a) Use the figure to define the S-Box substitution table.

X1	X2	X3	X4	Y1	Y2	Y3	Y4
0	0	0	0	1	0	0	0
0	0	0	1	0	0	1	0
0	0	1	0	1	1	0	1
0	0	1	1	0	1	1	0
0	1	0	0	1	1	1	1
0	1	0	1	1	1	0	0
0	1	1	0	1	1	1	0
0	1	1	1	0	1	0	0
1	0	0	0	1	0	1	0
1	0	0	1	0	0	1	1
1	0	1	0	0	1	0	1
1	0	1	1	0	0	0	1
1	1	0	0	1	0	1	1
1	1	0	1	0	0	0	0
1	1	1	0	1	0	0	1
1	1	1	1	0	1	1	1

b) Find the probability bias and the Linear Approximation table value of the followings: (Define the expressions for each and show your steps)

1. Input Sum = C and Output Sum = 6
2. Input Sum = B and Output Sum = 9
3. Input Sum = 5 and Output Sum = 7

c) Assume that we are analyzing a broadcast attack and we want to find the keyword that has been sent to several clients. The message is an integer number A" which gives a remainder of 2 when divided by 5, e remainder of 3 when divided by 7 and a reminder of 10 when divided by 11. Find the keyword A by describing your solution.