A generalized encryption scheme based on random graphs

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.