The future of computational complexity theory: part I
ACM SIGACT News
Sharing Random Bits with No Process Coordination
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
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This paper investigates the extent to which a public source of random bits can be used to obtain private random bits that can be safely used in cryptographic protocols. We consider two cases: (a) the case in which the part privatizing random bits is computationally more powerful than the adversary, and (b) the case in which the part privatizing random bits has a small number of private random bits. The first case corresponds to randomized hard functions and the second variant corresponds to randomized pseudo-random generators. We show the existence of strong randomized hard functions and pseudo-random generators. The randomized pseudo-random generator takes as input an exponentially long random string from a public source and a polynomially long private random string and outputs an exponentially long string which looks random to any adversary circuit of exponential size. The construction is very efficient and has provable safety. As a side effect, it is shown that relative to a random oracle P/poly is not measurable in $EXP$ in the resource-bounded theoretical sense and a very strong separation between sublinear time and $AC^0$ is obtained.