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Dual-form Elliptic Curves Simple Hardware Implementation

  • Jianxin Wang
  • Xingjun Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)

Abstract

Performing standard Weierstrass-form curves’ operations based on Edwards-form curves’ addition law, the overall security of elliptic curves can be strengthened while remain compatible with existing ECC system. We present a simplified algorithm for finding such dual-form elliptic curves over prime field F p with p ≡ 3 mod 4. Using the generated curves, algorithms for implementing dual-form operations on affine, projective and twisted coordinates are further discussed and optimized for the case of Weierstrass-form operations. The algorithms are implemented on FPGA and show competitive time and area performance both in Edwards form and Weierstrass form.

Keywords

Elliptic curve Edwards curve birational equivalence FPGA 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jianxin Wang
    • 1
  • Xingjun Wang
    • 1
  1. 1.Department of Electronic and EngineeringBeijing Tsinghua UniversityBeijingChina

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