We demonstrate in this paper a very simple method for "hiding" large cliques in random graphs. While the largest clique in a random graph is very likely to be of size about 2log2n, it is widely conjectured that no polynomial-time algorithm exists which finds a clique of size (1 + epsilon)log2n with significant probability for any constant epsilon > 0. We show that if this conjecture is true, then when a clique of size at most (2 - delta)log2n for constant delta > 0 is randomly inserted ("hidden") in a random graph, finding a clique of size (1 + epsilon)log2n remains hard. In particular, we show that if there exists a polynomial-time algorithm which finds cliques of size (1 + epsilon)log2n in such graphs with probability 1/poly, then the same algorithm will find cliques in completely random graphs with probability 1/poly. Given the conjectured hardness of finding large cliques in random graphs, we therefore show that hidden cliques may be used as cryptographic keys.
Title
Hidden Cliques as Cryptographic Keys
Published
1996-08-22
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
CSD-96-912
Type
Text
Extent
8 p
Archive
The Engineering Library
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