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I am not sure whether "linear decomposition" is appropriate to summary my question: We know that the traditional symmetric encryption/decryption algorithm (like AES, TDES) can be written as:

C = FUN_enc(key, P) P = FUN_dec(key, C)

Where FUN_enc is the encryption function/algorithm, FUN_dec is the decryption function, C is ciphertext, P is plaintext. For AES, FUN_enc and FUN_dec are AES encrypt and decrypt algorithms. Here we only consider the basic ECB mode.

OK, now comes my question: Does one encryption/decryption algorithm exists, that satisfy:

C1 = FUN_enc(key1, P) C2 = FUN_enc(key2, C1) and: C2 = FUN_enc(key3, P)

That is, one encryption can be splited into two individual encryption steps, and also give key1, key2, some algorithm can calculate key3.

One algorithm that can be decomposed to two:

FUN_enc(key, P) = FUN_enc(ke2, FUN_enc(key1, P)) and the algorithm FUN_enc SHALL also as secure as AES.

https://stackoverflow.com/questions/76967037/does-any-encryption-decryption-algorithm-supports-linear-decomposition

ZKM
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This would be a weakness and has been investigated under the name does DES form a group?

See question and answer here. A secure cipher should not have this property.

kodlu
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