Hard Instances of the Constrained Discrete Logarithm Problem

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 se...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Mironov, Ilya, Mityagin, Anton, Kobbi Nissim
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 24.07.2006
Subjects
Algorithms
Complexity
Cryptography
Lower bounds
Representations
Online AccessGet full text

Cover

More Information
Summary: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 Erd\"os 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.
ISSN:2331-8422