On the discrete logarithm problem

TL;DR

This paper discusses the distribution of discrete logarithms of numbers in arithmetic progressions modulo a prime, suggesting they are uniformly distributed and raising related questions.

Contribution

It provides an argument supporting the uniform distribution of discrete logarithms in arithmetic progressions and explores implications and open questions.

Findings

Discrete logarithms in arithmetic progressions are uniformly distributed.

Raises questions about the distribution properties of discrete logs.

Provides an argument supporting uniformity hypothesis.

Abstract

Let $p>2$ be prime and $g$ a primitive root modulo $p$. We present an argument for the fact that discrete logarithms of the numbers in any arithmetic progression are uniformly distributed in $[1,p]$ and raise some questions on the subject.