Cryptanalysis result of key expansion algorithms in AES and SM4 revealed that, (1) there exist weaknesses in their S-Boxes, and (2) the round key expansion algorithm is reversible, i.e., the initial key can be recovered from any round key, which may be an exploitable weakness by attacker. To solve these problems, first we constructed a non-degenerate 2D exponential hyper chaotic map (2D-ECM), derived the recursion formula to calculate the number of S-Boxes that satisfied three conditions, and designed a strong S-Box construction algorithm without weakness. Then based on 2D-ECM and S-Box, we designed an irreversible key expansion algorithm, to transform the initial key into independent round keys, to make the initial key can not be recovered from any round key. Security and statistical analysis demonstrated the flexible and effectiveness of the proposed irreversible key expansion algorithm.

翻译：AES 和 SM4 关键扩展算法的加密分析结果表明,(1) S-Boxes 中存在弱点,(2) 圆键扩展算法是可逆的,即最初的钥匙可以从任何圆键中回收,这可能是攻击者可以利用的弱点。为了解决这些问题,我们首先建造了非脱产2D指数性超混乱地图(2D-ECM),从循环公式中推导出符合三个条件的S-Boxs数量,并设计了强大的S-Box构建算法,没有弱点。然后,根据2D-ECM和S-Box,我们设计了一个不可逆转的钥匙扩展算法,将最初的钥匙转换为独立的圆键,使最初的钥匙无法从任何圆键中恢复。安全和统计分析表明了拟议的不可逆转的钥匙扩展算法的灵活性和有效性。