This problem concerns the RC4 cipher find its description in the book by Boneh and Shoup (available online) on page 77. Let us simplify the setup algorithm as follows: Suppose that the key length is 256 bytes (2048 bits), and it is written in the array of bytes T, i.e., T[0] is the 1st byte of the key, T[1] is the 2nd byte of the key, , T[255] is the 256th byte of the key. Also, suppose that the array S initially contains the values from 0 to 255 in the ascending order, i.e., S[0] = 0, S[1] = 1, , S[255] = 255. Now, the last for loop in the setup algorithm will be re-written as follows:

for i <- 0 to 255 do j <- S[i] + T[i] mod 256 swap(S[i],S[j]) Find the RC4 key (i.e., the contents of array T) which will leave the array S unchanged. That is, after running the setup algorithm, the elements of S will still be S[i] = i, for i = 0,...,255.