Abstract
In this paper we state a hypothesis which is an extension of NP ≠ CoNP. We show that this new hypothesis implies the following statement: If a decision problem A is solvable by a Nondeterministic Turing Machine (NDTM) — M in polynomial time, and there is at most one computational path of M which leads to a ‘yes’ answer — then A is not NP-hard. We apply this result to Cryptography, and show that if our new hypothesis is true then a well designed cryptosystem, whose cracking problem is NP-hard, contains a large subproblem which is not NP-hard.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Brassard, G.: "A Note on the Complexity of Cryptography". IEEE Trans. on Inf. Th., Vol. IT-25, March 1979.
Shamir, A.: "On the Cryptocomplexity of Knapsack Systems". Proc. of the 11-th Annual ACM Symposium on Theory of Computing, Atlanta, Georgia, April 30–May 2, 1979.
Even, S. and Yacobi, Y.: "On the Cryptocomplexity of a Public Key System". Research Report, July 1979.
Aho, Hopcroft and Ullman: The Design and Analysis of Computer Algorithms. Addison Wesley, 1974.
Even, S.: Graph Algorithms, Computer Science Press, 1979.
Ginsburg, S.: Private communication.
Ullian, J.S.: "Partial Algorithm Problems for Context Free Languages". Information and Control, Vol. 11, 1967, pp. 80–101.
Shannon, C.E.: "Communication Theory of Secrecy Systems", Bell Systems Technical Journal, Vol. 28, October 1949, pp. 656–715.
Hellman, M.E.: "An Extension of the Shannon Theory Approach to Cryptography", IEEE Trans. on Inf. Th., Vol. IT-23, No. 3, May 1977.
Even, S. and Yacobi, Y.: "Cryptosystems which are NP-hard to break", Research Report, July 1979.
Rabin, M.O.: "Digitalized Signatures", Foundations of Secure Computation, New York Academic Press, 1978, pp. 155–168, edited by R.A. De Millo et al.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Even, S., Yacobi, Y. (1981). An observation concerning the complexity of problems with few solutions and its application to cryptography. In: Noltemeier, H. (eds) Graphtheoretic Concepts in Computer Science. WG 1980. Lecture Notes in Computer Science, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10291-4_19
Download citation
DOI: https://doi.org/10.1007/3-540-10291-4_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10291-5
Online ISBN: 978-3-540-38435-9
eBook Packages: Springer Book Archive