Universal SNARK ⇒ SNARK

Fully-black-box reduction · standard model · folklore · security loss: none: the adversary and its advantage are unchanged

Statement

A universal SNARK yields a preprocessing SNARK: ${\mathsf{Setup}}^{\prime }(1^{\lambda },C)$ runs $\mathsf{Setup}(1^{\lambda },|C|)$ and outputs the resulting $\mathsf{srs}$ together with the keys of $C$ derived from it, and proving and verification use the derived keys. Completeness, knowledge soundness and succinctness for $C$ are those of the universal scheme with $C$‘s derived keys: an adversary against the per-circuit scheme is one against the universal scheme for the fixed circuit $C$, with the same advantage and the same extractor — folklore.