Abstract
The notion of Zero Knowledge introduced by Goldwasser, Micali and Rackoff in STOC 1985 is fundamental in Cryptography. Motivated by conceptual and practical reasons, this notion has been explored under stronger definitions. We will consider the following two main strengthened notions.
Statistical Zero Knowledge: here the zero-knowledge property will last forever, even in case in future the adversary will have unlimited power.
Concurrent Non-Malleable Zero Knowledge: here the zeroknowledge property is combined with non-transferability and the adversary fails in mounting a concurrent man-in-the-middle attack aiming at transferring zero-knowledge proofs/arguments.
Besides the well-known importance of both notions, it is still unknown whether one can design a zero-knowledge protocol that satisfies both notions simultaneously.
In this work we shed light on this question in a very strong sense. We show a statistical concurrent non-malleable zero-knowledge argument system for \(\mathcal{NP}\) with a black-box simulator-extractor.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Barak, B., Prabhakaran, M., Sahai, A.: Concurrent non-malleable zero knowledge. In: FOCS, p. 345 (2006); full version available on eprint arhive
Bellare, M., Micali, S., Ostrovsky, R.: The (true) complexity of statistical zero knowledge. In: STOC, pp. 494–502 (1990)
Catalano, D., Visconti, I.: Hybrid trapdoor commitments and their applications. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 298–310. Springer, Heidelberg (2005)
Catalano, D., Visconti, I.: Hybrid commitments and their applications to zero-knowledge proof systems. Theor. Comput. Sci. 374(1-3), 229–260 (2007)
Damgård, I., Groth, J.: Non-interactive and reusable non-malleable commitment schemes. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, San Diego, CA, USA, June 9-11, pp. 426–437. ACM (2003)
Damgård, I., Nielsen, J.B.: Perfect hiding and perfect binding universally composable commitment schemes with constant expansion factor. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 581–596. Springer, Heidelberg (2002)
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: STOC, pp. 542–552 (1991)
Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000); preliminary version in STOC 1991
Goldreich, O., Sahai, A., Vadhan, S.P.: Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge. In: STOC, pp. 399–408 (1998)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. In: Proc. 17th STOC, pp. 291–304 (1985)
Goyal, V., Lin, H., Pandey, O., Pass, R., Sahai, A.: Round-efficient concurrently composable secure computation via a robust extraction lemma. IACR Cryptology ePrint Archive 2012, 652 (2012)
Goyal, V., Moriarty, R., Ostrovsky, R., Sahai, A.: Concurrent statistical zero-knowledge arguments for np from one way functions. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 444–459. Springer, Heidelberg (2007)
Haitner, I., Nguyen, M.H., Ong, S.J., Reingold, O., Vadhan, S.P.: Statistically hiding commitments and statistical zero-knowledge arguments from any one-way function. SIAM J. Comput. 39(3), 1153–1218 (2009)
Halevi, S., Micali, S.: Practical and provably-secure commitment schemes from collision-free hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 201–215. Springer, Heidelberg (1996)
Lin, H., Pass, R.: Non-malleability amplification. In: STOC, pp. 189–198 (2009)
Lin, H., Pass, R.: Concurrent non-malleable zero knowledge with adaptive inputs. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 274–292. Springer, Heidelberg (2011)
Lin, H., Pass, R., Tseng, W.-L.D., Venkitasubramaniam, M.: Concurrent non-malleable zero knowledge proofs. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 429–446. Springer, Heidelberg (2010)
Lin, H., Pass, R., Venkitasubramaniam, M.: Concurrent non-malleable commitments from any one-way function. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 571–588. Springer, Heidelberg (2008)
Mahmoody, M., Xiao, D.: Languages with efficient zero-knowledge pcps are in szk. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 297–314. Springer, Heidelberg (2013)
Micciancio, D., Ong, S.J., Sahai, A., Vadhan, S.: Concurrent zero knowledge without complexity assumptions. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 1–20. Springer, Heidelberg (2006)
Okamoto, T.: On relationships between statistical zero-knowledge proofs. J. Comput. Syst. Sci. 60(1), 47–108 (2000)
Ostrovsky, R., Pandey, O., Visconti, I.: Efficiency preserving transformations for concurrent non-malleable zero knowledge. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 535–552. Springer, Heidelberg (2010)
Ostrovsky, R., Persiano, G., Visconti, I.: Constant-round concurrent non-malleable zero knowledge in the bare public-key model. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 548–559. Springer, Heidelberg (2008)
Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: Proc. 43rd FOCS (2002)
Sahai, A., Vadhan, S.P.: A complete problem for statistical zero knowledge. J. ACM 50(2), 196–249 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 International Association for Cryptologic Research
About this paper
Cite this paper
Orlandi, C., Ostrovsky, R., Rao, V., Sahai, A., Visconti, I. (2014). Statistical Concurrent Non-malleable Zero Knowledge. In: Lindell, Y. (eds) Theory of Cryptography. TCC 2014. Lecture Notes in Computer Science, vol 8349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54242-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-54242-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54241-1
Online ISBN: 978-3-642-54242-8
eBook Packages: Computer ScienceComputer Science (R0)