Quantum Oblivious Transfer: A Short Review

Quantum cryptography is the field of cryptography that explores the quantum properties of matter. Generally, it aims to develop primitives beyond the reach of classical cryptography and to improve existing classical implementations. Although much of the work in this field covers quantum key distribution (QKD), there have been some crucial steps towards the understanding and development of quantum oblivious transfer (QOT). One can show the similarity between the application structure of both QKD and QOT primitives. Just as QKD protocols allow quantum-safe communication, QOT protocols allow quantum-safe computation. However, the conditions under which QOT is fully quantum-safe have been subject to intense scrutiny and study. In this review article, we survey the work developed around the concept of oblivious transfer within theoretical quantum cryptography. We focus on some proposed protocols and their security requirements. We review the impossibility results that daunt this primitive and discuss several quantum security models under which it is possible to prove QOT security.     

Unconditional security of a three state quantum key distribution protocol

Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.     

Happy New Year

The collective phenomena of quantum interference, including wave particle duality and apparent non-locality, have intrigued the physics community for many years. It is only recently that we have begun to turn these somewhat counter intuitive quantum phenomena to good use. A leading force in that direction is quantum cryptography - absolute secure key exchange encoding data on the polarisation or phase of individual photons, or using the quantum correlations between pairs of particles. Technologies are now implemented to bring the various forms of quantum cryptography to commercial application. At the same time the possibility of communications applications has stimulated the study of a variety of novel quantum interference phenomena. Quantum information experiments involving two, three and four photons are planned and a novel Field of continuous variable (many photon) quantum information has emerged. These various aspects of quantum cryptography are considered in the conference “QUICK: Quan- tum interference and cryptographic keys: novel physics and advancing technologies", taking place in Cargese from April 7 to 13, 2001. Following that conference, we invite submission of original papers to a special issue of the European Physical Journal D, on the following topics: - quantum cryptography technologies, - quantum cryptography systems, - free space quantum cryptography and satellites, - pair-photon sources and multiphoton interference, - single photon sources, - continuous variable quantum information, - security aspects, - cryptographic protocols, - entanglement purification in cryptographic schemes, - novel physics and quantum gates for photonic qubits.     

Call for papers

The collective phenomena of quantum interference, including wave particle duality and apparent non-locality, have intrigued the physics community for many years. It is only recently that we have begun to turn these somewhat counter intuitive quantum phenomena to good use. A leading force in that direction is quantum cryptography - absolute secure key exchange encoding data on the polarisation or phase of individual photons, or using the quantum correlations between pairs of particles. Technologies are now implemented to bring the various forms of quantum cryptography to commercial application. At the same time the possibility of communications applications has stimulated the study of a variety of novel quantum interference phenomena. Quantum information experiments involving two, three and four photons are planned and a novel Field of continuous variable (many photon) quantum information has emerged. These various aspects of quantum cryptography are considered in the conference “QUICK: Quan- tum interference and cryptographic keys: novel physics and advancing technologies", taking place in Cargese from April 7 to 13, 2001. Following that conference, we invite submission of original papers to a special issue of the European Physical Journal D, on the following topics: - quantum cryptography technologies, - quantum cryptography systems, - free space quantum cryptography and satellites, - pair-photon sources and multiphoton interference, - single photon sources, - continuous variable quantum information, - security aspects, - cryptographic protocols, - entanglement purification in cryptographic schemes, - novel physics and quantum gates for photonic qubits. The submitted articles should be sent to the EPJ D Editorial Office in Orsay. The deadline is July 15, 2001. We look forward to a stimulating special issue.     

Call for papers Special issue on “Quantum interference and cryptographic keys: novel physics and advancing technologies"

The collective phenomena of quantum interference, including wave particle duality and apparent non-locality, have intrigued the physics community for many years. It is only recently that we have begun to turn these somewhat counter intuitive quantum phenomena to good use. A leading force in that direction is quantum cryptography - absolute secure key exchange encoding data on the polarisation or phase of individual photons, or using the quantum correlations between pairs of particles. Technologies are now implemented to bring the various forms of quantum cryptography to commercial application. At the same time the possibility of communications applications has stimulated the study of a variety of novel quantum interference phenomena. Quantum information experiments involving two, three and four photons are planned and a novel Field of continuous variable (many photon) quantum information has emerged. These various aspects of quantum cryptography are considered in the conference “QUICK: Quan- tum interference and cryptographic keys: novel physics and advancing technologies", taking place in Cargese from April 7 to 13, 2001. Following that conference, we invite submission of original papers to a special issue of the European Physical Journal D, on the following topics: - quantum cryptography technologies, - quantum cryptography systems, - free space quantum cryptography and satellites, - pair-photon sources and multiphoton interference, - single photon sources, - continuous variable quantum information, - security aspects, - cryptographic protocols, - entanglement purification in cryptographic schemes, - novel physics and quantum gates for photonic qubits. The submitted articles should be sent to the EPJ D Editorial Office in Orsay. The deadline is July 15, 2001. We look forward to a stimulating special issue.     

Call for papers Special issue on “Quantum interference and cryptographic keys: novel physics and advancing technologies"

The collective phenomena of quantum interference, including wave particle duality and apparent non-locality, have intrigued the physics community for many years. It is only recently that we have begun to turn these somewhat counter intuitive quantum phenomena to good use. A leading force in that direction is quantum cryptography - absolute secure key exchange encoding data on the polarisation or phase of individual photons, or using the quantum correlations between pairs of particles. Technologies are now implemented to bring the various forms of quantum cryptography to commercial application. At the same time the possibility of communications applications has stimulated the study of a variety of novel quantum interference phenomena. Quantum information experiments involving two, three and four photons are planned and a novel Field of continuous variable (many photon) quantum information has emerged. These various aspects of quantum cryptography are considered in the conference “QUICK: Quan- tum interference and cryptographic keys: novel physics and advancing technologies", taking place in Cargese from April 7 to 13, 2001. Following that conference, we invite submission of original papers to a special issue of the European Physical Journal D, on the following topics: - quantum cryptography technologies, - quantum cryptography systems, - free space quantum cryptography and satellites, - pair-photon sources and multiphoton interference, - single photon sources, - continuous variable quantum information, - security aspects, - cryptographic protocols, - entanglement purification in cryptographic schemes, - novel physics and quantum gates for photonic qubits. The submitted articles should be sent to the EPJ D Editorial Office in Orsay. The deadline is July 15, 2001. We look forward to a stimulating special issue.     

Multiparameter QKD authentication protocol design over optical quantum channel

Quantum cryptography is the first application of quantum physics at the single photon level. The most important application of quantum cryptography is Quantum Key Distribution (QKD). One of the biggest problems of QKD implementation is enormous number of possible attacks, which puts out specific need for more refined simulation strategies in bridging the gap between theoretic models and their implementation. In this work we have introduced generalized optical architecture which can provide various solutions of some actual problems for two mostly used QKD protocols: BB84 and B92 protocols. Simulations, which included the influence of optical losses over a quantum channel with concrete realistic lengths, have confirmed validity and high level of provable security of the proposed generalized QKD authentication architecture. Due to simplicity of the proposed architecture and obtained QKD B92 protocol communication efficiency, we believe that it can be implemented, solving out some of the most relevant implementation problems which are common for both QKD protocols.     

Quantum cryptography using partially entangled states

We show that non-maximally entangled states can be used to build a quantum key distribution (QKD) scheme where the key is probabilistically teleported from Alice to Bob. This probabilistic aspect of the protocol ensures the security of the key without the need of non-orthogonal states to encode it, in contrast to other QKD schemes. Also, the security and key transmission rate of the present protocol is nearly equivalent to those of standard QKD schemes and these aspects can be controlled by properly harnessing the new free parameter in the present proposal, namely, the degree of partial entanglement. Furthermore, we discuss how to build a controlled QKD scheme, also based on partially entangled states, where a third party can decide whether or not Alice and Bob are allowed to share a key.     

Structured codes improve the Bennett-Brassard-84 quantum key rate

A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates under various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution (QKD) protocol would be given by a single-letter formula involving optimization over a single use of an effective channel. We explore the possibility of such a formula for the simplest and most widely used QKD protocol, Bennnett-Brassard-84 with one-way classical postprocessing. We show that a conjectured single-letter formula is false, uncovering a deep ignorance about good private codes and exposing unfortunate complications in the theory of QKD. These complications are not without benefit-with added complexity comes better key rates than previously thought possible. The threshold for secure key generation improves from a bit error rate of 0.124 to 0.129.     

Quantum Stream Cipher Based on Holevo–Yuen Theory

In this review paper, we first introduce the basic concept of quantum computer-resistant cryptography, which is the cornerstone of security technology for the network of a new era. Then, we will describe the positioning of mathematical cryptography and quantum cryptography, that are currently being researched and developed. Quantum cryptography includes QKD and quantum stream cipher, but we point out that the latter is expected as the core technology of next-generation communication systems. Various ideas have been proposed for QKD quantum cryptography, but most of them use a single-photon or similar signal. Then, although such technologies are applicable to special situations, these methods still have several difficulties to provide functions that surpass conventional technologies for social systems in the real environment. Thus, the quantum stream cipher has come to be expected as one promising countermeasure, which artificially creates quantum properties using special modulation techniques based on the macroscopic coherent state. In addition, it has the possibility to provide superior security performance than one-time pad cipher. Finally, we introduce detailed research activity aimed at putting the quantum stream cipher into practical use in social network technology.     

Quantum Key-Distribution Protocols Based on a Quantum Version of the Monty Hall Game

This work illustrates a possible application of quantum game theory to the area of quantum information, in particular to quantum cryptography. The study proposed two quantum key-distribution (QKD) protocols based on the quantum version of the Monty Hall game devised by Flitney and Abbott. Unlike most QKD protocols, in which the bits from which the key is going to be extracted are encoded in a basis choice (as in BB84), these are encoded in an operation choice. The first proposed protocol uses qutrits to describe the state of the system and the same game operators proposed by Flitney and Abbott. The motivation behind the second proposal is to simplify a possible physical implementation by adapting the formalism of the qutrit protocol to use qubits and simple logical quantum gates. In both protocols, the security relies on the violation of a Bell-type inequality, for two qutrits and for six qubits in each case. Results show a higher ratio of violation than the E91 protocol.     

On the implementation of a deterministic secure coding protocol using polarization entangled photons

We demonstrate a prototype-implementation of deterministic information encoding for quantum key distribution (QKD) following the ping-pong coding protocol [K. Boström, T. Felbinger, Phys. Rev. Lett. 89 (2002) 187902-1]. Due to the deterministic nature of this protocol the need for post-processing the key is distinctly reduced compared to non-deterministic protocols. In the course of our implementation we analyze the practicability of the protocol and discuss some security aspects of information transfer in such a deterministic scheme.     

Quantum entanglement and composite keys in quantum cryptography

The security of quantum cryptography protocols after a quantum key distribution (QKD) session is formulated in terms of proximity between two situations: quantum states corresponding to real and ideal situations after QKD. The measure of proximity is the trace distance. It is more reasonable to formulate security directly in terms of the smallness of probability of successive guessing of keys by an eavesdropper after an arbitrary number of QKD sessions. There is a fundamental question the answer to which is a priori very unobvious: Is the security criterion in terms of the proximity of the real and ideal situations for a single QKD session sufficient to guarantee the security of keys in terms of the smallness of probability of guessing of keys by the eavesdropper after an arbitrary number of QKD sessions? It has been shown that the answer to this question is positive.     

Distinguishability of quantum states and shannon complexity in quantum cryptography

The proof of the security of quantum key distribution is a rather complex problem. Security is defined in terms different from the requirements imposed on keys in classical cryptography. In quantum cryptography, the security of keys is expressed in terms of the closeness of the quantum state of an eavesdropper after key distribution to an ideal quantum state that is uncorrelated to the key of legitimate users. A metric of closeness between two quantum states is given by the trace metric. In classical cryptography, the security of keys is understood in terms of, say, the complexity of key search in the presence of side information. In quantum cryptography, side information for the eavesdropper is given by the whole volume of information on keys obtained from both quantum and classical channels. The fact that the mathematical apparatuses used in the proof of key security in classical and quantum cryptography are essentially different leads to misunderstanding and emotional discussions [1]. Therefore, one should be able to answer the question of how different cryptographic robustness criteria are related to each other. In the present study, it is shown that there is a direct relationship between the security criterion in quantum cryptography, which is based on the trace distance determining the distinguishability of quantum states, and the criterion in classical cryptography, which uses guesswork on the determination of a key in the presence of side information.     

Error Estimation at the Information Reconciliation Stage of Quantum Key Distribution

Quantum key distribution (QKD) offers a practical solution for secure communication between two distinct parties via a quantum channel and an authentic public channel. In this work, we consider different approaches to the quantum bit error rate (QBER) estimation at the information reconciliation stage of the post-processing procedure. For reconciliation schemes employing low-density parity-check (LDPC) codes, we develop a novel syndrome-based QBER estimation algorithm. The algorithm suggested is suitable for irregular LDPC codes and takes into account punctured and shortened bits. Testing our approach in a real QKD setup, we show that an approach combining the proposed algorithm with conventional QBER estimation techniques allows one to improve the accuracy of the QBER estimation.     

Performance optimization for quantum key distribution in lossy channel using entangled photons

In quantum key distribution(QKD), the times of arrival of single photons are important for the keys extraction and time synchronization. The time-of-arrival(TOA) accuracy can affect the quantum bit error rate(QBER) and the final key rate. To achieve a higher accuracy and a better QKD performance, different from designing more complicated hardware circuits, we present a scheme that uses the mean TOA of M frequency-entangled photons to replace the TOA of a single photon. Moreover, to address the problem that the entanglement property is usually sensitive to the photon loss in practice,we further propose two schemes, which adopt partially entangled photons and grouping-entangled photons, respectively.In addition, we compare the effects of these three alternative schemes on the QKD performance and discuss the selection strategy for the optimal scheme in detail. The simulation results show that the proposed schemes can improve the QKD performance compared to the conventional single-photon scheme obviously, which demonstrate the effectiveness of the proposed schemes.