Cryptanalysis and designing chaos-based irreversible and parallel key expansion module over Galois field

TL;DR

This paper analyzes weaknesses in existing AES key expansion modules and proposes a new chaos-based, irreversible, and parallel key expansion method over Galois fields, demonstrating improved security and flexibility.

Contribution

It introduces a novel chaos-based irreversible key expansion module over Galois fields that enhances security and supports parallel processing.

Findings

Identified vulnerabilities in existing AES key expansion modules.

Designed a new chaos-based key expansion module with improved security.

Demonstrated the effectiveness and flexibility of the proposed module.

Abstract

From the security criteria of irreversibility, parallelizability and independence, we cryptanalyzed the key expansion modules of candidate block ciphers of AES, the results revealed that there exist some weaknesses inside, which may be explored by the attacker. Hence, we designed a more secure key expansion module that the round-key can satisfy three criteria above. First, we constructed a non-degenerate 2D chaotic map (2D-{\pi}eCM) with ergodicity in phase space and sufficient large chaotic range. Then based on 2D-{\pi}eCM and polynomial multiplication over Galois field, we designed an irreversible key expansion module, which could transform the initial key of arbitrary length to desired number of independent round keys in parallel. Security and statistical results demonstrated the flexible and effectiveness of the proposed key expansion module.