Stokes-operator-squeezed continuous-variable polarization states

We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincare sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.

Um estudo sobre criptografia

Pós-graduação em Matemática Universitária - IGCE

Informação quântica e relatividade

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On QKD industrialization

During the 25 years of existence of the first protocol for Quantum Key Distribution, much has been said and expected of what came to be termed as Quantum Cryptography. After all this time, much progress has been done but also the reality check and analysis that naturally comes with maturity is underway. A new panorama is emerging, and the way in which the challenges imposed by market requirements are tackled will determine the fate of Quantum Cryptography. The present paper attempts to frame a reasonable view on the issues of the security and market requirements that QKD should achieve to become a marketable technology.

QKD in dense WDM passive optical networks

Quantum cryptography in communications networks

Multiplexing QKD systems in Conventional Optical Networks

Current QKD designs try to keep the quantum channel as error free as possible by using a separate physical medium for this purpose. In the most common case, this means the exclusive use of an optical fiber for the quantum channel, precluding its use for any other purpose. In current optical networks, the fiber is the single most expensive element and this poses a major problem from a cost and availability point of view. Sharing the fiber is thus mandatory for the widespread adoption of QKD. The objective of this communication is to propose a general scheme and present some preliminary measurements of a metropolitan area network (MAN) designed to multiplex of the order of 64 addressable quantum channels and the associated QKD classical service signals on a single dark fibre. It uses as much existing components and infraestructure as possible in an attempt to simultaneously lower most of the practical barriers for the adoption of QKD.

Towards an Optimal Implementation of 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.

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.

Deploying QKD in Standard Optical Networks

In order to deploy QKD in a cost effective and scalable way, its integration with already installed optical networks is a logical step. If, for the sake of security, we require that no intermediate trusted nodes would be needed, the maximum distance/absorptions allowed by QKD systems limit ourselves to metropolitan area networks. Current metro networks are mostly all optical and passive, hence a transparent link can be established among any two points and this link can be used to transport the quantum channel. In this poster we report on our findings studying the problems arising when integrating QKD systems in standard telecommunications networks.

Entanglement generation and routing in optical networks

New telecom wavelength sources of polarization entangled photon pairs allow the distribution of entanglement through metro-access networks using standard equipment. This is essential to ease the deployment of future applications that can profit from quantum entanglement, such as quantum cryptography.

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%).

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.

Towards an optimal implementation of cascade

The aim of this contribution is to study the modifications of Cascade, comparing them with the original protocol on the grounds of a full set of parameters, so that the effect of these modifications can be fairly assessed. A number of simulations were performed to study not only the efficiency but also other characteristics of the protocol that are important for its practical application, such as the number of communications and the failure probability. Note that, although it is generally believed that the only price to pay for an improved efficiency is an increased interactivity, when looking at all the significant magnitudes a different view emerges, showing that, for instance, the failure probability eliminate some the supposed advantages of these improvements.

Networks based on QKD and weakly trusted repeaters

We study how to use quantum key distribution (QKD) in common optical network infrastructures and propose a method to overcome its distance limitations. QKD is the first technology offering information theoretic secret-key distribution that relies only on the fundamental principles of quantum physics. Point-to-point QKD devices have reached a mature industrial state; however, these devices are severely limited in distance, since signals at the quantum level (e.g. single photons) are highly affected by the losses in the communication channel and intermediate devices. To overcome this limitation, intermediate nodes (i.e. repeaters) are used. Both, quantum-regime and trusted, classical, repeaters have been proposed in the QKD literature, but only the latter can be implemented in practice. As a novelty, we propose here a new QKD network model based on the use of not fully trusted intermediate nodes, referred as weakly trusted repeaters. This approach forces the attacker to simultaneously break several paths to get access to the exchanged key, thus improving significantly the security of the network. We formalize the model using network codes and provide real scenarios that allow users to exchange secure keys over metropolitan optical networks using only passive components.

Métodos eficientes para criptografia baseada em reticulados.

Reticulados têm sido aplicados de diferentes maneiras em criptografia. Inicialmente utilizados para a destruição de criptossistemas, eles foram posteriormente aplicados na construção de novos esquemas, incluindo criptossistemas assimétricos, esquemas de assinatura cega e os primeiros métodos para encriptação completamente homomórfica. Contudo, seu desempenho ainda é proibitivamente lenta em muitos casos. Neste trabalho, expandimos técnicas originalmente desenvolvidas para encriptação homomórfica, tornando-as mais genéricas e aplicando-as no esquema GGH-YK-M, um esquema de encriptação de chave pública, e no esquema LMSV, a única construção homomórfica que não sucumbiu a ataques de recuperação de chaves IND-CCA1 até o momento. Em nossos testes, reduzimos o tamanho das chaves do GGH-YK-M em uma ordem de complexidade, especificamente, de O(n2 lg n) para O(n lg n), onde n é um parâmetro público do esquema. A nova técnica também atinge processamento mais rápido em todas as operações envolvidas em um criptossistema assimétrico, isto é, geração de chaves, encriptação e decriptação. A melhora mais significativa é na geração de chaves, que se torna mais de 3 ordens de magnitude mais rápida que resultados anteriores, enquanto a encriptação se torna por volta de 2 ordens de magnitude mais rápida. Para decriptação, nossa implementação é dez vezes mais rápida que a literatura. Também mostramos que é possível aumentar a segurança do esquema LMSV contra os ataques quânticos de recuperação de chaves recentemente publicados pela agência britânica GCHQ. Isso é feito através da adoção de reticulados não-ciclotômicos baseados em anéis polinomiais irredutíveis quase-circulantes. Em nossa implementação, o desempenho da encriptação é virtualmente idêntico, e a decriptação torna-se ligeiramente inferior, um pequeno preço a se pagar pelo aumento de segurança. A geração de chaves, porém, é muito mais lenta, devido à necessidade de se utilizar um método mais genérico e caro. A existência de métodos dedicados altamente eficientes para a geração de chaves nesta variante mais segura do LMSV permanece como um problema em aberto.