A Generic Security Proof for Quantum Key Distribution

Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, firstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides perfect security because, unlike its classical counterpart, it relies on the laws of physics rather than on ensuring that successful eavesdropping would require excessive computational effort. However, security proofs of quantum key distribution are not trivial and are usually restricted in their applicability to specific protocols. In contrast, we present a general and conceptually simple proof which can be applied to a number of different protocols. It relies on the fact that a cryptographic procedure called privacy amplification is equally secure when an adversary's memory for data storage is quantum rather than classical.Comment: Analysis of B92 protocol adde

Creating Secrets out of Erasures

Current security systems often rely on the adversary's computational limitations. Wireless networks offer the opportunity for a different, complementary kind of security, which relies on the adversary's limited network presence (i.e., that the adversary cannot be located at many different points in the network at the same time). We present a system that leverages this opportunity to enable N wireless nodes to create a shared secret S, in a way that an eavesdropper, Eve, obtains very little information on S. Our system consists of two steps: (1) The nodes transmit packets following a special pattern, such that Eve learns very little about a given fraction of the transmitted packets. This is achieved through a combination of beam forming (from many different sources) and wiretap codes. (2) The nodes participate in a protocol that reshuffles the information known to each node, such that the nodes end up sharing a secret that Eve knows very little about. Our protocol is easily implementable in existing wireless devices and scales well with the number of nodes; these properties are achieved through a combination of public feedback, broadcasting, and network coding. We evaluate our system through a 5-node testbed. We demonstrate that a group of wireless nodes can generate thousands of new shared secret bits per second, with their secrecy being independent of the adversary's computational capabilities

Device independent security of quantum key distribution from monogamy-of-entanglement games

We analyse two party non-local games whose predicate requires Alice and Bob to generate matching bits, and their three party extensions where a third player receives all inputs and is required to output a bit that matches that of the original players. We propose a general device independent quantum key distribution protocol for the subset of such non-local games that satisfy a monogamy-of-entanglement property characterised by a gap in the maximum winning probability between the bipartite and tripartite versions of the game. This gap is due to the optimal strategy for two players requiring entanglement, which due to its monogamy property cannot be shared with any additional players. Based solely on the monogamy-of-entanglement property, we provide a simple proof of information theoretic security of our protocol. Lastly, we numerically optimize the finite and asymptotic secret key rates of our protocol using the magic square game as an example, for which we provide a numerical bound on the maximal tripartite quantum winning probability which closely matches the bipartite classical winning probability. Further, we show that our protocol is robust for depolarizing noise up to about $2.2\%$, providing the first such bound for general attacks for magic square based quantum key distribution.Comment: 49 pages, 7 figures, 2 table

Privacy Amplification with Asymptotically Optimal Entropy Loss

We study the problem of ``privacy amplification\u27\u27: key agreement between two parties who both know a weak secret w, such as a password. (Such a setting is ubiquitous on the internet, where passwords are the most commonly used security device.) We assume that the key agreement protocol is taking place in the presence of an active computationally unbounded adversary Eve. The adversary may have partial knowledge about w, so we assume only that w has some entropy from Eve\u27s point of view. Thus, the goal of the protocol is to convert this non-uniform secret w into a uniformly distributed string $R$ that is fully secret from Eve. R may then be used as a key for running symmetric cryptographic protocols (such as encryption, authentication, etc.). Because we make no computational assumptions, the entropy in R can come only from w. Thus such a protocol must minimize the entropy loss during its execution, so that R is as long as possible. The best previous results have entropy loss of $\Theta(\kappa^2)$, where $\kappa$ is the security parameter, thus requiring the password to be very long even for small values of $\kappa$. In this work, we present the first protocol for information-theoretic key agreement that has entropy loss LINEAR in the security parameter. The result is optimal up to constant factors. We achieve our improvement through a somewhat surprising application of error-correcting codes for the edit distance. The protocol can be extended to provide also ``information reconciliation,\u27\u27 that is, to work even when the two parties have slightly different versions of w (for example, when biometrics are involved)

Security of Quantum Key Distribution

We propose various new techniques in quantum information theory, including a de Finetti style representation theorem for finite symmetric quantum states. As an application, we give a proof for the security of quantum key distribution which applies to arbitrary protocols.Comment: PhD thesis; index adde