The Discrete Logarithm Problem over Prime Fields can be transformed to a Linear Multivariable Chinese Remainder Theorem

TL;DR

This paper demonstrates that the discrete logarithm problem over prime fields can be reduced to solving a system of linear modular equations, offering a new approach to tackle this fundamental cryptographic challenge.

Contribution

It introduces a novel reduction of the discrete logarithm problem to linear modular equations, providing a potential new method for cryptanalysis.

Findings

Discrete logarithm problem reduced to linear modular equations

Potential for new cryptanalytic techniques

Simplifies understanding of discrete logarithm complexity

Abstract

We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.