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Relations between OWFs, PRGs and PRFs (revised) Jan-Erik Ekberg February 19, 2002 1 Introdu tion These le ture notes intend to give an overview of the provable relations between one-way fun tions (OWFs), pseudorandom generators (PRGs) and pseudorandom fun tions (PRFs). Only a sele ted number of proofs and redu tions are thoroughly presented in this paper (most are left to the referen es), but the sele tion hopefully gives the reader some notion of the way the random ora le model an be used for proving theorems. The reader should be warned that the onstru ts throughout the paper are based on fun tion ensembles (de nition later) in spite of the notation whi h is the same as is use for fun tions. In the few ases fun tions are onstru ted as parts of proofs the distin tion should be evident from the setting.