Resettable Statistical Zero-Knowledge for  \(\ensuremath {\textsf{NP}}\)

Resettable statistical zero-knowledge [Garg–Ostrovsky–Visconti–Wadia, TCC 2012] is a strong privacy notion that guarantees statistical zero-knowledge even when the prover uses the same randomness in multiple proofs. In this paper, we show an equivalence of resettable statistical zero-knowledge arguments for \(\ensuremath {\textsf{NP}}\) and witness encryption schemes for \(\ensuremath {\textsf{NP}}\) . The positive result is obtained by naturally extending existing techniques (and is likely to be already well-known among experts). The negative result is our main technical contribution. To explore workarounds for the negative result, we also consider resettable security in a model where the honest party’s randomness is only reused with fixed inputs. We show that resettable statistically hiding commitment schemes are impossible even in this model.