Non-interactive zero-knowledge (NIZK) systems are
fundamental cryptographic primitives used in many constructions,
including CCA2-secure cryptosystems, digital signatures, and various
cryptographic protocols. What makes them especially attractive, is
that they work equally well in a concurrent setting, which is
notoriously hard for interactive zero-knowledge protocols. However,
while for interactive zero-knowledge we know how to construct
statistical zero-knowledge argument systems for all NP languages, for
non-interactive zero-knowledge, this problem remained open since the
inception of NIZK in the late 1980's. Here we resolve two problems
regarding NIZK:
- we construct the first perfect NIZK argument system for any NP language.
- we construct the first UC-secure
NIZK protocols for any NP language in the presence
of a dynamic/adaptive adversary.

While it was already known how to construct efficient prover
computational NIZK proofs for any NP language, the known techniques
yield large common reference strings and large NIZK proofs. As an
additional implication of our techniques, we considerably reduce both the size of
the common reference string and the size of the proofs.