A New Method for Speeding Up Arithmetic on Elliptic Curves over Binary Fields

Kwang Ho Kim; So In Kim

Paper 2007/181

A New Method for Speeding Up Arithmetic on Elliptic Curves over Binary Fields

Kwang Ho Kim and So In Kim

Abstract

Now, It is believed that the best costs of a point doubling and addition on elliptic curves over binary fields are 4M+5S(namely, four finite field multiplications and five field squarings) and 8M+5S, respectively. In this paper we reduce the costs to less than 3M+3S and 8M+1S, respectively, by using a new projective coordinates we call PL-coordinates and rewriting the point doubling formula. Combining some programming skills, the method can speed up a elliptic curve scalar multiplication by about 15～20 percent in practice.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: elliptic curve cryptosystem binary field point doubling point addition
Contact author(s): kimkhhj1980 @ yahoo com cn
History: 2007-05-20: received
Short URL: https://ia.cr/2007/181
License: CC BY

BibTeX

@misc{cryptoeprint:2007/181,
      author = {Kwang Ho Kim and So In Kim},
      title = {A New Method for Speeding Up Arithmetic on Elliptic Curves over Binary Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/181},
      year = {2007},
      url = {https://eprint.iacr.org/2007/181}
}