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On the impossibility of constructing noninteractive statisticallysecret protocols from any trapdoor oneway function
(2002)

Marc Fischlin
 We show that noninteractive statisticallysecret bit commitment cannot be constructed from arbitrary blackbox onetoone trapdoor functions and thus from general publickey cryptosystems. Reducing the problems of noninteractive cryptocomputing, rerandomizable encryption, and noninteractive statisticallysenderprivate oblivious transfer and lowcommunication private information retrieval to such commitment schemes, it follows that these primitives are neither constructible from onetoone trapdoor functions and publickey encryption in general. Furthermore, our separation sheds some light on statistical zeroknowledge proofs. There is an oracle relative to which onetoone trapdoor functions and oneway permutations exist, while the class of promise problems with statistical zeroknowledge proofs collapses in P. This indicates that nontrivial problems with statistical zeroknowledge proofs require more than (trapdoor) onewayness.