Interactive and Noninteractive Zero Knowledge Coincide in the Help Model

We show that a problem in AM has a interactive zero-knowledge proof system if and only if it has a noninteractive zero knowledge proof system 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 result holds for both computational zero knowledge and statistical zero knowledge, and does not rely on any unproven complexity assumptions. We also show that help does not add power to interactive computational zero-knowledge proofs, paralleling a result of Ben-Or and Gutfreund for the case of statistical zero knowledge