Question 1.    What RC4 key value will completely invert S after the initial permutation (so that S[0] = 255, S[1] = 254, ..., S[254] = 1, S[255] = 0)?  Show your work.  (Explain how you got this.)

Hint:  It's known that the key value K[0] = K[1] = 0, K[2] = 255, K[3] = 254, ..., K[254] = 3, K[255] = 2 will leave S unchanged after the initial permutation.  This problem is similar, in that most of the key bytes differ from the adjacent byte by 1, but there are a couple places where there are huge jumps.

Question 2.    Consider the following proposal to deskew a skewed bitstream from a TRNG.  Consider the bitstream to be a sequence of groups ot n bits for some n > 2.  Take the first n bits, and output the parity of those n bits as the first bit in a deskewed bitstream.  Then take the n bits starting with the next bit, and use this to get the second bit in an allegedly deskewed bitstream.  To give you an example, consider the following bitstream of length 10 in which n=3:

Original bitstream:  0011101011

First 7 bits of output "deskewed" bitstream (each bit is the parity of the emboldened, italicized, underlined bits):

Bitstream

Output bit

0011101011

1

0011101011

0

0011101011

1

0011101011

0

0011101011

0

0011101011

1

0011101011

0

0011101011

0

Will this deskew the bitstream?  Justify your answer.