Year: 2026
Type: dissertation
Abstract: This dissertation presents a comprehensive analysis of discrete logarithm problems (DLPs) on algebraic curves with at least a single fully ramified point. While elliptic curves - a subset of these curves - typically only allow generic solvers, these more general curves provide additional structure that can be leveraged for novel solution approaches. This work introduces a unified framework for solving these DLPs. The focus lies on new algorithms based on the index calculus principle and an improved sieving method. These demonstrably require fewer arithmetic operations than previously known methods. Furthermore, the smoothness probability of ideals, crucial for the overall complexity, is analyzed in detail and extended to previously unstudied parameterizations. Finally, two optimized implementations prove the high efficiency: The new algorithms enable the solution of previously intractable DLPs using today's resources.
Author: Trei, Wilke Idäus
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140069480
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