The trail of a bit through an encryption is the set of bits at each step that depend on the initial bit. In this exercise, you will follow the trail of a bit through the AES encryption. For an example of how we will picture this, here is the trail of a bit through the S-box: each box represents a byte, each dot a bit, and the x's are the bits in the trail. X....... XXXXXXXX SubBytes The nature of the S-box is such that every output bit can depend on every input bit, so the trail of a single input bit through the S-box is the entire output byte. Here is another example: The MixColumns operation makes everything in the column depend on each byte in the column, so we have the following trail. XXXXXXXX ..... XXXXXXXX XXXXXXXX ..... MixColumns XXXXXXXX XXXXXXXX (a) Show the trail of a bit through the AddRoundKey function. (If a byte is entirely dots, you may leave it empty.) X... >AddRoundKey (b) Show the trail of several different bits through the ShiftRows function. (Note that there are four x's in the input below.) X....... X....... X....... X....... ShiftRows (c) Now that you have an idea of the trail through each of the four functions that make up AES encryption, show the trail of a plaintext hit through two rounds of encryption. X....... AddRoundKey SubBytes ShiftRows MixColumns AddRoundKey SubBytes ShiftRows MixColumns AddRoundKey