# Linear Complexity of A Family of Binary $pq^2$-periodic Sequences From Euler Quotients

## TL;DR

This paper introduces a new family of binary sequences based on Euler quotients with high linear complexity, useful for cryptographic applications, and provides their minimal polynomials under specific conditions.

## Contribution

The paper determines the minimal polynomials and linear complexities of a new family of binary $pq^2$-periodic sequences derived from Euler quotients, under certain modular conditions.

## Key findings

- Sequences have high linear complexity
- Minimal polynomials are explicitly determined
- Sequences are suitable for cryptographic use

## Abstract

We first introduce a family of binary $pq^2$-periodic sequences based on the Euler quotients modulo $pq$, where $p$ and $q$ are two distinct odd primes and $p$ divides $q-1$. The minimal polynomials and linear complexities are determined for the proposed sequences provided that $2^{q-1} \not\equiv 1 \mod{q^2}.$ The results show that the proposed sequences have high linear complexities.