# 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} }

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.

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SHOWING 1-7 OF 7 REFERENCES

Actions of $E-$dense semigroups and an application to the discrete log problem

- Mathematics
- 2017

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 of… Expand

Fundamentals of semigroup theory

- Mathematics
- 1995

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. Free… Expand

A reduction of Semigroup DLP to classic DLP

- Mathematics, Computer Science
- Des. Codes Cryptogr.
- 2013

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

- Mathematics
- 2008

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