Paper 2006/253 Original: eprint.iacr.org/2006/253 ↗
Hard Instances of the Constrained Discrete Logarithm Problem
Abstract
The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erdös et~al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2006-07-24: last updated
- 2006-07-24: published
- Short URL
- https://ia.cr/2006/253
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2006/253,
author = {Ilya Mironov and Anton Mityagin and Kobbi Nissim},
title = {Hard Instances of the Constrained Discrete Logarithm Problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2006/253},
year = {2006},
url = {https://eprint.iacr.org/2006/253}
}