On Cryptographic Primitives Based on Noisy Channels

The primitives of Oblivious Transfer (OT) and Bit Commitment (BC) are fundamental in the cryptographic protocol design. OT is a complete primitive for secure two-party computation, while zero-knowledge proofs are based on BC. In this work, the implementations of OT and BC with unconditional security for both parties are considered. The security of these protocols does not depend on unproven intractability assumptions. Instead, we assume that the players are connected by noisy channels. This is a very natural assumption since noise is inherently present in the real communication channels. We present and prove secure a protocol for OT based on a Discrete Memoryless Channel (DMC) with probability transition matrix of a general form. The protocol is secure for any non-trivial DMC. Some generalisations to this protocol for the particular case of Binary Symmetric Channel (BSC) are presented and their asymptotic behaviour is analysed. The security of OT and BC based on BSC is also analysed in the nonasymptotic case. We derive relations for the failure probabilities depending on the number of channel uses establishing trade-offs between their communication complexity on the one hand and the security on the other hand. We consider a modification to the Universally Composable (UC) framework for the case of unconditional two-party protocols. We argue that this modification is valid hereby preparing a ground for our results concerning OT based on Unfair Noisy Channels (UNC). In contrast to the noise models mentioned above, a corrupted party is given a partial control over the randomness introduced by UNC. We introduce a generic “compiler” which transforms any protocol implementing OT from a passive version of UNC and secure against passive cheating into a protocol that uses UNC for communications and builds an OT secure against active cheating. We exploit this result and a new technique for transforming between the weaker versions of OT in order to obtain new possibility results for OT based on UNC.