Key reconciliation for high performance Quantum Key Distribution

Quantum Key Distribution is carving its place among the tools used to secure communications. While a difficult technology, it enjoys benefits that set it apart from the rest, the most prominent is its provable security based on the laws of physics. QKD requires not only the mastering of signals at the quantum level, but also a classical processing to extract a secret-key from them. This postprocessing has been customarily studied in terms of the efficiency, a figure of merit that offers a biased view of the performance of real devices. Here we argue that it is the throughput the significant magnitude in practical QKD, specially in the case of high speed devices, where the differences are more marked, and give some examples contrasting the usual postprocessing schemes with new ones from modern coding theory. A good understanding of its implications is very important for the design of modern QKD devices.

Analysis of a rate-adaptive reconciliation protocol and the effect of leakage on the secret key rate

Quantum key distribution performs the trick of growing a secret key in two distant places connected by a quantum channel. The main reason is so that the legitimate users can bound the information gathered by the eavesdropper. In practical systems, whether because of finite resources or external conditions, the quantum channel is subject to fluctuations. A rate-adaptive information reconciliation protocol, which adapts to the changes in the communication channel, is then required to minimize the leakage of information in the classical postprocessing. We consider here the leakage of a rate-adaptive information reconciliation protocol. The length of the exchanged messages is larger than that of an optimal protocol; however, we prove that the min-entropy reduction is limited. The simulation results, both in the asymptotic and in the finite-length regime, show that this protocol allows to increase the amount of a distillable secret key.

Demystifying the information reconciliation protocol cascade

Cascade is an information reconciliation protocol proposed in the context of secret key agreement in quantum cryptography. This protocol allows removing discrepancies in two partially correlated sequences that belong to distant parties, connected through a public noiseless channel. It is highly interactive, thus requiring a large number of channel communications between the parties to proceed and, although its efficiency is not optimal, it has become the de-facto standard for practical implementations of information reconciliation in quantum key distribution. The aim of this work is to analyze the performance of Cascade, to discuss its strengths, weaknesses and optimization possibilities, comparing with some of the modified versions that have been proposed in the literature. When looking at all design trade-offs, a new view emerges that allows to put forward a number of guidelines and propose near optimal parameters for the practical implementation of Cascade improving performance significantly in comparison with all previous proposals.

Information reconciliation for Quantum Key Distribution

Secret-key agreement, a well-known problem in cryptography, allows two parties holding correlated sequences to agree on a secret key communicating over a public channel. It is usually divided into three different procedures: advantage distillation, information reconciliation and privacy amplification. The efficiency of each one of these procedures is needed if a positive key rate is to be attained from the legitimate parties? correlated sequences. Quantum key distribution (QKD) allows the two parties to obtain correlated sequences, provided that they have access to an authenticated channel. The new generation of QKD devices is able to work at higher speeds and in noisier or more absorbing environments. This exposes the weaknesses of current information reconciliation protocols, a key component to their performance. Here we present a new protocol based in low-density parity-check (LDPC) codes that presents the advantages of low interactivity, rate adaptability and high efficiency,characteristics that make it highly suitable for next generation QKD devices.

Fundamental finite key limits for information reconciliation in quantum key distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.

Information reconciliation methods in secret key distribution

We consider in this thesis the problem of information reconciliation in the context of secret key distillation between two legitimate parties. In some scenarios of interest this problem can be advantageously solved with low density parity check (LDPC) codes optimized for the binary symmetric channel. In particular, we demonstrate that our method leads to a significant efficiency improvement, with respect to earlier interactive reconciliation methods. We propose a protocol based on LDPC codes that can be adapted to changes in the communication channel extending the original source. The efficiency of our protocol is only limited by the quality of the code and, while transmitting more information than needed to reconcile Alice’s and Bob’s sequences, it does not reveal any more information on the original source than an ad-hoc code would have revealed.---ABSTRACT---En esta tesis estudiamos el problema de la reconciliación de información en el contexto de la destilación de secreto entre dos partes. En algunos escenarios de interés, códigos de baja densidad de ecuaciones de paridad (LDPC) adaptados al canal binario simétrico ofrecen una buena solución al problema estudiado. Demostramos que nuestro método mejora significativamente la eficiencia de la reconciliación. Proponemos un protocolo basado en códigos LDPC que puede ser adaptado a cambios en el canal de comunicaciones mediante una extensión de la fuente original. La eficiencia de nuestro protocolo está limitada exclusivamente por el código utilizado y no revela información adicional sobre la fuente original que la que un código con la tasa de información adaptada habría revelado.

An information reconciliation protocol for secret-key agreement with small leakage

We report on a variant of the so-called Cascade protocol that is well-known for its usage as information reconciliation protocol in quantum cryptography. A theoretical analysis of the optimal size of the parity check blocks is provided. We obtain a very small leakage which is for block sizes of 2^16 typically only 2.5% above the Shannon limit, and notably, this holds for a QBER between 1% and 50%. For a QBER between 1% and 6% the leakage is only 2% above the Shannon limit. As comparison, the leakage of the original Cascade algorithm is 20% (40%) above the Shannon limit for a QBER of 10% (35%).

Rate-Adaptive LDPC-based key reconciliation for high performance quantum key distribution

The postprocessing or secret-key distillation process in quantum key distribution (QKD) mainly involves two well-known procedures: information reconciliation and privacy amplification. Information or key reconciliation has been customarily studied in terms of efficiency. During this, some information needs to be disclosed for reconciling discrepancies in the exchanged keys. The leakage of information is lower bounded by a theoretical limit, and is usually parameterized by the reconciliation efficiency (or inefficiency), i.e. the ratio of additional information disclosed over the Shannon limit. Most techniques for reconciling errors in QKD try to optimize this parameter. For instance, the well-known Cascade (probably the most widely used procedure for reconciling errors in QKD) was recently shown to have an average efficiency of 1.05 at the cost of a high interactivity (number of exchanged messages). Modern coding techniques, such as rate-adaptive low-density parity-check (LDPC) codes were also shown to achieve similar efficiency values exchanging only one message, or even better values with few interactivity and shorter block-length codes.

Efficient information reconciliation for Continuous-Variable QKD using Non-Binary Low-Density Parity-Check Codes

We present here an information reconciliation method and demonstrate for the first time that it can achieve efficiencies close to 0.98. This method is based on the belief propagation decoding of non-binary LDPC codes over finite (Galois) fields. In particular, for convenience and faster decoding we only consider power-of-two Galois fields.

Expanding the functional human mitochondrial DNA database by the establishment of primate xenomitochondrial cybrids

The nuclear and mitochondrial genomes coevolve to optimize approximately 100 different interactions necessary for an efficient ATP-generating system. This coevolution led to a species-specific compatibility between these genomes. We introduced mitochondrial DNA (mtDNA) from different primates into mtDNA-less human cells and selected for growth of cells with a functional oxidative phosphorylation system. mtDNA from common chimpanzee, pigmy chimpanzee, and gorilla were able to restore oxidative phosphorylation in the context of a human nuclear background, whereas mtDNA from orangutan, and species representative of Old-World monkeys, New-World monkeys, and lemurs were not. Oxygen consumption, a sensitive index of respiratory function, showed that mtDNA from chimpanzee, pigmy chimpanzee, and gorilla replaced the human mtDNA and restored respiration to essentially normal levels. Mitochondrial protein synthesis was also unaltered in successful “xenomitochondrial cybrids.” The abrupt failure of mtDNA from primate species that diverged from humans as recently as 8–18 million years ago to functionally replace human mtDNA suggests the presence of one or a few mutations affecting critical nuclear–mitochondrial genome interactions between these species. These cellular systems provide a demonstration of intergenus mtDNA transfer, expand more than 20-fold the number of mtDNA polymorphisms that can be analyzed in a human nuclear background, and provide a novel model for the study of nuclear–mitochondrial interactions.

Primate species richness is determined by plant productivity: Implications for conservation

The explanation of patterns in species richness ranks among the most important tasks of ecology. Current theories emphasize the interaction between historical and geographical factors affecting the size of the regional species pool and of locally acting processes such as competitive exclusion, disturbance, productivity, and seasonality. Local species richness, or alpha diversity, of plants and primary consumers has been claimed to peak in habitats of low and intermediate productivity, which, if true, has major implications for conservation. Here, by contrast, we show that local richness of Neotropical primates (platyrrhines) is influenced by both historical biogeography and productivity but not by tree species richness or seasonality. This pattern indicates that habitats with the highest plant productivity are also the richest for many important primary consumers. We show further that fragmentation of Amazonian rain forests in the Pleistocene, if it occurred, appears to have had a negligible influence on primate alpha species richness.

Horizontal cells reveal cone type-specific adaptation in primate retina

The human cone visual system maintains contrast sensitivity over a wide range of ambient illumination, a property known as light adaptation. The first stage in light adaptation is believed to take place at the first neural step in vision, within the long, middle, and short wavelength sensitive cone photoreceptors. To determine the properties of adaptation in primate outer retina, we measured cone signals in second-order interneurons, the horizontal cells, of the macaque monkey. Horizontal cells provide a unique site for studying early adaptational mechanisms; they are but one synapse away from the photoreceptors, and each horizontal cell receives excitatory inputs from many cones. Light adaptation occurred over the entire range of light levels evaluated, a luminance range of 15–1,850 trolands. Adaptation was demonstrated to be independent in each cone type and to be spatially restricted. Thus, in primates, a major source of sensitivity regulation occurs before summation of cone signals in the horizontal cell.

Tarsier-like locomotor specializations in the Oligocene primate Afrotarsius

Tarsiers and extinct tarsier-like primates have played a central role in views of primate phylogeny and evolution for more than a century. Because of the importance of tarsiers in so many primatological problems, there has been particular interest in questions about the origin of tarsier specializations and the biogeography of early tarsioid radiations. We report on a new fossil of rare Afrotarsius that shows near identity to modern Tarsius in unique specializations of the leg, which provides information about the locomotor behavior and clarifies the phylogenetic position of this previously controversial primate. These specializations constitute evidence that Afrotarsius is a tarsiid, closely related to extant Tarsius; hence, it is now excluded from being a generalized sister taxon to Anthropoidea.

Memory fields of neurons in the primate prefrontal cortex

Many prefrontal (PF) neurons convey information about both an object’s identity (what) and its location (where). To explore how they represent conjunctions of what and where, we explored the receptive fields of their mnemonic activity (i.e., their “memory fields”) by requiring monkeys to remember both an object and its location at many positions throughout a wide portion of central vision. Many PF neurons conveyed object information and had highly localized memory fields that emphasized the contralateral, but not necessarily foveal, visual field. These results indicate that PF neurons can simultaneously convey precise location and object information and thus may play a role in constructing a unified representation of a visual scene.

Molecular origin of the mosaic sequence arrangements of higher primate α-globin duplication units

The human adult α-globin locus consists of three pairs of homology blocks (X, Y, and Z) interspersed with three nonhomology blocks (I, II, and III), and three Alu family repeats, Alu1, Alu2, and Alu3. It has been suggested that an ancient primate α-globin-containing unit was ancestral to the X, Y, and Z and the Alu1/Alu2 repeats. However, the evolutionary origin of the three nonhomologous blocks has remained obscure. We have now analyzed the sequence organization of the entire adult α-globin locus of gibbon (Hylobates lar). DNA segments homologous to human block I occur in both duplication units of the gibbon α-globin locus. Detailed interspecies sequence comparisons suggest that nonhomologous blocks I and II, as well as another sequence, IV, were all part of the ancestral α-globin-containing unit prior to its tandem duplication. However, sometime thereafter, block I was deleted from the human α1-globin-containing unit, and block II was also deleted from the α2-globin-containing unit in both human and gibbon. These were probably independent events both mediated by independent illegitimate recombination processes. Interestingly, the end points of these deletions coincide with potential insertion sites of Alu family repeats. These results suggest that the shaping of DNA segments in eukaryotic genomes involved the retroposition of repetitive DNA elements in conjunction with simple DNA recombination processes.