we discuss several algorithms and their corresponding hardware architecture for performing the scalar multiplication operation on elliptic curves defined over binary extension fields GF(2m). By applying parallel strategies at every stage of the design, we are able to obtain high speed implementations at the price of increasing the hardware resource requirements. Specifically, we study the following four different schemes for performing elliptic curve scalar multiplications,
  • Scalar multiplication applied on Hessian elliptic curves.

  • Montgomery Scalar Multiplication applied on Weierstrass elliptic curves.

  • Scalar multiplication applied on Koblitz elliptic curves.

  • Scalar multiplication using the Half-and-Add Algorithm.