computational complexity class of decryption of AES I haven't really seen what computational complexity class of decryption of AES is. Can anyone provide reference papers or answers here?
The time of AES encryption/decryption in any of the standard modes like CBC or CTR or GCM is polynomial (more precisely, linear) in the size of the message.  

Proof: One call to the AES encryption/decryption function takes some constant number of steps, which we can represent with the constant $c$.  For example, AES-128 makes one call to the key schedule to generate the round keys, one 'whitening' step with a round key, and then 10 calls to the round function, which itself takes a constant number of simpler steps - 16 parallel applications of the S-Box, one 'ShiftRows' transposition of bytes, 4 parallel applications of the MixColumns linear function (absent in the last round), and one AddRoundKey step.  AES-192 and AES-256 similarly make constant numbers of calls to the round function.  

For any of the standard modes and a message of bit-length $\ell$, the number of calls to the AES encryption/decryption function is some linear function, $f(\ell)$.  For example, the cipher-call function for CTR is: $f^{CTR}(\ell) = \lceil \frac{\ell}{128} \rceil$.  

Sometimes these modes have to do other things than make calls to the block cipher (e.g. GCM has to do one finite field multiplication per 128-bit message block), but in the standard modes these are also always linear or constant in the length of the message.  Let's say the function $g(\ell)$ returns the number of 'extraneous' (non-AES) steps as a function of the message length.

Therefore, the encryption/decryption time for AES in any of the standard modes is some linear function of the length of the message, $c \cdot f(\ell) + g(\ell)$.