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I have learned from Applied Cryptography that triple encryption with three independent keys in encryption-decryption-encryption (EDE) process gives security not higher then $2^{2n}$ when it comes to meet-in-the-middle attack, where $n$ is keysize. If the triple encryption is done in encryption-encryption-encryption (EEE) process instead, is the security still the same as in EDE process or less?

I'm just curious to know how and how much security does this middle decryption provide?

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EEE and EDE are effectively the same in terms of security. EDE is used because it is "backwards compatible:" by setting all three keys to be the same, it becomes equivalent to just single encryption (E) with that key.

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