I. V. Volovich, Ya. I. Volovich
Lectures on classical and quantum cryptography. Contents: Private key cryptosystems. Elements of number theory. Public key cryptography and RSA cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty relations. The no cloning theorem. The BB84 quantum cryptographic protocol. Security proofs. Bell`s theorem. The EPRBE quantum cryptographic protocol.
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Post Quantum Cryptography and its Comparison with Classical Cryptography
本文对比经典密码学与量子密码学，阐述量子密码学基于量子力学原理在检测和阻止窃听方面的优势，揭示其对安全通信格局的革命性影响。
Cryptography: Classical versus Post-Quantum
本综述探讨了后量子密码学相较于经典密码学的优势，论述了多种后量子密码学技术，并指出部署抗量子密码系统是未来安全通信的趋势，对保障后量子时代敏感信息安全至关重要。
With the rapid development of quantum computers the currently secure cryptographic protocols may not stay that way. Quantum mechanics provides means to create an inherently secure communication channel that is protected by the laws of physics and not by the computational hardness of certain mathematical problems. This paper is a non-technical overview of quantum key distribution, one of the most well-known application of quantum cryptography, a type of cryptography poised to exploit the laws of quantum mechanics directly.
Over decades quantum cryptography has been intensively studied for unconditionally secured data transmission in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels, however, the quantum cryptography is practically inefficient and even vulnerable to eavesdropping. Here, a method of unconditionally secured key distribution potentially compatible with current fiber-optic communications networks is proposed in a classical regime for high-speed optical backbone networks. The unconditional security is due to the quantum superpositi…
We consider the security of continuous-variable quantum cryptography as we approach the classical-limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10,000 times the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore, incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptograph…
Quantum cryptography exploits principles of quantum physics for the secure processing of information. A prominent example is secure communication, i.e., the task of transmitting confidential messages from one location to another. The cryptographic requirement here is that the transmitted messages remain inaccessible to anyone other than the designated recipients, even if the communication channel is untrusted. In classical cryptography, this can usually only be guaranteed under computational hardness assumptions, e.g., that factoring large integers is infeasible. In contrast, the security of q…
We discuss the unambiguous measurement of quantum nonorthogonal states in connection with the quantum cryptography. We show that checking a ratio of null one to signal is essential in detecting a certain kind of eavesdropping in the case of two nonorthogonal states quantum cryptography. We prove that it is not needed in the case of the four states quantum cryptography.
Quantum cryptography visualized: assessing visual attention on multiple representations with eye tracking in an AR-enhanced quantum cryptography student experiment
本研究针对量子教育实践需求，在AR增强的量子密码学学生实验中，用DeFT框架分析表征的概念学习潜力，并结合38名学生的试点眼动数据探究其对多种表征的视觉注意力。
This paper has been withdrawn by the authors because the results obtained have been reported earlier by other authors.
Elementary review article on quantum cryptography.
This is our Reply to Peres' Comment [quant-ph/9509003] to "Quantum Cryptography Based on Orthogonal States" [Phys. Rev. Lett. 75, 1239 (1995)].
The relation between the boolean functions and Bell inequalities for qubits is analyzed. The connection between the maximal quantum violation of a Bell inequality and the nonlinearity of the corresponding boolean function is discussed. A visualization scheme of boolean functions is proposed. An attempt to classify Bell inequalities for qubits is made, a weaker result (classification with respect to Jevons group) is obtained. The fractal structure of the classification is shown. All constructs are illustrated by Mathematica code.
When the 4-state or the 6-state protocol of quantum cryptography is carried out on a noisy (i.e. realistic) quantum channel, then the raw key has to be processed to reduce the information of an adversary Eve down to an arbitrarily low value, providing Alice and Bob with a secret key. In principle, quantum algorithms as well as classical algorithms can be used for this processing. A natural question is: up to which error rate on the raw key is a secret-key agreement at all possible? Under the assumption of incoherent eavesdropping, we find that the quantum and classical limits are precisely the…
Uniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and other applications.
Quantum cryptography is a new method for secret communications offering the ultimate security assurance of the inviolability of a Law of Nature. In this paper we shall describe the theory of quantum cryptography, its potential relevance and the development of a prototype system at Los Alamos, which utilises the phenomenon of single-photon interference to perform quantum cryptography over an optical fiber communications link.
We present a new approach to simulate quantum cryptography protocols using event-based processes. The method is validated by simulating the BB84 protocol and the Ekert protocol, both without and with the presence of an eavesdropper.
We report experimental studies on the effect of the depolarizing quantum channel on weak-pulse BB84 and SARG04 quantum cryptography. The experimental results show that, in real world conditions in which channel depolarization cannot be ignored, BB84 should perform better than SARG04.
Noise causes severe difficulties in implementing quantum computing and quantum cryptography. Several schemes have been suggested to reduce this problem, mainly focusing on quantum computation. Motivated by quantum cryptography, we suggest a coding which uses $N$ quantum bits ($N=n^2$) to encode one quantum bit, and reduces the error exponentially with $n$. Our result suggests the possibility of distributing a secure key over very long distances, and maintaining quantum states for very long times. It also provides a new quantum privacy amplification against a strong adversary.
We present a new quantum bit commitment (QBC) protocol based on counterfactual quantum cryptography. We analyze the security of this protocol, find that it can resist the attack presented by QBC's no-go theorem. Our protocol is simple, and probably give a new way of constructing QBC protocol.
Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.
Quantum discord is the minimal bipartite resource which is needed for a secure quantum key distribution, being a cryptographic primitive equivalent to non-orthogonality. Its role becomes crucial in device-dependent quantum cryptography, where the presence of preparation and detection noise (inaccessible to all parties) may be so strong to prevent the distribution and distillation of entanglement. The necessity of entanglement is re-affirmed in the stronger scenario of device-independent quantum cryptography, where all sources of noise are ascribed to the eavesdropper.
Hard Quantum Extrapolations in Quantum Cryptography
本文提出经典→量子外推任务，研究其困难性与量子承诺、量子公钥密码学和量子密钥分发等原语之间的等价或蕴含关系，并进一步提出完全量子类比，为理解量子密码学的最小假设提供新视角。
The paper has been withdrawn by the author since the protocol is not new. It is just the oldest version of BB84.
From Fundamental Dynamics to Applied Cryptography: Studies on the Quantum Speed Limit and Fully Passive Quantum Key Distribution
本文研究了量子信息处理的两个前沿领域：动态演变的基本物理限制和安全量子通信网络的实用实现。
We propose an alternative quantum cryptography protocol using the quantum interference effect. The efficiency of creating sifted key can reach 100\% in principle, which is higher than previous protocols. Especially, compared with the typical quantum key distribution, the present scheme does not require the authorized parties to check their bases. Because the potential eavesdropper can only access part of the quantum system, the proposed scheme has natural practical security advantages. The scheme can be implemented with current technologies and opens promising possibilities for quantum cryptog…
This paper describes how the communicating parties can employ intensity and state estimation to detect if the eavesdropper has siphoned off and injected photons in the received communication. This is of relevance in quantum cryptography based on random rotations of photon polarizations.
It has been shown that the predictions of some new phenomena (e.g., teleportation and cryptography) are based on some assumptions added to the quantum-mechanical model or modifying some of its basic axioms. The hitherto experiments presented as a support of the mentioned phenomena may be hardly regarded as sufficient, as they may be interpreted alternatively on the basis of simple interference processes.
We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure than protocols using two-dimensional states. We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.
A large number of quantum location verification protocols have been proposed. All existing protocols in this field are based on symmetric cryptography where verifiers and the prover use the same secret key. The prover obtains secret key from different verifiers, in pieces through public channels, which may result in security compromise. In this paper, we give a formulism to prove information-theoretic position-based quantum cryptography is possible in asymmetric quantum setting. We propose a quantum location verification protocol based on asymmetric quantum cryptographic where two different ke…
We propose and discuss a specific scheme allowing to realize a Quantum Cryptography qutrit protocol. This protocol exploits the polarization properties of single frequency and single spatial mode biphotons.
Post-quantum cryptography is inevitable. National Institute of Standards and Technology (NIST) starts standardizing quantum-resistant public-key cryptography (aka post-quantum cryptography). The reason is that investment in quantum computing is blooming which poses significant threats to our currently deployed cryptographic algorithms. As a security engineer, to prepare for the apocalypse in advance, I've been watching the development of quantum computers and post-quantum cryptography closely. Never mind, I simply made up an excuse to study these fascinating scientific fields. However, they ar…
This is a chapter on quantum cryptography for the book "A Multidisciplinary Introduction to Information Security" to be published by CRC Press in 2011/2012. The chapter aims to introduce the topic to undergraduate-level and continuing-education students specializing in information and communication technology.
By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme combines an asymmetric public key protocol with symmetric private ones and is intrinsecally secure against quantum eavesdropper attacks.
The no-cloning theorem asserts that, unlike classical information, quantum information cannot be copied. This seemingly undesirable phenomenon is harnessed in quantum cryptography. Uncloneable cryptography studies settings in which the impossibility of copying is a desired property, and achieves forms of security that are classically unattainable. The first example discovered and analyzed was in the context of cash. On the one hand, we want users to hold the cash; on the other hand, the cash should be hard to counterfeit. Quantum money uses variants of the no-cloning theorem to make counterfei…
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.
We propose a quantum transmission based on bi-photons which are doubly-entangled both in polarisation and phase. This scheme finds a natural application in quantum cryptography, where we show that an eventual eavesdropper is bound to introduce a larger error on the quantum communication than for a single entangled bi-photon communication, when steeling the same information.
A quantum cryptosystem is proposed using single-photon states with different frequency spectra as information carriers. A possible experimental implementation of the cryptosystem is discussed.
This is a Comment on Phys Rev Lett 75 (1995) 1239, by Goldenberg and Vaidman
This paper has been withdrawn by the author. It will be published again after submission to a journal.
We prove that in the BB84 quantum cryptography protocol Alice and Bob do not need to make random bases-choice for each qubit: they can keep the same bases for entire blocks of qubits. It suffices that the raw key consists of many such qubit-blocks. The practical advantage of reducing the need for random number is emphasized.
Continuous variable quantum cryptography
提出利用连续波光束的小相位和振幅调制携带密钥信息，并借助EPR型关联实现量子保护的连续变量量子密码方案。
Quantum Cryptography is on the verge of commercial application. One of its greatest limitations is over long distance - secret key rates are low and the longest fibre over which any key has been exchanged is currently 100 km. We investigate the quantum relay, which can increase the maximum distance at which quantum cryptography is possible. The relay splits the channel into sections, and sends a different photon across each section, increasing the signal to noise ratio. The photons are linked as in teleportation, with entangled photon pairs and Bell measurements. We show that such a scheme cou…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate why the density matrix is the main tool of quantum information theory. Then von Neumann entropy is introduced and with its help a great difference between classical and quantum information theory is presented: quantum entanglement. Moreover an information theoretic interpretation of quantum measurement is discussed. Data compression, error correction and nois…
Quantum Cryptography Beyond Quantum Key Distribution
本文面向不熟悉量子世界的密码学家，综述了理论量子密码学领域，重点探讨量子密钥分发之外的构造与局限性，涵盖量子货币、多方安全计算等应用及量子对手带来的挑战。
We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a previous result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical proof of this…
Methods of quantum mechanics promise information-theoretic security for various protocols in cryptography. However, impossibility of some cryptographic applications such as standard bit commitment, oblivious transfer, multiparty secure computations and ideal coin tossing in quantum regime leaves an obvious question on the completeness of quantum cryptography. Instead of using wide range of rules and techniques for a variety of cryptographic applications, we demonstrate here a unified structure for quantum cryptography based on quantum non-local correlations. The unified framework achieves same…
We assess the potential of quantum cryptography as a technology. We highlight the fact that academia and real world have rather different perspectives and interests. Then, we describe the various real life forces (different types of users, vendors of crypto-systems, conventional cryptographers, governments) behind the decision of the adoption (or rejection) of quantum cryptography and their different interests. Various roadblocks to the widespread application of quantum cryptography are discussed. Those roadblocks can be fundamental, technological, psychological, commercial or political and ma…
We describe how to modify the BB84 protocol for quantum cryptography in order to make it deterministic. We study both theoretical and experimental aspects of this issue, showing that the new scheme is as secure as the old one, more efficient on small-scale distances, and within the range of current technology.
The phenomenon of quantum erasure has long intrigued physicists, but has surprisingly found limited practical application. Here, we propose an erasure-based protocol for quantum key distribution (QKD) that promises inherent security against detector attacks.
BBN, Harvard, and Boston University are building the DARPA Quantum Network, the world's first network that delivers end-to-end network security via high-speed Quantum Key Distribution, and testing that Network against sophisticated eavesdropping attacks. The first network link has been up and steadily operational in our laboratory since December 2002. It provides a Virtual Private Network between private enclaves, with user traffic protected by a weak-coherent implementation of quantum cryptography. This prototype is suitable for deployment in metro-size areas via standard telecom (dark) fiber…
We present a game-based approach to teach Bell inequalities and quantum cryptography at high school. The approach is based on kinesthetic activities and allows students to experience and discover quantum features and their applications first-hand. We represent quantum states by the orientation of students, and mimic quantitative random behaviour and measurements using dice and apps.
In this paper we analyze the security of the so-called quantum tomographic cryptography with the source producing entangled photons via an experimental scheme proposed in Phys. Rev. Lett. 92, 37903 (2004). We determine the range of the experimental parameters for which the protocol is secure against the most general incoherent attacks.
A new cryptographic tool, anonymous quantum key technique, is introduced that leads to unconditionally secure key distribution and encryption schemes that can be readily implemented experimentally in a realistic environment. If quantum memory is available, the technique would have many features of public-key cryptography; an identification protocol that does not require a shared secret key is provided as an illustration. The possibility is also indicated for obtaining unconditionally secure quantum bit commitment protocols with this technique.
In a series of recent papers, Hirota and Yuen claim to have identified a fundamental flaw in the theory underlying quantum cryptography, which would invalidate existing security proofs. In this short note, we sketch their argument and show that their conclusion is unjustified --- it originates from a confusion between necessary and sufficient criteria for secrecy.
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstrated.
Security proof for quantum cryptography against entanglement-measurement attack
本文提出利用两种窃听检查方法证明量子密码对抗纠缠测量攻击的安全性，通过最大纠缠态协议演示证明过程。
This is a Reply to the Comment by Lydersen et al. [arXiv: 1106.3756v1].
This paper is replaced by arXiv:1009.2490. The new paper includes a general impossibility result and restricted possibility results, and it has two additional authors.
Quantum cryptography can, in principle, provide unconditional security guaranteed by the law of physics only. Here, we survey the theory and practice of the subject and highlight some recent developments.
A new quantum cryptography protocol, based on all unselected states of a qubit as a sort of alphabet with continuous set of letters, is proposed. Its effectiveness is calculated and shown to be essentially higher than those of the other known protocols.
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