### 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)
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}
}
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