On the security of pseudorandomized information-theoretically secure schemes

In this paper, we discuss a naive method of randomness reduction for cryptographic schemes, which replaces the required perfect randomness with output distribution of a computationally secure pseudorandom generator (PRG). We propose novel ideas and techniques for evaluating the indistinguishability between the random and pseudorandom cases, even against an adversary with computationally unbounded attack algorithm. Hence, the PRG-based randomness reduction can be effective even for information-theoretically secure cryptographic schemes, especially when the amount of information received by the adversary is small. In comparison to a preceding result of Dubrov and Ishai (STOC 2006), our result removes the requirement of generalized notion of 'nb-PRGs' and is effective for more general kinds of protocols. We give some numerical examples to show the effectiveness of our result in practical situations, and we also propose a further idea for improving the effect of the PRG-based randomness reduction.