Gate Elimination for Linear Functions and New Feebly Secure Constructions

Abstract. We consider gate elimination for linear functions and show two general forms of gate elimination that yield novel corollaries. Using these corollaries, we construct a new linear feebly secure trapdoor function that has order of security 5 which exceeds the previous record 4 for linear constructions. We also give detailed proofs for nonconstructive circuit complexity bounds on linear functions