2. AES Key Expansion

Keys in the AES Cryptosystem are 128 bits in length (16 bytes). To generate the round keys, the 16 bytes of the key are placed into the columns of a 4 by 4 matrix. 40 additional columns are then added to this matrix according to a recursive definition. Specifically, if i is not a multiple of 4, then column w(i) becomes w(i) = w(i-4) w(i-1). If i is a multiple of 4, then column w(i) becomes w(i) = w(i-4) T(w(i-1)), where T(w(i-1)) is formed by the following steps. If the components of w(i-1) are { a, b, c, d }, T(w(i-1)) is then { SBox(b) r(i) , SBox(c), SBox(d), SBox(a) }, where the SBox used for the substitutions is the same as from the byte substitution step of AES (the S-Box from page 163 of the textbook, Table 6.2.a).

For the remaining parts of this assignment, our AES key is (written in hex): 1A 00 50 12 BE 10 00 C0 01 20 40 34 07 10 00 01. Below, you see the first 4 columns of the key matrix filled in appropriately using the above key. Computethe next 8 rows. Feel free to use a calculator to compute any XORs (e.g., Windows calculator accessory placed in hexmode will make this step take a lot less time). The important thing is that you know what XORs to compute.

w(0) w(1) w(2) w(3) w(4) w(5) w(6) w(7) w(8) w(9) w(10) w(11)

1A		BE 01 07
00		10 20 10
50		00 40 00
12		C0 34 01