A Note on Constant-Round Zero-Knowledge Proofs of Knowledge

In this note, we show the existence of constant-round computational zero-knowledge proofs of knowledge for all $\mathcal {NP}$. The existence of constant-round zero-knowledge proofs was proven by Goldreich and Kahan (Journal of Cryptology, 1996), and the existence of constant-round zero-knowledge arguments of knowledge was proven by Feige and Shamir (CRYPTO, 1989). However, the existence of constant-round zero-knowledge proofs of knowledge for all $\mathcal {NP}$ is folklore, to the best of our knowledge, since no proof of this fact has been published.

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