Symmetric Cryptography

Keep others from knowing or understanding what happened.

1. SubBytes - each byte of the state is substituted for a different byte according to a lookup table (S-box).

   

   According to Shannon's Information Theory, for the secure cipher, just with given ciphertext, we have no way to learn anything about the key. Otherwise, we can express the relationship between ciphertext and key. For example, the Caesar cipher with ciphertext = plaintext + key relationship.

   For the linear transformations can be solved using techniques like Gaussian elimination. Even low-degree polynomials, e.g. an equation like \(x^4 + 51x^3 + x\) can be solved efficiently by algebraic methods. However, the high-degree of a polynomials can only be approximated by a larger and larger amount of linear functions.

Cause change of one bit in the plaintext to lead to a change as much as possible the bits of the ciphertext

1. ShiftRows - the last three rows of the state matrix are transposed -> shifted over a column or two or three.

   

1. MixColumns - matrix multiplication is performed on the columns of the state, combining the four bytes in each column. This is skipped in the final round.

   

1. AddRoundKey - the bytes of the current round_key are XOR'd with the bytes of the state.