The RC4 cipher consists of a lookup table S, which contains 256 byte values, and two indices, i and j .

a. The lookup table S is initialized to contain the identity permutation 0,1,2,…, 255 and at each step of the algorithm, S contains a permutation. How is this achieved? That is, why does S always contain a permutation?

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b. Where is RC4 used in the real world?

Implement the A5/1 algorithm. Suppose that, after a particular step, the values in the registers are

X = (x_{0},x_{1},…, x_{18}) = (1010101010101010101)

Y = (y_{o}, y_{1}, ■··, y_{21} ) = (1100110011001100110011)

Z = {z_{0}, z_{1},… , z_{22}) = (11100001111000011110000)

List the next 32 keystream bits and give the contents of X, Y, and Z after these 32 bits have been generated.

This problem deals with the A5/1 cipher. For each part, justify your answer.

a. On average, how often does the X register step?

b. On average, how often does the Y register step?

c. On average, how often does the Z register step?

d. On average, how often do all three registers step?

e. On average, how often do exactly two registers step?

f. On average, how often does exactly one register step?

g. On average, how often does no register step?

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