On the Oblivious Transfer Capacity of the Erasure Channel

One of the most important primitives in two-party distrustful cryptography is oblivious transfer, a complete primitive for two-party computation. Recently introduced, the oblivious transfer capacity of a noisy channel measures an efficiency of information theoretical reductions from 1-out-of-k, l-string oblivious transfer to noisy channels. It is defined as the maximal achievable ratio l/n, where l is the length of the strings which are to be transferred and n is the number of times the noisy channel is invoked. This quantity is unknown in a general case. For discrete memoryless channels, it is known to be non-negligible for honest-but-curious players, but the non-zero rates have not ever been proved achievable in the case of malicious players. Here, we show that in the particular case of the erasure channel, more precise answers can be obtained. We compute the OT capacity of the erasure channel for the case of honest-but-curious players and, for the fully malicious players, we give its lower bound