Unconditional security from noisy quantum storage

We consider the implementation of two-party cryptographic primitives based on the sole assumption that no large-scale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide security even against the most general attack. Such unconditional results were previously only known in the so-called bounded-storage model which is a special case of our setting. Our protocols can be implemented with present-day hardware used for quantum key distribution. In particular, no quantum storage is required for the honest parties.Comment: 25 pages (IEEE two column), 13 figures, v4: published version (to appear in IEEE Transactions on Information Theory), including bit wise min-entropy sampling. however, for experimental purposes block sampling can be much more convenient, please see v3 arxiv version if needed. See arXiv:0911.2302 for a companion paper addressing aspects of a practical implementation using block samplin

Secure Two-Party Computation over Unreliable Channels

We consider information-theoretic secure two-party computation in the plain model where no reliable channels are assumed, and all communication is performed over the binary symmetric channel (BSC) that flips each bit with fixed probability. In this reality-driven setting we investigate feasibility of communication-optimal noise-resilient semi-honest two-party computation i.e., efficient computation which is both private and correct despite channel noise. We devise an information-theoretic technique that converts any correct, but not necessarily private, two-party protocol that assumes reliable channels, into a protocol which is both correct and private against semi-honest adversaries, assuming BSC channels alone. Our results also apply to other types of noisy-channels such as the elastic-channel. Our construction combines tools from the cryptographic literature with tools from the literature on interactive coding, and achieves, to our knowledge, the best known communication overhead. Specifically, if $f$ is given as a circuit of size $s$, our scheme communicates $O(s + \kappa)$ bits for $\kappa$ a security parameter. This improves the state of the art (Ishai et al., CRYPTO\u27 11) where the communication is $O(s) + \text{poly}(\kappa \cdot \text{depth}(s))$

Robuster Combiners for Oblivious Transfer

Abstract. A(k; n)-robust combiner for a primitive F takes as input n candidate implementations of F and constructs an implementation of F, which is secure assuming that at least k of the input candidates are secure. Such constructions provide robustness against insecure implementations and wrong assumptions underlying the candidate schemes. In a recent work Harnik et al. (Eurocrypt 2005) have proposed a (2; 3)-robust combiner for oblivious transfer (OT), and have shown that (1; 2)-robust OT-combiners of a certain type are impossible. In this paper we propose new, generalized notions of combiners for two-party primitives, which capture the fact that in many two-party protocols the security of one of the parties is unconditional, or is based on an assumption independent of the assumption underlying the security of the other party. This fine-grained approach results in OT-combiners strictly stronger than the constructions known before. In particular, we propose an OT-combiner which guarantees secure OT even when only one candidate is secure for both parties, and every remaining candidate is flawed for one of the parties. Furthermore, we present an efficient uniform OT-combiner, i.e., a single combiner which is secure simultaneously for a wide range of candidates ’ failures. Finally, our definition allows for a very simple impossibility result, which shows that the proposed OT-combiners achieve optimal robustness