S-Boxes in AES and DES effect diffusion in these block cipher systems. I am trying to understand which aspects of these S-boxes attribute to the symmetry of the cipher system. (i.e. If encryption is in one direction, the decryption is in the reverse direction with the same key.)
Summarized, a symmetrical cryptosystem is such one where you can use the same key for en- and decryption.
Peter Breuer and Günter Fahrnberger are right. You mix up two terms. Symmetric-key usually means that sender and receiver use the same key for encryption and decryption.
You seem to mean why a symmetric-key cipher is a permutation. This is because each of its operation is maps each input uniquely to one distinct output.
The major purpose of S-boxes is only to some extent the diffusion: more importantly, they are non-linear. Without S-boxes, the DES or the AES could be written as a linear equational system. This would map every plaintext difference between a pair of plaintext P and P' with dP = P xor P' uniquely to a certain ciphertext difference dC = C xor C'. Then, we could take a second pair P'' and P''' with the same difference and predict the difference between their corresponding ciphertexts C'' xor C'''. This would yield a tremendously bad cipher.
The components that are relevant for diffusion are the bit permutation at the end of the DES' round function, and the ShiftRows and MixColumns in the AES.
Symmetric or asymmetric encryption algorithms:
Symmetric algorithms: Operation and inverse operation are performed whether it is permutation or substitution. For key addition it is operation and operation.
It is due to two main reasons.. first the key used for encryption is the same key used for decryption. second; both encryption and decryption algorithms are almost the same, except for minor changes(eg. revesing the order of subkeys in DES)
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