Abstract

We demonstrate how a well studied combinatorial optimization problem may be introduced as a new cryptographic function. The problem in question is that of finding a "large" clique in a random graph. While the largest clique in a random graph is very likely to be of size about 2 log 2 n, it is widely conjectured that no polynomial-time algorithm exists which finds a clique of size (1 + ffl) log 2 n with significant probability for any constant ffl ? 0. We present a very simple method of exploiting this conjecture by "hiding" large cliques in random graphs. In particular, we show that if the conjecture is true, then when a large clique -- of size, say, (1+2ffl) log 2 n -- is randomly inserted ("hidden") in a random graph, finding a clique of size (1 + ffl) log 2 n remains hard. Our result suggests several cryptographic applications, such as a simple one-way function. 1 Introduction Many hard graph problems involve finding a subgraph of an input graph G = (V; E) with a certain propert...

Citations