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Are there two symmetric commutative encryption features?

I am wondering if there is a strong (e.g. AES or so) encryption function that works as follows:

  • symetric
  • 2 keys: plaintext → 2keys → ciphertext, however it should not have key order values, i.e.

Key1 (Key2 (clear text)) == Key2 (Key1 (clear text)) for example "Commutative" (also required for decryption - you need two keys, it does not matter the order)

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This is not commutative encryption, but there are proven algorithms for secret exchanges (note that this is not the same as the "key agreement".)

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, CTR. CTR :

ciphertext = plaintext XOR cipher(key, counter)

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ciphertext = plaintext XOR cipher(key0, counter) XOR cipher(key1, counter)

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  • - IV. IV .
  • (key0, IV + ctr) ctr = 0... KS_A Charlie
  • (key1, IV + ctr) ctr = 0... KS_B Charlie
  • Charlie KS_A XOR KS_B XOR , .
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  • , KS_A XOR KS_A = D_A Charlie
  • , KS_B XOR KS_B = D_B Charlie
  • KS = D_A XOR D_B = KS_A XOR KS_B
  • Charlie plaintext = ciphertext XOR KS

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CTR, CTR , , , , CBC. :

sessionkey = RANDOM
IV_0 = RANDOM
IV_1 = RANDOM
enc_sessionkey = sessionkey XOR cipher(key0, IV_0) XOR cipher(key1, IV_0)
ciphertext = enc_sessionkey + IV_0 + IV_1 + cipherCBC(IV_1, sessionkey, plaintext)

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