Abstract
A (t, n)-locally random reduction maps a problem instancex into a set of problem instancesy 1,...,y n in such a way that it is easy to construct the answer tox from the answers toy 1,...,y n, and yet the distribution ont-element subsets ofy 1,...,y n depends only on |x|. In this paper we formalize such reductions and give improved methods for achieving them. Then we give a cryptographic application, showing a new way to prove in perfect zero knowledge that committed bitsx 1,...,x m satisfy some predicateQ. Unlike previous techniques for such perfect zero-knowledge proofs, ours uses an amount of communication that is bounded by a fixed polynomial inm, regardless of the computational complexity ofQ.
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