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Cambridge University Press eBooks

Quantum Cryptography

Daniel F. Styer

Published Feb 24, 2000• 0 citations
Publisher

Abstract

Quantum mechanics is valuable because it opens a discussion about the nature of reality, because it demonstrates the power of reason in revealing the truth even when common sense is an obstacle, and simply because it is good to know how our universe ticks (“knowledge is better than ignorance”). But it is also valuable because a host of practical devices, from lasers to transistors to superconductors, all work because of quantum mechanics. Most of these applications are beyond the scope of this book. I could tell you in vague terms how a laser works, but I could never convince you that my description was correct — you would have to accept it on my authority, and acceptance on the basis of authority is the very antithesis of scientific thought. However, there is one very recent, very exciting application of quantum mechanics that can be treated in full within the “rigorous but not technical” style of this book, namely the use of quantum mechanics to send coded messages. (You may skip this chapter without interrupting the flow of the book's argument.) Can you keep a secret? Sending coded messages is a part of life. Governments and businesses need to transmit secrets that would be deadly in the wrong hands (military plans, formulas for explosives, etc.). But even you have information that you don't want everyone in the world to know: your bank balance, your voting record, your vacation plans. I'm not suggesting that you should be embarrassed about your bank balance, but it's your private information and no eavesdropper has any right to it.

DOI
10.1017/cbo9781107050709.014

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For thousands of years, code-makers and code-breakers have been competing for supremacy. Their arsenals may soon include a powerful new weapon: quantum mechanics. Cryptography — the art of code-making — has a long history of military and diplomatic applications, dating back to the Babylonians. In World World Two, the Allies ’ feat of breaking the legendary German code, Enigma, contributed greatly to the final Allied victory. Nowadays, cryptography is becoming increasingly important in commercial applications for electronic business and electronic commerce. Sensitive data such as credit card numbers and personal identification numbers (PINs) are routinely transmitted in encrypted form. Quantum mechanics is a new tool for both code-breakers and code-makers in their eternal arms race. It has the potential to revolutionize cryptography both by creating perfectly secure codes and by breaking standard encryption schemes. The most well-known application of cryptography is secure communication [1]. Suppose Alice would like to send a message to Bob, but there is an eavesdropper, Eve, who is wiretapping the channel. To prevent Eve from knowing the message, Alice and Bob may perform encryption, i.e., transform the message to something that is not intelligible to Eve during the communication. On receiving the message, Bob inverts the transformation and recovers the message (see figure 1). Bob’s advantage over Eve lies in his knowledge of a secret, commonly called the key, that he shares with Alice. The key tells him how to decode the message. For example: The rumble of Soviet tanks shook the Prague hotel room (number 117) as secret agent John Blond finished decoding his orders from his superior N. He tore the used page from the codebook and immediately burned it with his lighter. Blond is using a perfectly unbreakable cipher, a “one-time pad. ” The secret codebook allows N and Blond to share a long secret binary string — the key —

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THE GREAT CHAIN OF QUANTUM BEING: WHAT THE PHYSICISTS ARE TELLING US / Louis Gallo listen: there's a hell of a good universe next door; let's go —cummings Max Planck's announcement in 1900 that energy flows in discrete bundles rather than uniformly, as energy "should," did not instantly destroy the foundations of a classical world view that had prevailed since Newton's day. It took physicists nearly a quarter of a century to grasp the full significance of quantum theory. But 1900 is too convenient a date to ignore, and without distorting the history of ideas unduly we can refer to it as the point in time when science launched its relentless assault upon reason and common sense, an assault that continues to this day. This is nothing new, of course. Everyone knows how weird quantum theory is, how it toppled the Newtonian clockwork and so on. The purpose of this essay is to explain in ordinary language, if such a thing can be done, why physicists are saying some of the outrageous things we read about in the popular media. Because new particles, along with new theories to account for them, are being created at such a prodigious rate today, it has become extraordinarily difficult for non-scientists to keep up with the latest breakthroughs. The deluge of popular books on black holes and particle physics, outmoded before they go to press, reflects this information gap. I can hardly expect to beat the popularizers at their own game, but my intention is nevertheless to present a non-technical overview of the great chain of quantum being according to current theory. It can be suggested by way of preliminary assessment that the Theater of the Absurd did not die at some point in the early 1970s; its greatest production is and may always have been our meditations on the cosmos itself. We begin, however, with some thoughts on common sense rather than absurdity. Physicists have traditionally linked common sense with the twin doctrines of causality and determinism. Given thorough enough information about prior conditions, causality guarantees the predictability of all events and states ofbeing. French mathematician Pierre Laplace actually believed that such knowledge could be used to chart the entire history of the universe. Causality, then, is a way of thinking about individual events; determinism, a way of thinking about events 264 · The Missouri Review cumulatively. Both doctrines presume the existence of an objective, quantifiable external world populated by observers (ourselves). One cannot overemphasize the importance of the term "objective." It haunts modern physics at every turn. Indeed, the crucial difference between classical and quantum physics lies in their respective acceptance or rejection of objective reality. The early giants of quantum physics had a hard time accepting the implications of their own mathematics. Max Planck and Einstein—who is not, strictly speaking, a quantum physicist but who contributed much to the theory—refused to accept them. Yet the fate of objectivity may be traced by moving from Planck's position on the subject to that of Erwin Schrödinger, whose work culminated in the late 1920s. This chronology roughly reflects the order in which quantum theory emerged. Here is what Planck had to say in his book The New Science: "A science that starts off by predicating the denial of objectivity has already passed sentence on itself"; and "the quantum hypothesis will eventually find its exact expression in certain equations which will be a more exact formulation of the law of causality." Einstein spent most of his life searching for that "exact expression" and failed. Werner Heisenberg offered a similar but highly qualified version of Planck's statement. In Across the Frontiers Heisenberg says that quantum measurements do in fact measure objective states but also intrude upon those states. "It is," he writes, "no longer the objective states but rather the probabilities for the occurrence of certain events that can be stated in mathematical formulae." Schrödinger, in Mind and Matter, comes right out with it: "Mind has erected the objective outside world of the natural philosophers out of its own stuff." He means this literally, and the equations he contributed to quantum theory imply as much. Bohr...

The Missouri Review•Jan 1, 1984•0 citations
Quantum mechanics is valuable because it opens a discussion about the nature of reality, because it demonstrates the power of reason in revealing the truth even when common sense is an obstacle, and simply because it is good to know how our universe ticks (“knowledge is better than ignorance”). But it is also valuable because a host of practical devices, from lasers to transistors to superconductors, all work because of quantum mechanics. Most of these applications are beyond the scope of this book. I could tell you in vague terms how a laser works, but I could never convince you that my description was correct — you would have to accept it on my authority, and acceptance on the basis of authority is the very antithesis of scientific thought. However, there is one very recent, very exciting application of quantum mechanics that can be treated in full within the “rigorous but not technical” style of this book, namely the use of quantum mechanics to send coded messages. (You may skip this chapter without interrupting the flow of the book's argument.) Can you keep a secret? Sending coded messages is a part of life. Governments and businesses need to transmit secrets that would be deadly in the wrong hands (military plans, formulas for explosives, etc.). But even you have information that you don't want everyone in the world to know: your bank balance, your voting record, your vacation plans. I'm not suggesting that you should be embarrassed about your bank balance, but it's your private information and no eavesdropper has any right to it.
For thousands of years, code-makers and code-breakers have been competing for supremacy. Their arsenals may soon include a powerful new weapon: quantum mechanics. Cryptography — the art of code-making — has a long history of military and diplomatic applications, dating back to the Babylonians. In World World Two, the Allies ’ feat of breaking the legendary German code, Enigma, contributed greatly to the final Allied victory. Nowadays, cryptography is becoming increasingly important in commercial applications for electronic business and electronic commerce. Sensitive data such as credit card numbers and personal identification numbers (PINs) are routinely transmitted in encrypted form. Quantum mechanics is a new tool for both code-breakers and code-makers in their eternal arms race. It has the potential to revolutionize cryptography both by creating perfectly secure codes and by breaking standard encryption schemes. The most well-known application of cryptography is secure communication [1]. Suppose Alice would like to send a message to Bob, but there is an eavesdropper, Eve, who is wiretapping the channel. To prevent Eve from knowing the message, Alice and Bob may perform encryption, i.e., transform the message to something that is not intelligible to Eve during the communication. On receiving the message, Bob inverts the transformation and recovers the message (see figure 1). Bob’s advantage over Eve lies in his knowledge of a secret, commonly called the key, that he shares with Alice. The key tells him how to decode the message. For example: The rumble of Soviet tanks shook the Prague hotel room (number 117) as secret agent John Blond finished decoding his orders from his superior N. He tore the used page from the codebook and immediately burned it with his lighter. Blond is using a perfectly unbreakable cipher, a “one-time pad. ” The secret codebook allows N and Blond to share a long secret binary string — the key —
Abstract The Internet can be thought of as a channel of information being sent from you to everyone else connected to the Internet. If you wanted to transmit your sensitive information (such as bank account numbers or military secrets) over the Internet, then you have to ensure that only the persons you intend to read your information have access to your sensitive data. Otherwise, everyone would be able to read your information, e.g., access to your bank account details and transfer money out of your account. Therefore, one needs to encrypt any data sent over the Internet. Encryption, in this context, ensures that only the intended sender and receiver can understand any message being sent over an Internet channel.
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.
The concept of quantum computing is based on two fundamental principles of quantum mechanics: superposition and entanglement. Instead of using bits, qubits are used in quantum computing, which is a key indicator in the high level of safety and security this type of cryptography ensures. If interfered with or eavesdropped in, qubits will delete or refuse to send, which keeps the information safe. This is vital in the current era where sensitive and important personal information can be digitally shared online. In computer networks, a large amount of data is transferred worldwide daily, including anything from military plans to a country’s sensitive information, and data breaches can be disastrous. This is where quantum cryptography comes into play. By not being dependent on computational power, it can easily replace classical cryptography.Limitations and Future Applications of Quantum Cryptography is a critical reference that provides knowledge on the basics of IoT infrastructure using quantum cryptography, the differences between classical and quantum cryptography, and the future aspects and developments in this field. The chapters cover themes that span from the usage of quantum cryptography in healthcare, to forensics, and more. While highlighting topics such as 5G networks, image processing, algorithms, and quantum machine learning, this book is ideally intended for security professionals, IoT developers, computer scientists, practitioners, researchers, academicians, and students interested in the most recent research on quantum computing
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.
THE GREAT CHAIN OF QUANTUM BEING: WHAT THE PHYSICISTS ARE TELLING US / Louis Gallo listen: there's a hell of a good universe next door; let's go —cummings Max Planck's announcement in 1900 that energy flows in discrete bundles rather than uniformly, as energy "should," did not instantly destroy the foundations of a classical world view that had prevailed since Newton's day. It took physicists nearly a quarter of a century to grasp the full significance of quantum theory. But 1900 is too convenient a date to ignore, and without distorting the history of ideas unduly we can refer to it as the point in time when science launched its relentless assault upon reason and common sense, an assault that continues to this day. This is nothing new, of course. Everyone knows how weird quantum theory is, how it toppled the Newtonian clockwork and so on. The purpose of this essay is to explain in ordinary language, if such a thing can be done, why physicists are saying some of the outrageous things we read about in the popular media. Because new particles, along with new theories to account for them, are being created at such a prodigious rate today, it has become extraordinarily difficult for non-scientists to keep up with the latest breakthroughs. The deluge of popular books on black holes and particle physics, outmoded before they go to press, reflects this information gap. I can hardly expect to beat the popularizers at their own game, but my intention is nevertheless to present a non-technical overview of the great chain of quantum being according to current theory. It can be suggested by way of preliminary assessment that the Theater of the Absurd did not die at some point in the early 1970s; its greatest production is and may always have been our meditations on the cosmos itself. We begin, however, with some thoughts on common sense rather than absurdity. Physicists have traditionally linked common sense with the twin doctrines of causality and determinism. Given thorough enough information about prior conditions, causality guarantees the predictability of all events and states ofbeing. French mathematician Pierre Laplace actually believed that such knowledge could be used to chart the entire history of the universe. Causality, then, is a way of thinking about individual events; determinism, a way of thinking about events 264 · The Missouri Review cumulatively. Both doctrines presume the existence of an objective, quantifiable external world populated by observers (ourselves). One cannot overemphasize the importance of the term "objective." It haunts modern physics at every turn. Indeed, the crucial difference between classical and quantum physics lies in their respective acceptance or rejection of objective reality. The early giants of quantum physics had a hard time accepting the implications of their own mathematics. Max Planck and Einstein—who is not, strictly speaking, a quantum physicist but who contributed much to the theory—refused to accept them. Yet the fate of objectivity may be traced by moving from Planck's position on the subject to that of Erwin Schrödinger, whose work culminated in the late 1920s. This chronology roughly reflects the order in which quantum theory emerged. Here is what Planck had to say in his book The New Science: "A science that starts off by predicating the denial of objectivity has already passed sentence on itself"; and "the quantum hypothesis will eventually find its exact expression in certain equations which will be a more exact formulation of the law of causality." Einstein spent most of his life searching for that "exact expression" and failed. Werner Heisenberg offered a similar but highly qualified version of Planck's statement. In Across the Frontiers Heisenberg says that quantum measurements do in fact measure objective states but also intrude upon those states. "It is," he writes, "no longer the objective states but rather the probabilities for the occurrence of certain events that can be stated in mathematical formulae." Schrödinger, in Mind and Matter, comes right out with it: "Mind has erected the objective outside world of the natural philosophers out of its own stuff." He means this literally, and the equations he contributed to quantum theory imply as much. Bohr...