Secure two-party computation over a Z-channel

In secure two-party computation, two mutually distrusting parties are interested in jointly computing a function, while preserving the privacy of their respective inputs. However, when communicating over a clear channel, security against computationally unbounded adversaries is impossible. Thus is the importance of noisy channels, over which we can build Oblivious Transfer (OT), a fundamental primitive in cryptography and the basic building block for any secure multi-party computation. The noisy channels commonly used in current constructions are mostly derived from the Binary Symmetric Channel (BSC), which is modified to extend the capabilities of an attacker. Still, these constructions are based on very strong assumptions, in particular on the error probability, which makes them hard to implement. In this paper, we provide a protocol achieving oblivious transfer over a Z-channel, a natural channel model in various contexts, ranging from optical to covert communication. The protocol proves to be particularly efficient for a large range of error probabilities p (e.g., for 0.17 ≤ p ≤ 0.29 when a security parameter ε = 10 ^-9 is chosen), where it requires a limited amount of data to be sent through the channel. Our construction also proves to offer security against unfair adversaries, who are able to select the channel probability within a fixed range. We provide coding schemes that can further increase the efficiency of the protocol for probabilities distant from the range mentioned above, and also allow the use of a Z-channel with an error probability greater than 0.5. The flexibility and the efficiency of the construction make an actual implementation of oblivious transfer a more realistic prospect.