Abstract
Even, Selman, and Yacobi [ESY84, SY82] formulated a conjecture that in current terminology asserts that there do not exist disjoint NP-pairs all of whose separators are NP-hard viaTuring reductions. In this paper we consider a variant of this conjecture—there do not exist disjoint NP-pairs all of whose separators are NP-hard via bounded-truth-table reductions. We provide evidence for this conjecture. We also observe that if the original conjecture holds, then some of the known probabilistic public-key cryptosystems are not NP-hard to crack.
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.
Similar content being viewed by others
References
Ajtai, M., Dwork, C.: A public-key cryptosystem with worst-case/average-case equivalence. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, STOC 1997, pp. 284–293. ACM, New York (1997)
Agrawal, M.: Pseudo-random generators and structure of complete degrees. In: 17th Annual IEEE Conference on Computational Complexity, pp. 139–145 (2002)
Adleman, L., Manders, K.: Reducibility, randomness, and intractability. In: Proc. 9th ACM Symp. Theory of Computing, pp. 151–163 (1977)
Ambos-Spies, K., Bentzien, L.: Separating NP-completeness under strong hypotheses. Journal of Computer and System Sciences 61(3), 335–361 (2000)
Ambos-Spies, K., Fleischhack, H., Huwig, H.: Diagonalizations over polynomial time computable sets. Theoretical Computer Science 51, 177–204 (1987)
Ambos-Spies, K., Neis, H., Terwijn, A.: Genericity and measure for exponential time. Theoretical Computer Science 168(1), 3–19 (1996)
Ambos-Spies, K., Terwijn, A., Zheng, X.: Resource bounded randomness and weakly complete problems. Theoretical Computer Science 172(1), 195–207 (1997)
Buhrman, H., Hescott, B., Homer, S., Torenvliet, L.: Non-uniform reductions. Theory of Computing Systems 47(2), 317–241 (2010)
Balcazar, J., Mayordomo, E.: A note on genericty and bi-immunity. In: Proceedings of the Tenth Annual IEEE Conference on Computational Complexity, pp. 193–196 (1995)
Even, S., Selman, A., Yacobi, Y.: The complexity of promise problems with applications to public-key cryptography. Information and Control 61(2), 159–173 (1984)
Fortnow, L.: Personal Communication
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC 2009, pp. 169–178 (2009)
Gu, X., Hitchcock, J., Pavan, A.: Collapsing and separating completeness notions under average-case and worst-case hypotheses. In: STACS 2010. LIPIcs, vol. 5, pp. 429–440. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2010)
Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comp. System Sci. 28, 270–299 (1984)
Goldreich, O.: On Promise Problems: A Survey. In: Goldreich, O., Rosenberg, A.L., Selman, A.L. (eds.) Shimon Even Festchrift. LNCS, vol. 3895, pp. 254–290. Springer, Heidelberg (2006)
Grollmann, J., Selman, A.: Complexity measures for public-key cryptosystems. SIAM Journal on Computing 17(2), 309–355 (1988)
Glaßer, C., Selman, A., Sengupta, S., Zhang, L.: Disjoint NP-pairs. SIAM J. Comput. 33(6), 1369–1416 (2004)
Glaßer, C., Selman, A., Zhang, L.: Canonical disjoint NP-pairs of propositional proof systems. Theoretical Computer Science 370(1), 60–73 (2007)
Hitchcock, J., Pavan, A.: Comparing reductions to NP-complete sets. Information and Computation 205(5), 694–706 (2007); In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 465–476. Springer, Heidelberg (2006)
Lutz, J.H., Mayordomo, E.: Cook versus Karp-Levin: Separating completeness notions if NP is not small. Theoretical Computer Science 164, 141–163 (1996)
Nguyên, P.Q., Stern, J.: Cryptanalysis of the Ajtai-Dwork Cryptosystem. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 223–242. Springer, Heidelberg (1998)
Pavan, A., Selman, A.: Separation of NP-completeness notions. SIAM Journal on Computing 31(3), 906–918 (2002)
Pavan, A., Selman, A.: Bi-immunity separates strong NP-completeness notions. Information and Computation 188, 116–126 (2004)
Pudlak, P.: On reducibility and symmetry of disjoint NP-pairs. In: Electronic Colloquium on Computational Complexity, technical reports (2001)
Razborov, A.: On provably disjoint NP pairs. Technical Report 94-006, ECCC (1994)
Schoenfield, J.: Degrees of models. Journal of Symbolic Logic 25, 233–237 (1960)
Selman, A., Yacobi, Y.: The Complexity of Promise Problems. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 502–509. Springer, Heidelberg (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hughes, A., Pavan, A., Russell, N., Selman, A. (2012). A Thirty Year Old Conjecture about Promise Problems. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_40
Download citation
DOI: https://doi.org/10.1007/978-3-642-31594-7_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31593-0
Online ISBN: 978-3-642-31594-7
eBook Packages: Computer ScienceComputer Science (R0)