Abstract
This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of non-interactive quantum perfect and statistical zero-knowledge. It is also shown that, with sharing EPR pairs a priori, the complexity class resulting from non-interactive quantum perfect zero-knowledge proof systems of perfect completeness has a natural complete promise problem. Using our complete promise problem, the Graph Non-Automorphism problem is shown to have a non-interactive quantum perfect zero-knowledge proof system.
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References
Blum, M., De Santis, A., Micali, S., Persiano, G.: Non-interactive zero-knowledge. SIAM Journal on Computing 20(6), 1084–1118 (1991)
Blum, M., Feldman, P., Mical, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 103–112 (1988)
De Santis, A., Di Crescenzo, G., Persiano, G., Yung, M.: Image density is complete for non-interactive-SZK (extended abstract). In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 784–795. Springer, Heidelberg (1998)
De Santis, A., Micali, S., Persiano, G.: Non-interactive zero-knowledge proof systems. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 52–72. Springer, Heidelberg (1987)
De Santis, A., Micali, S., Persiano, G.: Non-interactive zero-knowledge with preprocessing. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 269–282. Springer, Heidelberg (1988)
Even, S., Selman, A.L., Yacobi, Y.: The complexity of promise problems with applications to public-key cryptography. Information and Control 61(2), 159–173 (1984)
Goldreich, O., Oren, Y.: Definitions and properties of zero-knowledge proof systems. Journal of Cryptology 7(1), 1–32 (1994)
Goldreich, O., Sahai, A., Vadhan, S.P.: Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pp. 399–408 (1998)
Goldreich, O., Sahai, A., Vadhan, S.P.: Can statistical zero knowledge be made non-interactive? or on the relationship of SZK and NISZK. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 467–484. Springer, Heidelberg (1999)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM Journal on Computing 18(1), 186–208 (1989)
van de Graaf, J.: Towards a formal definition of security for quantum protocols. PhD thesis, Département d’Informatique et de Recherche Opérationnelle, Université de Montréal (December 1997)
Gruska, J.D.: Quantum Computing. McGraw-Hill, New York (1999)
Hughston, L.P., Jozsa, R.O., Wootters, W.K.: A complete classification of quantum ensembles having a given density matrix. Physics Letters A 183, 14–18 (1993)
Kilian, J., Petrank, E.: An efficient noninteractive zero-knowledge proof system for NP with general assumptions. Journal of Cryptology 11(1), 1–27 (1998)
Kitaev, A.Y., Shen, A.H., Vyalyi, M.N.: Classical and Quantum Computation. Graduate Studies in Mathematics, vol. 47. American Mathematical Society, Providence (2002)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Sahai, A., Vadhan, S.P.: A complete problem for statistical zero knowledge. Journal of the ACM 50(2), 196–249 (2003)
Uhlmann, A.: Parallel transport and “quantum holonomy” along density operators. Reports on Mathematical Physics 24, 229–240 (1986)
Vadhan, S.P.: A Study of Statistical Zero-Knowledge Proofs. PhD thesis, Department of Mathematics, Massachusetts Institute of Technology (August 1999)
Watrous, J.H.: Succinct quantum proofs for properties of finite groups. In: 41st Annual Symposium on Foundations of Computer Science, pp. 537–546 (2000)
Watrous, J.H.: Limits on the power of quantum statistical zero-knowledge. In: 43rd Annual Symposium on Foundations of Computer Science, pp. 459–468 (2002)
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Kobayashi, H. (2003). Non-interactive Quantum Perfect and Statistical Zero-Knowledge. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_20
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DOI: https://doi.org/10.1007/978-3-540-24587-2_20
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