# Lyapunov Exponent Evaluation of the CBC Mode of Operation

## TL;DR

This paper investigates the chaotic behavior of the CBC encryption mode by computing its Lyapunov exponent, providing a new quantitative measure of its dynamical properties.

## Contribution

It extends previous research by quantitatively analyzing the CBC mode's chaos through Lyapunov exponent calculation.

## Key findings

- CBC mode exhibits chaotic behavior under certain conditions
- Lyapunov exponent provides a measure of chaos intensity
- Quantitative analysis enhances understanding of CBC dynamics

## Abstract

The Cipher Block Chaining (CBC) mode of encryption was invented in 1976, and it is currently one of the most commonly used mode. In our previous research works, we have proven that the CBC mode of operation exhibits, under some conditions, a chaotic behavior. The dynamics of this mode has been deeply investigated later, both qualitatively and quantitatively, using the rigorous mathematical topology field of research. In this article, which is an extension of our previous work, we intend to compute a new important quantitative property concerning our chaotic CBC mode of operation, which is the Lyapunov exponent.