Abstract
We consider the problem of constructing round-efficient public-coin argument systems, that is, interactive proof systems that are only computationally sound with a constant number of rounds. We focus on argument systems for NTime (T(n)) where either the communication complexity or the verifier’s running time is subpolynomial in T(n), such as Kilian’s argument system for NP [Kil92] and universal arguments [BG02,Mic00]. We begin with the observation that under standard complexity assumptions, such argument systems require at least 2 rounds. Next, we relate the existence of non-trivial 2-round argument systems to that of hard-on-average search problems in NP and that of efficient public-coin zero-knowledge arguments for NP. Finally, we show that the Fiat-Shamir paradigm [FS86] and Babai-Moran round reduction [BM88] fails to preserve computational soundness for some 3-round and 4-round argument systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barak, B.: How to go beyond the black-box simulation barrier. In: Proc. 42nd FOCS (2001)
Barak, B.: Non-Black-Box Techniques in Cryptography. Ph.D., Weizmann Institute of Science (January 2004)
Brassard, G., Chaum, D., Crépeau, C.: Minimum disclosure proofs of knowledge. JCSS 37(2), 156–189 (1988)
Barak, B., Goldreich, O.: Universal arguments and their applications. In: Proc. CCC 2002 (2002)
Bellare, M., Impagliazzo, R., Naor, M.: Does parallel repetition lower the error in computationally sound protocols? In: Proc. 38th FOCS (1997)
Barak, B., Lindell, Y., Vadhan, S.: Lower bounds for non-black-box zero knowledge. Cryptology ePrint Archive, Report 2004/226 (2004), Extended abstract in Proc. 44th FOCS (2003)
Babai, L., Moran, S.: Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class. JCSS 36(2), 254–276 (1988)
Barak, B., Pass, R.: On the possibility of one-message weak zero-knowledge. In: Proc. 1st TCC (2004)
Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. In: Proc. 30th STOC (1998)
Dwork, C., Langberg, M., Naor, M., Nissim, K., Reingold, O.: Succint proofs for NP and spooky interactions (2004) (manuscript)
Dwork, C., Naor, M.: Zaps and their applications. In: Proc. 41st FOCS (2000)
Dwork, C., Naor, M., Reingold, O., Stockmeyer, L.: Magic functions. JACM 50(6), 852–921 (2003)
Feige, U., Lapidot, D., Shamir, A.: Multiple noninteractive zero knowledge proofs under general assumptions. SICOMP 29(1), 1–28 (1999)
Fortnow, L.: The complexity of perfect zero-knowledge. Advances in Computing Research 5, 429–442 (1989)
Fiat, A., Shamir, A.: How to prove to yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Goldreich, O., Håstad, J.: On the complexity of interactive proofs with bounded communication. IPL 67(4), 205–214 (1998)
Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: Proc. 44th FOCS (2003)
Goldreich, O., Oren, Y.: Definitions and properties of zero-knowledge proof systems. J. Cryptology 7(1), 1–32 (1994)
Goldreich, O.: Foundations of Cryptography: Basic Tools. Cambridge University Press, Cambridge (2001)
Gennaro, R., Trevisan, L.: Lower bounds on efficiency of generic cryptographic constructions. In: Proc. 41st FOCS (2000)
Kilian, J.: A note on efficient zero-knowledge proofs and arguments. In: Proc. 24th STOC (1992)
Kilian, J., Petrank, E.: An efficient noninteractive zero-knowledge proof system for NP with general assumptions. J. Cryptology 11(1), 1–27 (1998)
Micali, S.: Computationally sound proofs. SICOMP 30(4), 1253–1298 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wee, H. (2005). On Round-Efficient Argument Systems. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_12
Download citation
DOI: https://doi.org/10.1007/11523468_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27580-0
Online ISBN: 978-3-540-31691-6
eBook Packages: Computer ScienceComputer Science (R0)