Paper 2010/208

Efficient Implementation of Elliptic Curve Point Operations Using Binary Edwards Curves

Richard Moloney, Aidan O'Mahony, and Pierre Laurent


This paper presents a deterministic algorithm for converting points on an ordinary elliptic curve (defined over a field of characteristic 2) to points on a complete binary Edwards curve. This avoids the problem of choosing curve parameters at random. When implemented on a large (512 bit) hardware multiplier, computation of point multiplication using this algorithm performs significantly better, in terms of code complexity, code coverage and timing, than the standard implementation. In addition, we propose a simple modification to the birational equivalence detailed in the paper by Bernstein et al. which both reduces the number of inversions required in the affine mapping and has fewer exceptional points. Finally, we compare software implementations using this efficient point multiplication for binary Edwards curves with computations on elliptic curves in Weierstrass form.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
elliptic curve cryptosystemhardware implementationedwards curve
Contact author(s)
richard moloney @ ucd ie
2010-04-19: received
Short URL
Creative Commons Attribution


      author = {Richard Moloney and Aidan O'Mahony and Pierre Laurent},
      title = {Efficient Implementation of Elliptic Curve Point Operations Using Binary Edwards Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2010/208},
      year = {2010},
      note = {\url{}},
      url = {}
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