Lower bounds for oblivious transfer reductions

Abstract

We prove the first general and non-trivial lower bound for the number of times a 1-out-of-n Oblivious Transfer of strings of length should be invoked so as to obtain, by an information-theoretically secure reduction, a 1-out-of-N Oblivious Transfer of strings of length L. Our bound is tight in many significant cases. We also prove the first non-trivial lower bound for the number of random bits needed to implement such a reduction whenever the receiver sends no messages to the sender. This bound is also tight in many significant cases.