Encryption dynamics and avalanche parameter for "delayed dynamics"-based cryptosystems

TL;DR

This paper analyzes the encryption dynamics of delayed dynamics-based block ciphers, using Hamming distance to evaluate their performance, and compares two variants, EDDy and ExEDDy, with cellular automata-based ciphers.

Contribution

It introduces a detailed analysis of delayed dynamics encryption algorithms and demonstrates that the extended version ExEDDy significantly outperforms the original EDDy.

Findings

ExEDDy outperforms EDDy in encryption performance.

Hamming distance effectively quantifies encryption change.

Comparison with cellular automata-based ciphers highlights differences.

Abstract

The presented article attempts to characterize the encryption dynamics of delayed dynamics based block ciphers, designed for the encryption of binary data. For such encryption algorithms, the encryption process relies on a coupling dynamics with time delay between different bits in the plaintext (i.e.\ the "initial" message to be encrypted). Here, the principal dynamics of the encryption process is examined and the Hammingdistance is used to quantify the change in ciphertext (i.e.\ the plaintext after encryption) upon changing a single bit in the plaintext message or slightly perturbing the key used during encryption. More precisely, the previously proposed "encryption via delayed dynamics" (in short: EDDy) algorithm as well as its extended version (termed ExEDDy) are analyzed by means of numerical simulations. As a result it is found that while EDDy exhibits a rather poor perfomance, ExEDDy performes considerably better and hence constitutes a significant improvement over EDDy. Consequently, the results are contrasted with those obtained for a block cipher that implements the encryption/decryption dynamics by means of reversible cellular automata.