Generalized Oblivious Transfer Protocols Based on Noisy Channels

Abstract

The main cryptographic primitives (Bit Commitment (BC) and Oblivious Transfer (OT) protocols) based on noisy channels have been considered in [1] for asymptotic case. Non-asymptotic behavior of BC protocol has been demonstrated in [2]. The current paper provides stricter asymptotic conditions on Binary Symmetric Channel (BSC) to be feasible OT protocol proposed in [1]. We also generalize this protocol using different encoding and decoding methods that require to regain formulas for Renyi entropy. Nonasymptotic case (finite length of blocks transmitted between parties) is also presented. Some examples are given to demonstrate that these protocols are in fact reliable and information-theoretically secure. We also discuss the problem - how to extend (2 1)-OT protocol to (L 1)-OT protocol and how to arrange BSC connecting parties. Both BC and OT protocols can be used as components of more complex and more important for practice protocols like Digital cash, Secure election or Distance bounding.