# Strongly Non-zero Points and Elliptic Pseudoprimes

## TL;DR

This paper explores strongly non-zero points on elliptic curves and their role in elliptic pseudoprimes, providing probabilistic insights into their existence for random points and curves.

## Contribution

It introduces the concept of strongly non-zero points and applies it to analyze various types of elliptic pseudoprimes, offering new probabilistic results.

## Key findings

- Probabilistic existence results for strong elliptic pseudoprimes
- Introduction of strongly non-zero points as a tool in elliptic pseudoprime analysis
- Insights into the distribution of elliptic pseudoprimes for random points and curves

## Abstract

We examine the notion of strongly non-zero points and use it as a tool in the study of several types of elliptic pseudoprimes. Moreover, we give give some probabilistic results about the existence of strong elliptic pseudoprimes for a randomly chosen point on a randomly chosen elliptic curve.