The key expansion algorithm is an important part of a general iterated block cipher, because its security determines the security level of the encryption scheme. Thus, generating secure round keys with statistical independence and sensitivity is desirable. An irreversible parallel key expansion algorithm is proposed based on a chaotic map in this paper. First, an enhanced nondegenerate 2D exponential chaotic map (2D-ECM) with ergodicity is constructed, with analysis results demonstrating that it has better dynamical characteristics. Then, an irreversible key expansion algorithm is designed based on the 2D-ECM, which has high sensitivity to initial key with independence between round keys. Experimental results and performance analysis demonstrate that the algorithm is feasible and can resist the side channel power attack.
Cryptanalysis of key expansion algorithms in AES and SM4 revealed that (1) there exists 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 explored by the attacker. To solve these problems, first we constructed a nondegenerate 2D exponential hyper chaotic map (2D-EQCM), derived a recursion formula to calculate the number of S-Boxes, and designed a strong S-Box construction algorithm without such weakness. Then based on 2D-EQCM and S-Box, we designed an irreversible parallel key expansion algorithm, which could transform the initial key to any number of relatively independent round keys. Security and statistical analysis demonstrated the flexibility and effectiveness of the proposed irreversible parallel key expansion algorithm.
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