Question

Show the first eight words of the AES key expansion for a 128-bit key of all ONES

Answer 1

Ans:

Calculating w[4] :

Here, i = 4

temp = w[i-1] =w[3] = ffffffff

RotWord(temp) = ffffffff

SubWord(RotWord(temp)) = 16161616 (using the S-box table)

Rcon[4/4] = 01000000 (using round constant table)

XORing SubWord withRcon[4/4] : temp=16161616 XOR 01000000 = 17161616

XORing w[4-4] with temp we get w[4] , hencew[4] = w[0] XOR temp= ffffffff XOR 17161616 =e8e9e9e9

The next three keys are just calculated using XORS with ffffffff.

These are:

w[5] = 17 16 16 16

w[6] = e8 e9 e9 e9

w[7] = 17 16 16 16

Calculating w[8] :

Here, i = 8

temp = w[i-1] =w[7] = 17161616

RotWord(temp) = 16161617

SubWord(RotWord(temp)) = 474747f0 (using the S-box table)

Rcon[8/4] = 02000000 (using round constant table)

XORing SubWord withRcon[8/4] : temp=474747f0 XOR 02000000 = 454747f0

XORing w[8-4] with temp we get w[8] , hencew[8] = w[4] XOR temp= e8e9e9e9 XOR 454747f0 =adaeae19

The next three keys are just calculated using XORS with the appropriate previous values:

w[9] = ba b8 b8 0f

w[10] = 52 51 51 e6

w[11] = 45 4747 f0