On the Commitment Capacity of Unfair Noisy Channels

Noisy channels are a valuable resource from a cryptographic point of view. They can be used for exchanging secret-keys as well as realizing other cryptographic primitives such as commitment and oblivious transfer. To be really useful, noisy channels have to be consider in the scenario where a cheating party has some degree of control over the channel characteristics. Damg\r{a}rd et al. (EUROCRYPT 1999) proposed a more realistic model where such level of control is permitted to an adversary, the so called unfair noisy channels, and proved that they can be used to obtain commitment and oblivious transfer protocols. Given that noisy channels are a precious resource for cryptographic purposes, one important question is determining the optimal rate in which they can be used. The commitment capacity has already been determined for the cases of discrete memoryless channels and Gaussian channels. In this work we address the problem of determining the commitment capacity of unfair noisy channels. We compute a single-letter characterization of the commitment capacity of unfair noisy channels. In the case where an adversary has no control over the channel (the fair case) our capacity reduces to the well-known capacity of a discrete memoryless binary symmetric channel

A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM

Commitment and Oblivious Transfer in the Bounded Storage Model with Errors

The bounded storage model restricts the memory of an adversary in a cryptographic protocol, rather than restricting its computational power, making information theoretically secure protocols feasible. We present the first protocols for commitment and oblivious transfer in the bounded storage model with errors, i.e., the model where the public random sources available to the two parties are not exactly the same, but instead are only required to have a small Hamming distance between themselves. Commitment and oblivious transfer protocols were known previously only for the error-free variant of the bounded storage model, which is harder to realize

On the Composability of Statistically Secure Random Oblivious Transfer

We show that random oblivious transfer protocols that are statistically secure according to a definition based on a list of information-theoretical properties are also statistically universally composable. That is, they are simulatable secure with an unlimited adversary, an unlimited simulator, and an unlimited environment machine. Our result implies that several previous oblivious transfer protocols in the literature that were proven secure under weaker, non-composable definitions of security can actually be used in arbitrary statistically secure applications without lowering the security

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

Building Oblivious Transfer on Channel Delays

In the information-theoretic setting, where adversaries have unlimited computational power, the fundamental cryptographic primitive Oblivious Transfer (OT) cannot be securely achieved if the parties are communicating over a clear channel. To preserve secrecy and security, the players have to rely on noise in the communication. Noisy channels are therefore a useful tool to model noise behavior and build protocols implementing OT. This paper explores a source of errors that is inherently present in practically any transmission medium, but has been scarcely studied in this context: delays in the communication. In order to have a model for the delays that is both general and comparable to the channels usually used for OT – such as the Binary Symmetric Channel (BSC) – we introduce a new noisy channel, the Binary Discrete-time Delaying Channel (BDDC). We show that such a channel realistically reproduces real-life communication scenarios where delays are hard to predict and we propose a protocol for achieving oblivious transfer over the BDDC. We analyze the security of our construction in the semi-honest setting, showing that our realization of OT substantially decreases the protocol sensitivity to the user’s knowledge of the channel compared to solutions relying on other channel properties, and is very efficient for wide ranges of delay probabilities. The flexibility and generality of the model opens the way for future implementation in media where delays are a fundamental characteristic

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