Lower Bounds for Oblivious Transfer Reductions

We prove the rst 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 signiicant cases. We also prove the rst 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 signiicant cases.