  We study the role of help in Non-Interactive Zero-Knowledge protocols and its
relation to the standard interactive model. In the classical case, we show that
help and interaction are equivalent, answering an open question of Ben-Or and
Gutfreund. This implies a new complete problem for the class SZK, the Image
Intersection Density. For this problem, we also prove a polarization lemma
which is stronger than the previously known one.
  In the quantum setting, we define the notion of quantum help and show in a
more direct way that help and interaction are again equivalent. Moreover, we
define quantum Non-Interactive Zero-Knowledge with classical help and prove
that it is equal to the class of languages that have classical honest-Verifier
Zero Knowledge protocols secure against quantum Verifiers. Last, we provide new
complete problems for all these quantum classes.
  Similar results were independently discovered by Dragos Florin Ciocan and
Salil Vadhan.
