On generic complexity of the quadratic residuosity problem

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. Many classical undecidable or hard algorithmic problems become feasible in the generic case. But there are generically hard problems. For example, this is the classical discrete logarithm problem. In this talk, we consider generic complexity of the quadratic residuosity problem. We fit this problem in the frameworks of generic complexity and prove that its natural subproblem is generically hard provided that the quadratic residuosity problem is hard in the worst case.