Paper 2025/2169
Multivariate exponential equations with unknown coefficients
Abstract
We introduce a novel class of equations defined over Euclidean domains. These abstract equations establish a unified framework for deriving new, concrete computational problems useful for cryptography. We prove that solving a single such equation is NP-hard. For systems of these equations, we further prove NP-hardness, average-case hardness, random self-reducibility, search-to-decision reducibility, and trapdoorizability. Based on the hardness of solving these systems, we construct various cryptographic primitives. Our results are proved in an abstract, domain-agnostic manner and hold for a wide range of Euclidean domains. This generality allows the framework to accommodate rich mathematical structures, providing both theoretical depth and flexibility for diverse cryptographic applications.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. Advances in Mathematics of Communications
- DOI
- 10.3934/amc.2026001
- Keywords
- Multivariate Exponential EquationsEuclidean DomainsNP-HardnessSelf-ReducibilitySearch-to-DecisionPost-Quantum
- Contact author(s)
- trey li @ manchester ac uk
- History
- 2025-12-01: approved
- 2025-11-28: received
- See all versions
- Short URL
- https://ia.cr/2025/2169
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/2169,
author = {Trey Li},
title = {Multivariate exponential equations with unknown coefficients},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/2169},
year = {2025},
doi = {10.3934/amc.2026001},
url = {https://eprint.iacr.org/2025/2169}
}
