In this paper, we construct a 6-round simultaneously resettable sound resettable \((T, \epsilon )\) -zero knowledge protocol for \(\mathsf {NP \cap coNP}\) in the Public Key model under standard assumptions, comparing with the 27-round simultaneously resettable zero knowledge protocol in the BPK model by Deng et al. in 2011, we have achieved a significant reduction in the round complexity. Our model assumes that both prover and verifier hold public keys, we call it the Public Key model. It is a variation of the traditional BPK model where only the verifier is assumed to hold public keys. In the original BPK model, under the sub-exponential hardness assumption of factoring, we construct a 2-round simultaneously resettable sound resettable \((T,\epsilon )\) -zero knowledge protocol for \(\textsf{NP}\) .
