An Improved Lower Bound on Oblivious Transfer Capacity Using Polarization and Interaction

TL;DR

This paper introduces novel methods using polarization and interaction to improve lower bounds on the oblivious transfer capacity of binary symmetric channels, surpassing previous bounds for certain crossover probabilities.

Contribution

It presents new OT construction techniques employing polarization and interaction, extending emulation to non-BSEC GECs and enhancing lower bounds on BSC OT capacity.

Findings

New lower bounds surpass previous ones for certain crossover probabilities

At zero crossover probability, the OT capacity slope is unbounded

Methods leverage polarization and interactive communication for GEC emulation

Abstract

We consider the oblivious transfer (OT) capacities of noisy channels against the passive adversary; this problem has not been solved even for the binary symmetric channel (BSC). In the literature, the general construction of OT has been known only for generalized erasure channels (GECs); for the BSC, we convert the channel to the binary symmetric erasure channel (BSEC), which is a special instance of the GEC, via alphabet extension and erasure emulation. In a previous paper by the authors, we derived an improved lower bound on the OT capacity of BSC by proposing a method to recursively emulate BSEC via interactive communication. In this paper, we introduce two new ideas of OT construction: (i) via ``polarization" and interactive communication, we recursively emulate GECs that are not necessarily a BSEC; (ii) in addition to the GEC emulation part, we also utilize interactive communication in the key agreement part of OT protocol. By these methods, we derive lower bounds on the OT capacity of BSC that are superior to the previous one for a certain range of crossover probabilities of the BSC. Via our new lower bound, we show that, at the crossover probability being zero, the slope of tangent of the OT capacity is unbounded.