Non-Interactive Zero-Knowledge with Preprocessing
Non-Interactive Zero-Knowledge Proof Systems have been proven to exist under a specific complexity assumption; namely, under the Quadratic Residuosity Assumption which gives rise to a specific secure probabilistic encryption scheme.
In this paper we prove that the existence of any secure probabilistic encryption scheme, actually any one-way encryption scheme, is enough for Non-Interactive Zero-Knowledge in a modified model. That is, we show that the ability to prove a randomly chosen theorem allows to subsequently prove non-interactively and in Zero-Knowledge any smaller size theorem whose proof is discovered.
KeywordsEncryption Scheme Proof System Language Versus Truth Assignment Random String
- [BGGHKMR]M. Ben-Or, O. Goldreich, S. Goldwasser, J. Hastad, J. Kilian, S. Micali, and P. Rogaway, Everything Provable is Provable in Zero-Knowledge, CRYPTO 88.Google Scholar
- [BlFeMi]M. Blum, P. Feldman, and S. Micali, Non-Interactive Zero-Knowledge Proof Systems and Applications, Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, 1988, pp. 103–112.Google Scholar
- [DeMiPe]A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero-Knowledge Proof Systems, in “Advances in Cryptology-CRYPTO 87 Proceedings”, pp. 52–72, vol. 293 of “Lecture Notes in Computer Science”, Springer Verlag.Google Scholar
- [GoMiRa]S. Goldwasser, S. Micali, and C. Rackoff, The Knowledge Complexity of Interactive Proof-Systems, Proceedings of the 17th Annual ACM Symposium on Theory of Computing, Providence, RI, May 1985, pp. 291–304.Google Scholar
- [GoMiWi]O. Goldreich, S. Micali, and A. Wigderson, Proofs that yield nothing but their validity and a methodology of cryptographic protocol design, Proceedings of the 27th Annual Symposium on Foundations of Computer Science, October 1986, pp. 174–187.Google Scholar
- [Ya]A. C. Yao, Theory and Applications of Trapdoor Functions, Proceedings of the 23rd IEEE Symposium on Foundation of Computer Science, 1982, pp. 80–91.Google Scholar