We show that the security of some well-known cryptographic protocols, primitives and assumptions (e.g., the Schnorr identification scheme, commitments secure under adaptive selectivedecommitment, the "one-more" discrete logarithm assumption) cannot be based on any standard assumption using a Turing (i.e., black-box) reduction. These results follow from a general result showing that Turing reductions cannot be used to prove security of constant-round sequentially witness-hiding special-sound protocols for unique witness relations, based on standard assumptions; we emphasize that this result holds even if the protocol makes non-black-box use of the underlying assumption.
In STOC '11, Pass REF presented a broad separation result showing that the security of constant-round, public-coin, (generalized) computational special-sound arguments for unique witness relations cannot be based on any standard assumption.
Limits of provable security from standard assumptions
STOC '11
Computer Science