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Cryptanalysis result of key expansion algorithms in AES and SM4 revealedthat, (1) there exist weaknesses in their S-Boxes, and (2) the round keyexpansion algorithm is reversible, i.e., the initial key can be recovered fromany round key, which may be an exploitable weakness by attacker. To solve theseproblems, first we constructed a non-degenerate 2D exponential hyper chaoticmap (2D-ECM), derived the recursion formula to calculate the number of S-Boxesthat satisfied three conditions, and designed a strong S-Box constructionalgorithm without weakness. Then based on 2D-ECM and S-Box, we designed anirreversible key expansion algorithm, to transform the initial key intoindependent round keys, to make the initial key can not be recovered from anyround key. Security and statistical analysis demonstrated the flexible andeffectiveness of the proposed irreversible key expansion algorithm.

Cryptanalyze and design strong S-Box using 2D chaotic map and apply to irreversible key expansion