# The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives

## TL;DR

This paper explores the discrete logarithm problem over prime fields in the safe prime case, linking it to the concept of logarithmic derivatives to potentially inform cryptographic analysis.

## Contribution

It introduces a novel connection between the discrete logarithm problem and logarithmic derivatives specifically for safe prime fields.

## Key findings

- Establishes a theoretical link between discrete logs and logarithmic derivatives.
- Provides insights into the structure of safe prime fields in cryptography.
- Suggests new avenues for cryptanalysis based on this connection.

## Abstract

In this brief note we connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.