The problem is easy when one of the inputs is even probability of the event34 and is hence non negligible thus there is a nonnegligible fraction of the inputs for which fx is easy to invert these functions are not captured by our rather restrict ID: 12108
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1 One-way FunctionsDebdeep MukhopadhyayIIT Kharagpur Informally, easy to computef can be inverted only with a negligible 2 Strong One-way {0,1}A function f:{0,1}{0,1} is (t,)-one way if f is computable in poly(n) time and for all adversaries A running in time bounded by t(n):Pr[(())(())]()Afxffxn Consider the problem of finding non-trivial factors.The problem is easy when one of the probability of the event=3/4 and is hence non-negligible.thus there is a non-negligible fraction of the these functions are not captured by our rather 5 The first step x{0,1}Suppose there is a PPT algorithm A:Pr[(())(())]'(),Pr[{0,1};((...))((...))]Thus A takes ... as input and outputs ..., such that () for aimmAgxggxpmnorxAgxxggxxyyzzfzyââ> ll with probability� : To construct A' that uses A to invert with probability 1- (that is violate the weakone-wayness of )Goalf Adversary A A' repeats the following procedure 2() times:Procedure IFor i=1 to m let y for all ji, pick x{0,1} and let y() let z...(...) if f(z), output z elsnmpn f zAyyâ ==e output fail