A.) Consider a Linear Feedback Shift Register (LFSR) with polynomial given by x⁸+x⁴+x³+x+1. Let the initial vector be given by all 1 sequence. Find the sequence of the output for the first 24 bits.

B.) Verify if the S box given by S₁ is linear or non-linear. Take any 2 inputs, find their outputs of the S-box for those inputs. Then find the output for the modulo-2 sum of those inputs. Show your steps.

C.) Find the output of the first round of DES when the input and key are both all 0 sequences.

D.) Assume that we are given one pair of plaintext and cipher text for a DES system. What is the worst case of number of keys to test? What is the average number of keys to test?