Hashing into Hessian Curves

Reza Rezaeian Farashahi

Paper 2010/373 Original: eprint.iacr.org/2010/373 ↗

Hashing into Hessian Curves

Reza Rezaeian Farashahi

Abstract

We describe a hashing function from the elements of the finite field $\F_q$ into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. Moreover, a point on the image set of the function is uniquely given by its abscissa. For ordinary Hessian curves, the cardinality of the image set of the function is exactly given by $(q+i)/2$ for some $i=1,2,3$.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2010-07-02: last updated; 2010-07-02: published
Short URL: https://ia.cr/2010/373
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2010/373,
      author = {Reza Rezaeian Farashahi},
      title = {Hashing into Hessian Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/373},
      year = {2010},
      url = {https://eprint.iacr.org/2010/373}
}