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The representation problem based on factoring
(2002)

Marc Fischlin
Roger Fischlin
 We review the representation problem based on factoring and show that this problem gives rise to alternative solutions to a lot of cryptographic protocols in the literature. And, while the solutions so far usually either rely on the RSA problem or the intractability of factoring integers of a special form (e.g., Blum integers), the solutions here work with the most general factoring assumption. Protocols we discuss include identification schemes secure against parallel attacks, secure signatures, blind signatures and (nonmalleable) commitments.

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.