Zero-error communication over networks

Zero-Error communication investigates communication without any error. By defining channels without probabilities, results from Elias can be used to completely characterize which channel can simulate which other channels. We introduce the ambiguity of a channel, which completely characterizes the possibility in principle of a channel to simulate any other channel. In the second part we will look at networks of players connected by channels, while some players may be corrupted. We will show how the ambiguity of a virtual channel connecting two arbitrary players can be calculated. This means that we can exactly specify what kind of zero-error communication is possible between two players in any network of players connected by channels.Comment: 10 pages, full version of the paper presented at the 2004 IEEE International Symposium on Information Theor

Composable Security in the Bounded-Quantum-Storage Model

We present a simplified framework for proving sequential composability in the quantum setting. In particular, we give a new, simulation-based, definition for security in the bounded-quantum-storage model, and show that this definition allows for sequential composition of protocols. Damgard et al. (FOCS '05, CRYPTO '07) showed how to securely implement bit commitment and oblivious transfer in the bounded-quantum-storage model, where the adversary is only allowed to store a limited number of qubits. However, their security definitions did only apply to the standalone setting, and it was not clear if their protocols could be composed. Indeed, we first give a simple attack that shows that these protocols are not composable without a small refinement of the model. Finally, we prove the security of their randomized oblivious transfer protocol in our refined model. Secure implementations of oblivious transfer and bit commitment then follow easily by a (classical) reduction to randomized oblivious transfer.Comment: 21 page

On the Efficiency of Classical and Quantum Secure Function Evaluation

We provide bounds on the efficiency of secure one-sided output two-party computation of arbitrary finite functions from trusted distributed randomness in the statistical case. From these results we derive bounds on the efficiency of protocols that use different variants of OT as a black-box. When applied to implementations of OT, these bounds generalize most known results to the statistical case. Our results hold in particular for transformations between a finite number of primitives and for any error. In the second part we study the efficiency of quantum protocols implementing OT. While most classical lower bounds for perfectly secure reductions of OT to distributed randomness still hold in the quantum setting, we present a statistically secure protocol that violates these bounds by an arbitrarily large factor. We then prove a weaker lower bound that does hold in the statistical quantum setting and implies that even quantum protocols cannot extend OT. Finally, we present two lower bounds for reductions of OT to commitments and a protocol based on string commitments that is optimal with respect to both of these bounds

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

Oblivious transfer and quantum channels

We show that oblivious transfer can be seen as the classical analogue to a quantum channel in the same sense as non-local boxes are for maximally entangled qubits.Comment: Invited Paper at the 2006 IEEE Information Theory Workshop (ITW 2006