Abstract We give an efficient deterministic algorithm which ex-tracts \Omega (n2g) almost-random bits from sources where n 12 +g of the n bits are uniformly random and the rest are fixed inadvance. This improves on previous constructions which required that at least n=2 of the bits be random. Our construc-tion also gives explicit adaptive exposure-resilient functions and in turn adaptive all-or-nothing transforms. For sourceswhere instead of bits the values are chosen from [d], ford? 2, we give an algorithm which extracts a constant frac-tion of the randomness. We also give bounds on extractin
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