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While the reliable use of some NP-complete problem in tandem with theassumption that P is not equal to NP has eluded cryptographers due to lack ofresults showing average-case hardness, one alternative which has been exploredis reliance on assumptions that solving certain NP-hard optimization problemswithin some degree of accuracy is computationally difficult in specificinstance classes. In this work, we explore one such example of this effortwhich attempts to provide cryptographic primitives by relying on the plantedclique conjecture. More specifically, we (1) present this construction insummary, (2) propose a simple cryptanalytic method using only approximationalgorithms, and (3) consider the feasibility of such cryptanalysis in thecontext of existing approximation algorithms for the maximum clique problem. Weultimately find that recent advances in the area of combinatoric approximationalgorithms fatally hinders the prospect of any serious application of existingcandidate constructions based upon the planted clique conjecture.

On the Cryptanalysis via Approximation of Cryptographic Primitives Relying on the Planted Clique Conjecture