A noninteractive proof may be viewed as a variation of an interactive proof [3], with two differences. Firstly, the interaction between the prover and the verifier is limited to the exchange of a single message, which is sent by the prover to the verifier. Secondly, both the prover and verifier are given access to a uniformly random bit string, referred to as the common reference string. Intuitively, the common reference string provides a way to challenge the prover (even though the verifier is not allowed to send any message to the prover).
A noninteractive zero-knowledge proof, as introduced in [1, 2], is a noninteractive proof satisfying the zero-knowledge property. In this case, the zeroknowledge property holds if it is possible to efficiently generate both the common reference string and a (valid) noninteractive zero-knowledge proof.
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References
Blum, M., A. De Santis, S. Micali, and G. Persiano (1991). “Non-interactive zero-knowledge proof systems.” SIAM Journal on Computing, 20 (6), 1084–1118.
Blum, M., P. Feldman, and S. Micali (1988). “Non-interactive zero-knowledge and its applications.” Proceedings of the 20th ACM Symposium on the Theory of Computing, 103–112.
Goldreich, O. (2001). Foundations of Cryptography—Basic Tools. Cambridge University Press, Cambridge
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Schoenmakers, B. (2005). Noninteractive Proof. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_273
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