Interactive And Noninteractive Zero Knowledge Are Equivalent In The Help Model

We show that interactive and noninteractive zero-knowledge are equivalent in the 'help model' of Ben-Or and Gutfreund (J. Cryptology, 2003). In this model, the shared reference string is generated by a probabilistic polynomial-time dealer who is given access to the statement to be proven. Our results do not rely on any unproven complexity assumptions and hold for statistical zero knowledge, for computational zero knowledge restricted to AM, and for quantum zero knowledge when the help is a pure quantum state.