Paper 2024/085

Simultaneously simple universal and indifferentiable hashing to elliptic curves

Dmitrii Koshelev
Abstract

The present article explains how to generalize the hash function SwiftEC (in an elementary quasi-unified way) to any elliptic curve $E$ over any finite field $\mathbb{F}_{\!q}$ of characteristic $> 3$. The new result apparently brings the theory of hash functions onto elliptic curves to its logical conclusion. To be more precise, this article provides compact formulas that define a hash function $\{0,1\}^* \to E(\mathbb{F}_{\!q})$ (deterministic and indifferentible from a random oracle) with the same working principle as SwiftEC. In particular, both of them equally compute only one square root in $\mathbb{F}_{\!q}$ (in addition to two cheap Legendre symbols). However, the new hash function is valid with much more liberal conditions than SwiftEC, namely when $3 \mid q-1$. Since in the opposite case $3 \mid q-2$ there are already indifferentiable constant-time hash functions to $E$ with the cost of one root in $\mathbb{F}_{\!q}$, this case is not processed in the article. If desired, its approach nonetheless allows to easily do that mutatis mutandis.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Preprint.
Keywords
absolute irreducibilityconicshyperelliptic curveshashing to elliptic curvesunirationality problem
Contact author(s)
dimitri koshelev @ gmail com
History
2024-01-29: revised
2024-01-18: received
See all versions
Short URL
https://ia.cr/2024/085
License
No rights reserved
CC0

BibTeX

@misc{cryptoeprint:2024/085,
      author = {Dmitrii Koshelev},
      title = {Simultaneously simple universal and indifferentiable hashing to elliptic curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/085},
      year = {2024},
      url = {https://eprint.iacr.org/2024/085}
}
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