# A Probabilistic Baby-Step Giant-Step Algorithm

## TL;DR

This paper introduces a probabilistic algorithm for solving the discrete logarithm problem that reveals potential vulnerabilities in NIST prime field curves by combining a baby-step giant-step approach with randomized parallel collision search.

## Contribution

The paper presents a novel probabilistic algorithm that exploits the order of discrete logs and parallel collision search to identify weaknesses in NIST prime field curves.

## Key findings

- Indicates potential weaknesses in NIST prime field curves
- Uses a probabilistic approach with parallelized collision search
- Suggests possible cryptographic vulnerabilities

## Abstract

In this paper, a new algorithm to solve the discrete logarithm problem is presented which is similar to the usual baby-step giant-step algorithm. Our algorithm exploits the order of the discrete logarithm in the multiplicative group of a finite field. Using randomization with parallelized collision search, our algorithm indicates some weakness in NIST curves over prime fields which are considered to be the most conservative and safest curves among all NIST curves.