4. (a) Alice and Bob communicate reqularly, agreeing a secret key before each se- cure communication. In order to enhance security, they use a random number generator to produce a sequence of random bits. Bob suspects that an agent from Eve may have secretly installed a determin- istic number generator into his system to allow her to know his secret key. The sequence of 22 bits produced (top line) and the first six cyclic permuta- tions of this sequence are given in the table below. 1 1 1 1 1 1 1 0 1 1 1 1 1 0. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Use Golomb's postulates to confirm that Bob's random number generator is NOT producing a random sequence. Comment on anything which may seem unusual about the sequence of bits.

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