The authors present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophisticated cryptographic device. They also present an application to quantum cryptography.>
The authors present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophisticated cryptographic device. They also present an application to quantum cryptography.>
) Claude Cr'epeau Department of Computer Science MIT Joe Kilian y Mathematics Department MIT Abstract A useful paradigm in studying cryptographic scenarios is that of protocol minimalism. That is, given a cryptographic model, one wishes to determine the simplest protocols one needs in order to be able to implement secure protocols in general. In the standard cryptographic model, this approach allows one to encapsulate ones cryptographic assumptions. In other, nonstandard scenarios, the approach can greatly simplifying the task of developing protocols without cryptographic assumptions. Oblivious transfer protocols, first introduced by Rabin [R], are conceptually very simple, yet can be used to implement a wide variety of protocols([EGL],[BCR1],[K]). The versatility of these games amply motivates a wider study of the power of simple two-party games. In this paper, we present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studie...
Reducing the minimum assumptions needed to construct various cryptographic primitives is an important andinteresting task in theoretical cryptography. Oblivious Transfer, one of the most basic cryptographic building blocks, is also studied under this scenario. Reducing the minimum assumptions for Oblivious Transfer seems not an easy task, as there are a few impossibility results under black-box reductions. Until recently, it is widely believed that Oblivious Transfer can be constructed with trapdoor permutations but not trapdoor functions in general. In this paper, we enhance previous results and show one Oblivious Transfer protocol based on a collection of trapdoor functions with some extra properties. We also provide reasons for adding the extra properties and argue that the assumptions in the protocol are nearly minimum.
There are various practical obstacles in quantum cryptography. These include the problems that arise in implementing quantum cryptographic protocols with current and near-term technology, and those that come with the development and security analysis of new protocols. In this work, we examine a few of these obstacles and, for each one, we highlight an approach that aims to mitigate it. We start by examining the setting of device-independence, with oblivious transfer in the bounded-quantum-storage-model as the primitive of interest. The typical approach to enabling device-independence is the use of a Bell-inequality violation, which requires a strict non-communication assumption that is practically difficult to enforce. We develop and analyze the security of a device-independent oblivious transfer protocol that replaces the Bell-inequality violation approach with a computational assumption, thereby relaxing the non-communication assumption. Our second topic examines the problem of noise in a quantum money scheme. We show how to achieve noise-tolerance in the public-key setting. Our scheme can be seen as a generalization of the [AC12] scheme: a valid banknote is now a subspace state possibly affected by noise, and verification is performed by using classical oracles to check for membership in "larger spaces." Additionally, a banknote in our scheme is minted by preparing conjugate coding states and applying a unitary. For our last topic, we consider the general task of proving security against a specious adversary, which is the quantum analogue of the classical semi-honest adversary. A useful feature of specious adversaries is that security against them can guarantee security against stronger adversaries [DNS12]. This motivates the search for a canonical specious adversary, where proving security against such an adversary guarantees security against the entire class of specious adversaries. Within a restricted setting, we define a particular specious adversary and show that it satisfies our definition of canonical.
Oblivious transfer is a primitive of paramount importance in cryptography or, more precisely, two- and multi-party computation due to its universality. Unfortunately, oblivious transfer cannot be achieved in an unconditionally secure way for both parties from scratch. Therefore, it is a natural question what information-theoretic primitives or computational assumptions oblivious transfer can be based on. The results in our thesis are threefold. First, we present a protocol that implements oblivious transfer from a weakened oblivious transfer called universal oblivious transfer, where one of the two players may get additional information. Our reduction is about twice as efficient as previous results. Weak oblivious transfer is an even weaker form of oblivious transfer, where both players may obtain additional information about the other player's input, and where the output can contain errors. We give a new, weaker definition of weak oblivious transfer, as well as new reductions with a more detailed analysis. Finally, we carry over our results to the computational setting and show how a weak oblivious transfer that is sometimes incorrect and only mildly secure against computationally bounded adversaries can be strengthened.
Abstract. Various results show that oblivious transfer can be implemented using the assumption of noisy channels. Unfortunately, this assumption is not as weak as one might think, because in a cryptographic setting, these noisy channels must satisfy very strong security requirements. Unfair noisy channels, introduced by Damg˚ard, Kilian and Salvail [Eurocrypt ’99], reduce these limitations: They give the adversary an unfair advantage over the honest player, and therefore weaken the security requirements on the noisy channel. However, this model still has many shortcomings: For example, the adversary’s advantage is only allowed to have a very special form, and no error is allowed in the implementation. In this paper we generalize the idea of unfair noisy channels. We introduce two new models of cryptographic noisy channels that we call the weak erasure channel and the weak binary symmetric channel, and show how they can be used to implement oblivious transfer. Our models are more general and use much weaker assumptions than unfair noisy channels, which makes implementation a more realistic prospect. For example, these are the first models that allows the parameters to come from experimental evidence. 1
Motivated by the applications of secure multi-party computation as a privacy-protecting data analysis tool, and identifying oblivious transfer as one of its main practical enablers, we propose a practical realization of randomized quantum oblivious transfer. By using only symmetric cryptography primitives to implement commitments, we construct computationally secure randomized oblivious transfer without the need for public-key cryptography or assumptions imposing limitations on the adversarial devices. We show that the protocol is secure under an indistinguishability-based notion of security and demonstrate an experimental implementation to test its real-world performance. Its security and performance are then compared to both quantum and classical alternatives, showing potential advantages over existing solutions based on the noisy storage model and public-key cryptography.