  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.
