Hashing Functions can Simplify Zero-Knowledge Protocol Design (too)
In Crypto93, Damgård showed that any constant-round protocol in which the verifier sends only independent, random bits and which is zero-knowledge against the honest verifier can be transformed into a protocol (for the same problem) that is zero-knowledge in general. His transformation was based on the interactive hashing technique of Naor, Ostrovsky, Venkatesan and Yung, and thus the resulting protocol had very large round-complexity.
We adopt Damgård's methods, using ordinary hashing functions, instead of the abovementioned interactive hashing technique. Typically, the protocols we derive have much lower round-complexity than those derived by Damgård's transformation. As in Damgård's transformation, our transformation preserves statistical/perfect zero-knowledge and does not rely on any computational assumptions. However, unlike Damgård's transformation, the new transformation is not applicable to argument systems or to proofs of knowledge.