Paper 2020/1513
Indifferentiable hashing from Elligator 2
Mike Hamburg
Abstract
Bernstein et al. recently introduced a system ``Elligator'' for steganographic key distribution. At the heart of their construction are invertible maps between a finite field $\mathbb{F}$ and an elliptic curve $\mathcal{E}$ over $\mathbb{F}$. There are two such maps, called $\phi$ in the ``Elligator 1'' system, and $\psi$ in the ``Elligator 2'' system. Here we show two ways to construct hash functions from $\psi$ which are indifferentiable from a random oracle. Because $\psi$ is relatively simple, our analyses are also simple. One of our constructions uses a novel ``wallpapering'' approach, whereas the other uses the hash-twice-and-add approach of Brier et al.
Note: I wrote this paper 2013, but I'm posting it in 2020 because it's relevant to the CFRG hash-to-curve discussion.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Indifferentiabilityhashing to elliptic curvesElligator
- Contact author(s)
- mike @ shiftleft org
- History
- 2020-12-02: received
- Short URL
- https://ia.cr/2020/1513
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/1513,
author = {Mike Hamburg},
title = {Indifferentiable hashing from Elligator 2},
howpublished = {Cryptology ePrint Archive, Paper 2020/1513},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/1513}},
url = {https://eprint.iacr.org/2020/1513}
}
