Abstract
A probabilistic encryption scheme is generalized in such a way that an encryption is sometimes ambiguous (the same object might be an encryption of both 0 and 1), but a probability of this event is very low. Such a generalization is sufficient for a large number of applications.
An implementation of the scheme presented in the paper is based on random graphs. From the point of view of the worst-case complexity, the problem of decrypting is provable NP-complete, while classical encryption schemes use always problems from NPP∩coNPP (and most graph problems of this class are either easily solvable or related to linear programming, which makes it possible to use the ellipsoidal method to break such a scheme). However, it is not known whether there are polynomial time deterministic or probabilistic decoding algorithms with probability of success bounded away form 1/2. It is shown that some obvious polynomial time attacks are too weak to break the scheme with sufficiently large probability.
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References
Babai,L.,Kučera,L.,Canonical labelling of graphs in linear average time, 20th Annual Symposium on Foundations of Computer Science, Puerto Rico 1979, 39–46
Bollobás B., Random Graphs, Academic Press, London 1985.
Even, S. and Yakobi, Y., Cryptocomplexity and N P-completeness, In Proc. 8th Colloq. on Automata, Languages, and Programming, Lecture Notes in Computer Science, 195–207, Springer Verlag, Berlin, 1980.
Goldwasser,S., Micali,S., Rackoff,C., The knowledge complexity of interactive proofs, 17th Annual Symposium on Foundations of Computer Science, Providence, RI, 1985,291–305.
Levin, L., Average case complete problems, SIAM J. Computing, 15 (1986), 285–286.
Levin,L., personal communication.
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© 1992 Springer-Verlag Berlin Heidelberg
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Kučera, L. (1992). A generalized encryption scheme based on random graphs. In: Schmidt, G., Berghammer, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 1991. Lecture Notes in Computer Science, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55121-2_17
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DOI: https://doi.org/10.1007/3-540-55121-2_17
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