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From Quantum Cheating to Quantum Security

Daniel Gottesman, Hoi‐Kwong Lo

Published Jan 1, 2000• 44 citations
OpenAlex

Abstract

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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Cryptography—the art of code-making—has a long history of military and diplomatic applications, dating back to the Babylonians. In World War II, the Allies' feat of breaking the legendary German code Enigma contributed greatly to their final victory. Nowadays, cryptography is becoming increasingly important in commercial applications for electronic business. 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.

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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.

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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).

Cambridge University Press eBooks•Jul 19, 2012•0 citations
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 —
Cryptography—the art of code-making—has a long history of military and diplomatic applications, dating back to the Babylonians. In World War II, the Allies' feat of breaking the legendary German code Enigma contributed greatly to their final victory. Nowadays, cryptography is becoming increasingly important in commercial applications for electronic business. 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.
ABSTRACT Q uantum mechanics can revolutionize the art of code-making by breaking standard encryption schemes and by making unbreakable codes. In this document, I survey the motivation, power and limitation of quantum code-making. * Keywords: Quantum computing, quantum information, quantum cryptography, security, key distribution,cryptography 1. INTRODUCTION Human desire to keep written messages secret is almost as old as writing itself. Indeed, cryptography—the artof code-making—dated back to the Babylonians. For thousands of years, code-makers and code-breakers have engaged in an escalating arms race with each other.' Cryptographers do not sleep well. Every innovation in code-making has so far been defeated by new innovation in code-breaking with disastrous consequence tothe unsuspecting users of those insecure codes. For instance, Queen Mary of Scotland was executed by QueenElizabeth following the decoding of encrypted communications between Queen Mary and her conspirators whichprovided the irrefutable proof of her quilt in plotting against Queen Elizabeth. In the Second World War, thebreaking of the legendary German Engima code by the Allied code-breakers contributed significantly to theoutcome of the war. In cryptography, one must expect the unexpected and even the unthinkable.Q uantum mechanics has made a recent entry in this life and death struggle between code-makers and code-23 In this document, I will address the following frequently asked questions:(1) What quantum code-breaking can do?(2) What quantum code-making can do?(3) What quantum code-making cannot do?
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.
A product is on the way that relies on the quantum properties of photons to keep out eavesdroppers. All of them. The battle between codemakers and codebreakers is centuries old, but at the start of the 21st century, could it finally be drawing to a close? Physicists are putting the finishing touches to a method of encrypting messages that is more secure than anything that has gone before. Unlike the ciphers of the past, this new method has the potential to be absolutely unbreakable, not just practically unbreakable, but theoretically unbreakable. Mathematicians believe they can prove it. Central to the technique are the strange laws of quantum mechanics. Already experimental messages encrypted using quantum mechanics are being sent over tens of kilometers of optical fibers and received securely. Researchers are confident that it will not be long before ultra-secret messages are routinely transmitted in this way. But while quantum cryptography may be perfect in theory, practical considerations introduce security loopholes that an eavesdropper can exploit. The seriousness of these is still unclear, and physicists believe they can plug most of the holes with more efficient equipment. Still, enough cracks remain to maintain a healthy interest among cryptographers.
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).