AES column mixing and S-Box confusion I am trying to understand the AES encryption algorithm. I know that we process 128 bits at a time for a 128 bit key in a 4x4 octet form, but am confused by the following:


How does the substitution subround work, as the size of the Rijndael's S-box is 16x16 Octets and size of the input is 4x4?
How does the mixed column operation work on the 4-octet column?
You should think of Rijndael's S-box as a function that maps bytes to bytes, where a byte (octet) is considered to be a member of a finite field of size $2^8$ (with xor as addition). It's not seen as a 16x16 octet array, really. 

The substitution is then just done byte-wise: every octet in the 4x4 block is replaced by its function value under the S-box table.

The mix column is just a matrix multiplication of the column with a 4x4 matrix, all in the field of size $2^8$. See the wikipedia entry for a worked example.