I'm wondering why we use encrypt-decrypt-encrypt sequence in 3DES with three keys instead of three times encryption with three different keys ?
thanks
I'm largely restating what is said here: https://security.stackexchange.com/questions/1886/why-triple-des-used-in-ede-mode
Encrypt-decrypt-encrypt (EDE) is the preferred method because if a single key is used for all 3 operations it is equivalent to regular 56-bit DES. That is, a 56-bit DES implementation can decrypt that message. This makes this version of 3DES backwards compatible with DES.
Encrypt-encrypt-encrypt (EEE) is also a valid method though. It is no more or less valid than EDE. However, EDE is usually preferred for the reasons mentioned above.