Paper 2010/037
Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves
Pierre-Alain Fouque and Mehdi Tibouchi
Abstract
Let E be a non-supersingular elliptic curve over a finite field F_q. At CRYPTO 2009, Icart introduced a deterministic function F_q->E(F_q) which can be computed efficiently, and allowed him and Coron to define well-behaved hash functions with values in E(F_q). Some properties of this function rely on a conjecture which was left as an open problem in Icart's paper. We prove this conjecture as well as analogues for other hash functions. See also Farahashi, Shparlinski and Voloch, _On Hashing into Elliptic Curves_, for independent results of a similar form.
Note: Fixed an error in Prop. 4
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Latincrypt 2010
- Keywords
- Elliptic CurvesFunction FieldsHash Functions
- Contact author(s)
- mehdi tibouchi @ ens fr
- History
- 2010-08-04: last of 3 revisions
- 2010-01-26: received
- See all versions
- Short URL
- https://ia.cr/2010/037
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/037,
author = {Pierre-Alain Fouque and Mehdi Tibouchi},
title = {Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/037},
year = {2010},
url = {https://eprint.iacr.org/2010/037}
}
