Learning to Impersonate

Abstract

Consider Alice and Bob, who have some shared secret which helps Alice to identify Bob-impersonators, and Eve, who does not know their secret. Eve wants to impersonate Bob and "fool" Alice. If Eve is computationally unbounded, how long does she need to observe Bob before she can impersonate him? What is a good strategy for Eve? If (cryptographic) one-way functions exist, an efficient Eve cannot impersonate even very simple Bobs, but if they do not exist, can Eve learn to impersonate any efficient Bob?We formalize these questions in a new computational learning model, which we believe captures a wide variety of natural learning tasks, and tightly bound the number of observations Eve makes in terms of the secret's entropy. We then show that if one-way functions do not exist, then an efficient Eve can learn to impersonate any efficient Bob nearly as well as an unbounded Eve. For the full version of this work see (Naor & Rothblum, 2006).