Paper 2010/382
Deterministic Encoding and Hashing to Odd Hyperelliptic Curves
Pierre-Alain Fouque and Mehdi Tibouchi
Abstract
In this paper we propose a very simple and efficient encoding function from F_q to points of a hyperelliptic curve over F_q of the form H: y^2=f(x) where f is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves. Our new encoding is nearly a bijection to the set of F_q-rational points on H. This makes it easy to construct well-behaved hash functions to the Jacobian J of H, as well as injective maps to J(F_q) which can be used to encode scalars for such applications as ElGamal encryption. The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux's supersingular elliptic curves.
Note: (Fixed a typo in the definition of an "odd" hyperelliptic curve).
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Pairing 2010
- Keywords
- Hyperelliptic Curve CryptographyDeterministic EncodingHashing
- Contact author(s)
- mehdi tibouchi @ normalesup org
- History
- 2010-09-11: last of 4 revisions
- 2010-07-07: received
- See all versions
- Short URL
- https://ia.cr/2010/382
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/382,
author = {Pierre-Alain Fouque and Mehdi Tibouchi},
title = {Deterministic Encoding and Hashing to Odd Hyperelliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/382},
year = {2010},
url = {https://eprint.iacr.org/2010/382}
}
