A dynamical systems approach to the discrimination of the modes of operation of cryptographic systems

TL;DR

This paper introduces a novel dynamical systems approach using Lyapunov exponents to distinguish and classify cryptographic modes of operation based on their divergence signatures, enhancing understanding of their security properties.

Contribution

It presents a new algorithm that applies chaos theory concepts to cryptography, enabling mode discrimination and strength classification of various block ciphers.

Findings

Successfully distinguishes six cryptographic modes using multiple ciphers.

Provides a method to classify modes based on their divergence behavior.

Enhances analysis of cryptographic system security through dynamical systems theory.

Abstract

Evidence of signatures associated with cryptographic modes of operation is established. Motivated by some analogies between cryptographic and dynamical systems, in particular with chaos theory, we propose an algorithm based on Lyapunov exponents of discrete dynamical systems to estimate the divergence among ciphertexts as the encryption algorithm is applied iteratively. The results allow to distinguish among six modes of operation, namely ECB, CBC, OFB, CFB, CTR and PCBC using DES, IDEA, TEA and XTEA block ciphers of 64 bits, as well as AES, RC6, Twofish, Seed, Serpent and Camellia block ciphers of 128 bits. Furthermore, the proposed methodology enables a classification of modes of operation of cryptographic systems according to their strength.