Computing a Discrete Logarithm in O(n^3)

TL;DR

This paper introduces an algorithm with worst-case O(n^3) complexity for computing discrete logarithms in cyclic groups, utilizing a novel reduction to finding zeros of periodic functions, akin to an analog cipher approach.

Contribution

It proposes a new algorithm that reduces the discrete logarithm problem to zero-finding of periodic functions, offering a different computational perspective.

Findings

Algorithm achieves O(n^3) worst-case complexity

Reduces discrete log problem to zero-finding in real functions

Provides a novel analog cipher interpretation

Abstract

This paper presents a means with time complexity of at worst O(n^3) to compute the discrete logarithm on cyclic finite groups of integers modulo p. The algorithm makes use of reduction of the problem to that of finding the concurrent zeros of two periodic functions in the real numbers. The problem is treated as an analog to a form of analog rotor-code computed cipher.