Corpus ID: 119658715

Completely Regular Semigroups and the Discrete Log Problem

@article{Renshaw2018CompletelyRS,
  title={Completely Regular Semigroups and the Discrete Log Problem},
  author={James Renshaw},
  journal={arXiv: Group Theory},
  year={2018}
}
  • J. Renshaw
  • Published 31 January 2018
  • Mathematics
  • arXiv: Group Theory
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear to offer protection to a standard trial multiplication attack. 

Figures from this paper

References

SHOWING 1-7 OF 7 REFERENCES
Actions of $E-$dense semigroups and an application to the discrete log problem
We describe the structure of $E-$dense acts over $E-$dense semigroups in an analogous way to that for inverse semigroup acts over inverse semigroups. This is based, to a large extent, on the work ofExpand
Fundamentals of semigroup theory
1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. FreeExpand
A reduction of Semigroup DLP to classic DLP
TLDR
A polynomial-time reduction of the discrete logarithm problem (DLP) in any periodic semigroup (Semigroup DLP) to the classic DLP in a subgroup of the same semigroup is presented. Expand
PROBABILITY THAT AN ELEMENT OF A FINITE GROUP HAS A SQUARE ROOT
Let G be a finite group of even order. We give some bounds for the probability p(G) that a randomly chosen element in G has a square root. In particular, we prove that p(G) ≤ 1 − ⌊ p |G|⌋/|G|.Expand
Über relative Primzahlen
  • Journal für die reine und angewandte Mathematik, Band
  • 1911
E−dense actions of semigroups and an application to the discrete log problem
  • submitted
  • 1712