# On the expansion complexity of sequences over finite fields

## TL;DR

This paper introduces a modified version of expansion complexity for cryptographic sequences, analyzes both classical and new measures, and studies their behavior in specific generators, enhancing understanding of sequence complexity in finite fields.

## Contribution

It proposes the irreducible-expansion complexity, compares it with classical expansion complexity, and applies these concepts to the explicit inversive congruential generator.

## Key findings

- Irreducible-expansion complexity is more suitable for certain applications.
- Analysis of classical and modified expansion complexities.
- Study of expansion complexity in the explicit inversive congruential generator.

## Abstract

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. In this paper, we slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for certain applications. We analyze both, the classical and the modified expansion complexity. Moreover, we also study the expansion complexity of the explicit inversive congruential generator.