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Oxford University Press eBooks

Quantum cryptography

Stephen Mark Barnett

Published May 28, 2009• 1 citation
Publisher

Abstract

The practical implementation of quantum information technologies requires, for the most part, highly advanced and currently experimental procedures. One exception is quantum cryptography, or quantum key distribution, which has been successfully demonstrated in many laboratories and has reached an advanced level of development. It will probably become the first commercial application of quantum information. In quantum key distribution, Alice and Bob exploit a quantum channel to create a secret shared key comprising a random string of binary digits. This key can then be used to protect a subsequent communication between them. The principal idea is that the secrecy of the key distribution is ensured by the laws of quantum physics. Proving security for practical communication systems is a challenging problem and requires techniques that are beyond the scope of this book. At a fundamental level, however, the ideas are simple and may readily be understood with the knowledge we have already acquired. Quantum cryptography is the latest idea in the long history of secure (and not so secure) communications and, if it is to develop, it will have to compete with existing technologies. For this reason we begin with a brief survey of the history and current state of the art in secure communications before turning to the possibilities offered by quantum communications. The history of cryptography is a long and fascinating one. As a consequence of the success or, more spectacularly, the failure of ciphers, wars have been fought, battles decided, kingdoms won, and heads lost. In the information age, ciphers and cryptosystems have become part of everyday life; we use them to protect our computers, to shop over the Internet, and to access our money via an ATM (automated teller machine). One of the oldest and simplest of all ciphers is the transposition or Caesarean cipher (attributed to Julius Caesar), in which the letters are shifted by a known (and secret) number of places in the alphabet. If the shift is 1, for example, then A is enciphered as B, B→C, · · ·, Y→Z, Z→A. A shift of five places leads us to make the replacements A→F, B→G, · · ·, Y→D, Z→E.

DOI
10.1093/oso/9780198527626.003.0006

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The practical implementation of quantum information technologies requires, for the most part, highly advanced and currently experimental procedures. One exception is quantum cryptography, or quantum key distribution, which has been successfully demonstrated in many laboratories and has reached an advanced level of development. It will probably become the first commercial application of quantum information. In quantum key distribution, Alice and Bob exploit a quantum channel to create a secret shared key comprising a random string of binary digits. This key can then be used to protect a subsequent communication between them. The principal idea is that the secrecy of the key distribution is ensured by the laws of quantum physics. Proving security for practical communication systems is a challenging problem and requires techniques that are beyond the scope of this book. At a fundamental level, however, the ideas are simple and may readily be understood with the knowledge we have already acquired. Quantum cryptography is the latest idea in the long history of secure (and not so secure) communications and, if it is to develop, it will have to compete with existing technologies. For this reason we begin with a brief survey of the history and current state of the art in secure communications before turning to the possibilities offered by quantum communications. The history of cryptography is a long and fascinating one. As a consequence of the success or, more spectacularly, the failure of ciphers, wars have been fought, battles decided, kingdoms won, and heads lost. In the information age, ciphers and cryptosystems have become part of everyday life; we use them to protect our computers, to shop over the Internet, and to access our money via an ATM (automated teller machine). One of the oldest and simplest of all ciphers is the transposition or Caesarean cipher (attributed to Julius Caesar), in which the letters are shifted by a known (and secret) number of places in the alphabet. If the shift is 1, for example, then A is enciphered as B, B→C, · · ·, Y→Z, Z→A. A shift of five places leads us to make the replacements A→F, B→G, · · ·, Y→D, Z→E.
Cryptography has evolved alongside the development of communication and computing technologies, transitioning from simple manual techniques to complex quantum-resistant algorithms. This journey reflects humanity’s need to secure information in an increasingly interconnected world. The evolution of cryptographic methods highlights humanity’s continuous effort to protect privacy and secure communication. As the world transitions into the quantum era, cryptography must advance to meet the challenges posed by emerging technologies. During the early age, techniques such as Substitution and Transposition ciphers were used. In Substitution Cipher, letters in a message were replaced with other letters according to a fixed rule, and in Transposition Ciphers, the letters of a message were reordered to obscure its meaning. The limitations were that it was easily broken once the substitution or transposition rule was discovered. Subsequently, devices like Enigma machine used rotors for implementing complex substitution ciphers, and the breaking of the Enigma code by allied cryptanalysts marked a turning point in cryptography and cryptanalysis.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).
Lack of understanding of the ideas of quantum physics leads to the fact that the very word "quantum" begins to be perceived as a synonym for something mysterious, incomprehensible, and even doubtful. The arising errors sometimes lead to inadequate media coverage of the development of quantum technologies, as the case with the ignorant reaction of the press in June 2016 to the statement of the Russian authorities about the prospects of quantum teleportation, which some media presented as teleportation from science fiction. Such misunderstandings can impede the formation of the necessary trust in quantum technologies on the part of the business community, politicians and the public. In part, the reason for this state of the art may be the insufficient attention of physicists themselves to the development of popular scientific and pedagogical discourse, which makes it possible to correctly introduce the ideas of quantum mechanics into the context of general culture. For decades, physicists have flaunted the kind of esotericism of quantum mechanics. Journalists love to quote the classics of quantum physics: “Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niels Bohr); “I think I can safely say that nobody understands quantum mechanics” (Richard Feynman); “Quantum mechanics is absolutely meaningless” (Roger Penrose) [1]. Indeed, for many quantum-scale phenomena, no analogues have yet been found in the everyday world, and they are difficult to express in our everyday language. As a result, the introduction to quantum mechanics begins with a description of the mathematical formalism, which becomes an obstacle for the untrained listener and is not suitable for popularization. Moreover, such an approach creates problems for physicists themselves: many of them, studying the mathematical formalism of quantum mechanics and being convinced in practice of its effectiveness, do not ask the question of how the founders of this science were able to go in the opposite direction and, starting from experience, find the required formalism. As a result, important problematic and heuristic aspects of the development of science may drop off even professional physicists’ radar. In view of the above, an important task is to find effective explanatory techniques that allow one to talk about quantum phenomena without resorting to mathematical apparatus and without abuse of doubtful metaphors. This article attempts to find such an approach to explaining quantum cryptography. The choice in its favor is determined by the fact that it is one of the most mature quantum technologies of the second generation, which is already beginning to generate a demand for technical specialists to set up and maintain secure quantum communication lines. This activity requires a general understanding of the ideas of quantum mechanics underlying the technology, but at the same time, it does not require full knowledge of the mathematical apparatus that is used in research and development. In accordance with this, the task was set to outline the principle of quantum cryptography without resorting to such abstract concepts as the state space of a quantum system, its bases and the choice between them in quantum measurement. In a popular scientific sense, the advantage of quantum cryptography is a simplicity for understanding. Our experience shows that its main points can be explained to students in about half an hour without extraordinary mental effort. It is also enigmatical and fascinating, since, on the one hand, it is associated with spy codes, and on the other hand, it provides protection based on the laws of nature. Methodologically, the positive aspect of quantum cryptography is valuable. Many fundamental premises of quantum physics are negative: the impossibility of making any measurement without affecting the system, the Heisenberg uncertainty principle, the nocloning theorem. At the same time, quantum cryptography, on the contrary, allows an absolutely secure distribution of the encryption key.
Quantum computing and quantum cryptography are two areas of research that have the potential to transform modern computing and communication. Quantum computing promises to solve computational problems that are beyond the reach of classical computers, while quantum cryptography provides a way to secure communication channels that is immune to eavesdropping. Quantum cryptography is one of the emerging topics in the field of computer industry. This article focuses on quantum cryptography and how this technology makes a valuable contribution to an intensive defense strategy of completely secure key distribution. The scope of this article covers the weaknesses of modern digital cryptographic systems, the basic concepts of quantum cryptography, the practical implementations of this technology, and its limitations. , and finally the future direction that quantum cryptography is headed. We describe the result of an apparatus and protocol designed to perform quantum key distribution, whereby two users do not share any secret information (no private or public keys are known). previously known) initially exchanges a random quantum transmission consisting of veryweakly polarized light rays. In particular, readers can explore the following topics in depth: current cryptographic schemes (symmetric and asymmetric), the difference between quantum and classical computing, challenges of quantum computing, quantum algorithms (Shor and Grover), public key cryptographic schemes affected, symmetry affected schemes, impact on hash functions and post-quantum cryptography
ABSTRACT. The combination of physics, mathematics, and computer science in quantum computing has developed from a visionary idea to one of the most fascinating and promising areas of quantum mechanics in the past two decades. Research in the field of quantum cryptography promises extremely fast, robust, and impenetrable electronic and photonic security; almost unbreakable! Moreover, the long standing eavesdropping problem of the “man in the middle ” attack may finally be solved once and for all. As computing power increases, and as hackers and attackers become more sophisticated, it is feared that sooner or later, traditional cryptography based on mathematically intractable algorithms may be no match for parallelized quantum based processors. For this reason, quantum cryptography, based on the laws of quantum statistical mechanics provides a welcome solution to this fear. This paper explores the basic tenets of quantum cryptography and how the mathematical principles therein apply to the quantum key distribution problem; a central concern in the implementation of quantum cryptography in distributed networks. The quantum key distribution protocol implemented in BB84 protocol is also described and compared to traditional cryptographic systems. A short overview of recent commercial implementations of quantum cryptography is presented with the encountered successes and limitations discussed. This paper explores the development of quantum networks, from the onset of the development of secure communication based on quantum cryptography and concludes with a brief outline of the key challenges facing quantum cryptography implementation in wireless applications and long haul communications.
Quantum Cryptography is a novel approach to make the information and network world more secure. Unlike classical cryptography, quantum cryptography ensures the security of communication because it is based on the laws of Quantum Mechanics; a branch of physics that deals with the fundamental behavior of matter and their energies to the levels of subatomic particles. These particles and their intrinsic properties such as photon polarization and entanglement allow us to develop an unbreakable system of cryptographic information. Conventionally, the security has been primarily concerned with the secured distribution of secret key carried over an insecure channel. However, in Quantum Cryptographic systems the transmission of secret key is done using aforementioned laws of nature through a secured quantum channel highly susceptible to intrusion detection. Consequently, the Quantum Key Distribution (QKD), in conjunction with protocols such as BB84 protocol has emerged as an ultimate modern secured communication system. This article concentrates on briefly reviewing quantum cryptography, some recent developments and reports of its vulnerabilities.