**Efficient Implementation of Elliptic Curve Point Operations Using Binary Edwards Curves**

*Richard Moloney and Aidan O'Mahony and Pierre Laurent*

**Abstract: **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.

**Category / Keywords: **public-key cryptography / elliptic curve cryptosystem, hardware implementation, edwards curve

**Date: **received 14 Apr 2010

**Contact author: **richard moloney at ucd ie

**Available format(s): **PDF | BibTeX Citation

**Version: **20100419:174637 (All versions of this report)

**Short URL: **ia.cr/2010/208

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