In a paper by Raphael Pass, he writes (page 162):... most natural problems that we believe are hard on average for polynomial  time are also believed hard for quasi-polynomial time.In another post by Turkistany, he mentioned that the log-CLIQUE problem is solvable in quasi-polynomial time.What are some other natural problems which we believe are hard on average for polynomial time, but can be decided/solved in quasi-polynomial time?
Hard-on-Average, Quasi-Polynomial-Time Problems
cc.complexity theory;average case complexity