How to Generate Cryptographically Strong Sequences of Pseudorandom Bits

We give a set of conditions that allow one to generate 50–50 unpredictable bits.Based on those conditions, we present a general algorithmic scheme for constructing polynomial-time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo-random bits. We give an implementation of our scheme and exhibit a pseudo-random bit generator for which any efficient strategy for predicting the next output bit with better than 50–50 chance is easily transformable to an “equally efficient” algorithm for solving the discrete logarithm problem. In particular: if the discrete logarithm problem cannot be solved in probabilistic polynomial time, no probabilistic polynomial-time algorithm can guess the next output bit better than by flipping a coin: if “head” guess “0”, if “tail” guess “1”

• SIAM Journal on Computing
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