Paper 2023/160
Practically optimizing multi-dimensional discrete logarithm calculations: Implementations in subgroups of $\mathbb{Z}^{*}_{p}$ relevant to electronic voting and cash schemes
Abstract
Discrete logarithm problem(DLP) is the pillar of many cryptographical schemes. We propose an improvement to the Gaudry-Schost algorithm, for multi-dimensional DLP. We have derived the cost estimates in general and specialized cases, which prove efficiency of our new method. We report the implementation of our algorithm, which confirms the theory. Both theory and experiments val- idate the fact that the advantage of our algorithm increases for large sizes, which helps in practical scenarios. Our method is applicable to speed-up electronic voting, cash schemes, along with other ar- eas associated with multi-dimensional discrete logarithms (point-counting, speeding-up elliptic-curve arithmetic, group-actions, CSIDH etc.).
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Discrete logarithm problemMulti-Dimensional discrete logGaudry-Schost algoElectronic-votingcash schemesCSIDH
- Contact author(s)
- mukhopadhyaymadhurima @ gmail com
- History
- 2024-04-03: last of 3 revisions
- 2023-02-09: received
- See all versions
- Short URL
- https://ia.cr/2023/160
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/160,
author = {Madhurima Mukhopadhyay},
title = {Practically optimizing multi-dimensional discrete logarithm calculations: Implementations in subgroups of $\mathbb{Z}^{*}_{p}$ relevant to electronic voting and cash schemes},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/160},
year = {2023},
url = {https://eprint.iacr.org/2023/160}
}
