Question 4. (25 points) To generate her cryptographic keys with a uniform distribution, Alice needs an unbiased random-bit generator that produces a stream of independent bits each of which has 0.5 probability of being 1 and 0.5 probability of being 0. But all Alice has is a random-bit generator that is defective in that it is biased: It generates more ls than O's (but the bits it generates are independent and are identically distributed). That is, if po denotes the probability that the next bit generated is 0, and p1 denotes the probability that the next bit generated is 1, then pi > Po (of course po + p1 = 1). However, what Alice really needs is a random-bit generator that is unbiased (i.e., po = pi = 0.5) and whose bits are independent. Explain how Alice can use her biased random-bit generator to generate an unbiased random bit string whose bits are independent; your scheme should not assume that Alice knows po or p1 (she just knows that p1 # po). =