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[12.0] Frontiers In Cryptology

v2.4.0 / chapter 12 of 13 / 01 sep 16 / greg goebel

* The general public now has access to very strong ciphers, a fact which has led to political controversy. New, even stronger, ciphers and codebreaking schemes based on the subtle principles of quantum physics are in the works. This chapter discusses the politics of ciphers and quantum cryptology.


[12.1] ENCRYPTION WARS
[12.2] THE ENCRYPTION QUANDARY
[12.3] QUANTUM COMPUTING & CODEBREAKING
[12.4] QUANTUM CRYPTOGRAPHY

[12.1] ENCRYPTION WARS

* Phil Zimmermann's problems with the authorities over PGP were the leading edge of a war over public cryptosystems. Zimmermann and other civil-liberty activists felt private citizens had a right to strong encryption, while the government believed such technologies would give away too much to terrorists and criminals.

In 1994, worried about the spread of encryption, the Clinton White House announced the intent to set up a cryptosystem in which the government would perform "key escrow", retaining the private keys of all the users. The cryptosystem was known as the "American Escrowed Encryption Standard". It involved two encryption standards, one named "Clipper" for telephone communications and the other named "Capstone" for computer communications. In this scheme, Alice could buy a phone with a Clipper chip in it, and when she obtained the phone, the government would receive the private key for it. The key would be split in half, with each key provided to a different government organization. A law enforcement agency would have to go to both organizations to obtain the full key.

The US government mandated the use of Clipper and Capstone for its own use, and pressured companies doing business with the government to do the same. There was some basis for a private key escrow system; it would provide insurance for an organization in case a private key was lost, or an angry employee left a company and didn't bother to tell anyone the key, and so on. Critics suggested that the government's desire to escrow cipher keys had about the same level of logic and desireability as would a government effort to escrow keys to the doors of all the homes of citizens.

The government, however, was the only entity in favor of the scheme. The industry response was overwhelmingly negative -- one protest being that the Clipper Chip would make US products unattractive to foreign buyers. By 1996, the Clipper Chip had been effectively abandoned. In the spring of 1999, the German government announced that it would help support the development of GNUPG and recommend it to German citizens. The French government formally scrapped attempts at key escrow; the Canadian government formally announced a "hands-off" policy towards encryption, and in the US the Clinton Administration announced in a policy statement on cryptographic export that stated: "Americans will remain free to use any encryption system domestically."

In the summer of 2000, the Clinton Administration followed up this move by relaxing the restrictive export controls on cryptographic software that had been the law, much to the relief of US crypto-technology companies. A precedent of sorts had been set for the right to strong encryption, but the difficulty was that no definitive decision was made in court.

* In any case, the issue went silent for over a decade. Even the destruction of the World Trade Center towers in New York City by Islamic terrorists on 11 September 2001 did not revive the public controversy over strong encryption. It did, however, result in an energetic, if low profile, drive by the NSA to develop a more comprehensive and powerful system for mass surveillance of digital traffic. The centerpiece of the effort would be codenamed PRISM -- which was a system in which the NSA monitored the traffic of major US internet service providers.

PRISM performed "bulk collection" of the "metadata" that made up the traffic to pick out patterns from the flood. If suspicious individuals were picked out, they were then subjected to "targeted surveillance" -- subject to a warrant by a Federal court that had been established by the 1978 Foreign Intelligence Surveillance Act (FISA). With the expansion in surveillance, the FISA court expanded to become what some claimed was "almost a parallel Supreme Court". Congressional committees also performed oversight.

As surveillance ramped up, new encryption technologies emerged to complicate the issue:

Much to the exasperation of the authorities, TOR and bitcoin helped promote the emergence of an illicit "dark web", which was used for dealing in drugs and other criminal transactions. However, it wasn't until 2013 that the encryption issue really went back on the front pages, when Edward Snowden -- an NSA contractor -- fled the US and publicly disclosed extensive NSA documents on PRISM and the NSA's public mass-surveillance program. The result was an international uproar over US surveillance. Privacy advocates regarded Snowden, who obtained asylum in Russia, as a hero, while the government regarded him as a traitor.

It doesn't appear Snowden had access to any big secrets, his revelations being painted in loud colors but with a very broad brush. Nothing that was revealed was much surprise to those knowledgeable of US intelligence activities; public reaction was overheated and exaggerated. For example, claims that the US had tapped the phone of German Chancellor Angela Merkel were investigated by the German authorities, and were found to be false.

The German authorities did register concerns over the extent of US surveillance -- though US intelligence collaborated closely with German intelligence on sharing of data on terrorists. Other protests by the French were even more dubious; the French not only collaborated with the US on intelligence, but had their own public surveillance systems. Due to ongoing terrorist attacks on French soil, the French government gave their intelligence services well more leash than the US government gave the NSA.

In early 2014, US President Barack Obama announced changes to the US surveillance system -- but critics judged them largely cosmetic. Obama said he had no reason to believe that the NSA gone beyond the bounds, and heads were not going to roll. Mass surveillance would continue, though oversight would be enhanced. The limited response was not surprising: if a major terrorist attack took place on US soil, the government would be pilloried for not having taken every reasonable, or even unreasonable, step to prevent it.

* That did not, however, mean a return to business as usual. Snowden's revelations led a number of tech companies to integrate encryption more tightly and seamlessly into their products, and enabling it as a default setting. Computer-maker Apple released their iOS 8 operating system in 2014, which established security as a major selling point; internet giant Google soon followed with a security-focused release of their Android operating system. Apple, however, went beyond the competition by telling the world that Apple's business model didn't involve harvesting and mining user data the way that, say, Google, Facebook, and Amazon did.

The authorities grew restless as vendors began to push security, worried that it would allow terrorists and criminals to "go dark", to successfully evade surveillance. The stage was set for a collision between Apple and the US government.

On 2 December 2015, In San Bernadino CA Syed Rizwan Farook, who worked for the San Bernadino county department of public health, and his wife Tashfeen Malik gunned down 14 people and wounded 22 others at a department holiday luncheon. The killers were gunned down themselves later that day in a shootout with police.

The FBI canvassed the residence of the late terrorists, and found among other things three smartphones. Two had been broken, but the third was intact. It technically wasn't Farook's phone; it belonged to San Bernadino county and Farook used it as his work phone. It didn't seem likely there was much of interest on the third smartphone -- otherwise it would have been broken as well -- but the FBI wanted to inspect it anyway. The problem was that the phone demanded a four-digit passcode and used login throttling, delaying for a longer time after each failed passcode input. After ten failed attempts, the phone would wipe its contents.

The FBI had been talking to Apple about things to try to get into the phone. When they all failed, the FBI asked Apple to create a special version of the phone operating system without login throttling and the ten-guess limit, then install it on Farook's phone. Apple officials gave the matter serious thought, and then replied: NO.

A fury of public condemnation descended on Apple -- but Apple also had friends, with a torrent of "amicus curae" briefs in defense of the firm being sent to the courts by technology firms such as AT&T, eBay, Kickstarter, Twitter, and Cisco. Even Apple's direct competitors -- Amazon, Facebook, Google, and Microsoft -- stood up to defend the company.

Indeed, while Apple's position might have seemed outrageous at first hearing, once the issues were laid out, a sensible person would have had second thoughts. In the first place, the internet is an insecure place, full of Black Hats; Apple officials felt the company had an obligation to its customers to make sure the Apple products being used were secure, to the extent that even Apple couldn't break into them. If Apple could break in, so could the Black Hats.

On the other side of that coin, anybody could find strong encryption tools on the global internet, and there was no realistic way of prevent them from doing so. The only result of preventing Apple and other technology firms from providing strong encryption would be to drive users into the hands of foreign, possibly dodgy, providers of encryption systems. The slogan emerged that it made no sense to improve internet security by undermining it.

The FBI argued in reply that all the government wanted was for Apple to break into one phone, with the permission of the owners of that phone -- San Bernadino county. Apple was unimpressed, saying that once on iPhone was broken open, any other one could be as well, and doing so would set a legal precedent, which the FBI conceded. Apple would then get a stream of court orders, demanding the company crack more iPhones; district attorneys were already standing in line to do so.

Having opened the gate, could it ever be closed again? Apple Chief Executive Officer Tim Cook said: "This case was domestic terrorism, but a different court might view that robbery is one. A different one might view that a tax issue is one. A different one might view that a divorce issue would be okay. And so we saw this huge thing opening and thought: You know, if this is where we're going, somebody should pass a law that makes it very clear what the boundaries are. This thing shouldn't be done court by court by court by court."

Also, what would happen if China demanded that Apple crack an iPhone belonging to a political dissident? To be sure, American legal precedent doesn't mean much in China -- but Apple only does business in China subject to Chinese law, and once Apple demonstrated they would crack open a phone, that's all the precedent the Chinese government would need.

* As Cook also pointed out, the authorities didn't really have much to complain about. They could, legally and without much difficulty, get their hands on torrents of data that simply didn't exist a generation ago: social media, phone connections, security cameras, the growing "internet of things". The law could obtain the call records for the San Bernadino terrorists, detailing who they called.

By that time, the authorities had even figured out ways of penetrating bitcoin networks. There was a subtle bias in the "shell game" that bitcoin played that allowed messages to be traced back to their sources in the bitcoin network. Bitcoin enthusiasts had played it up as impregnable -- but that was an ancient delusion of cryptology. The underlying blockchain proved a trap to bitcoin traders, since it provided a validated record of all their bitcoin transactions.

In other words, even without the cooperation of vendors, the authorities could still crack cryptosystems, though it might take a lot of effort. Cook said: "Going dark? This is a crock! No one's going dark ... We should take a step back and look at the total that's available, because there's a mountain of information about us."

As Cook put it: "It wasn't very long ago when you wouldn't even think about there being health information on the smartphone. There's financial information. There's your conversations, there's business secrets. There's probably more information about you on here than exists in your home."

Cook echoed the findings of a report published earlier in 2016 by Harvard's Berkman Center for Internet & Society, signed by an impressive roster of legal and security professionals. The report pointed out how business data-mining; the growth of cloud computing; and the expanding internet of things all undermine privacy and security: "These are prime mechanisms for surveillance, alternative vectors for information-gathering that could more than fill many of the gaps left behind by sources that have gone dark -- so much so that they raise troubling questions about how exposed to eavesdropping the general public is poised to become."

Tim Cook accepted that as the reality; but then wondered, if we can't draw the line of intrusion at strong encryption, is there any line at all? He questioned the right of the government to have access to data that runs through Apple's pipelines, when the company itself didn't feel it had a right to access that data: "I think [Apple customers] should have a reasonable expectation that your communication is private."

The confrontation was abruptly called off when the FBI announced that a third party -- believed to the mysterious NSO Group, a cryptological firm in Israel but owned by an American company -- had cracked the iPhone. The issue hadn't really been resolved, however, no legal precedent having been set on the propriety of strong encryption for the public. The authorities were poised to move against Apple again when events required it, while Apple worked to make sure the iPhone was even more impregnable. One way or another, things are going to be resolved, but nobody really knows how or when.

BACK_TO_TOP

[12.2] THE ENCRYPTION QUANDARY

* The struggle between the FBI and Apple was no more than the tip of the iceberg of the fundamental dilemma of modern information technology (IT). We have embraced IT to the point where it has become essential to society, and often essential to individuals. At the same time, it has inescapably left citizens wide-open to a high level of surveillance -- and there's limits to what can or even should be done about it.

The state does have a right -- not unrestricted -- to conduct surveillance to protect public safety, and a right -- again, not unrestricted -- to keep secrets. The state has an obligation to prevent the Black Hats from committing acts of terror, and the state will necessarily keep secrets in that effort; otherwise, the Black Hats would be able to stay a step ahead of the authorities. Although civil libertarians question both these premises, they are in practice unassailable. The only question is where the rights of citizens lie, and so where the state must draw the line.

The line cannot and will not be drawn at an unrestricted right to privacy. Those who assert a right to complete privacy may on the other hand maintain that public officials do not have that same right, since such secrecy is not in the public interest. This line of reasoning could be gradually stretched to corporate officials; officials of religious groups; officials of non-profit organizations, such as political and advocacy groups; and back to individuals again. We do have a right to privacy, but we also have an obligation to transparency, and there has to be a balance between the two.

The US Constitution does not assert a specific right to privacy. When privacy concerns face off with First Amendment freedom-of-speech issues in US courts, privacy often loses. The Fourth Amendment, which outlaws unreasonable search and seizure, and the Fifth Amendment, which requires the US government to provide compensation for seizure of properties, do have implications for privacy, and the US Supreme Court judged in 1984 that Fifth Amendment protection of property extends to data. Following that precedent, more recent lower court decisions have established that defendants may "plead the Fifth" -- invoke their Fifth Amendment right to not incriminate themselves -- and not provide passwords to a court.

However, there are few specific guarantees for privacy in the law. The US government's right to wiretapping has been well established, though certain legal safeguards are required. The 1974 Federal Privacy Act restricted the US government to storing only "relevant and necessary" data on citizens, but this is obviously vague. US states have passed their own privacy laws, only to open up loopholes, such as permitting the mandatory drug testing of college athletes.

Western European countries take a different approach to the issue of individual rights than the US. For example, few of these governments have any stated rights of free public expression comparable to those expressed by the US First Amendment, but in compensation many of these governments have passed privacy laws far stronger than any in the United States. The European Union "Common Position" document for the European Parliament proclaims a "fundamental right" to the privacy of personal data. The document also proposes that EU governments not provide data to governments that do not meet such privacy guidelines, and so some European countries have banned provision of marketing or other personal data to the US government and US companies. However, this could be seen more as a trade-protection tactic than a defense of ethical principles.

* How privacy actually works, or could work, online brings more ambiguities into the picture. If we are sending personal emails to each other, we do have a proper right that they shouldn't be read by anyone but the parties involved. However, the email service provider has to know, and keep track of, where the emails are coming from and where they are going, and also has to filter the emails for spam and malware. Just as with a wiretap, the authorities can also gain access to the email via a warrant.

We can, of course, perform encryption on our emails -- indeed, there are emailers and messengers built from the ground-up with encryption in mind -- but only the paranoid do, and they can only really get away with encryption if they're communicating with other paranoids who want to play that game. Most people don't bother, with the sensible realizing that their emails are insecure. Not everyone is of course so sensible, with indiscreet emails being a major source of trouble in corporate life.

Personal emails are insecure enough; it's even worse on the open internet. Many people would like to be anonymous and untraceable in their online transactions, but there's fundamental difficulties in trying to be so. If people can claim a right to online anonymity, they can also claim a right not to deal with people who won't identify themselves, it's simply not safe. Anyone familiar with the internet knows there are many people online who use anonymity to make nuisances of themselves, vandalizing cyberspace as a malign and idle amusement.

We do not have an unrestricted right to anonymity. In most countries, it is not possible to drive a car without registration plates, a licence, or insurance. Most countries require babies to be registered at birth, and issue numbers to track payments in and out of social-security systems. People do not expect to live in an anonymous house, draw an anonymous income or -- at least in the 21st century -- open an anonymous bank account, and conduct anonymous transactions with a bank.

Besides, in practice, much of the time we don't want to be anonymous. While people complain about the lack of privacy online, all but the most paranoid give away vast amounts of personal information; and hardly complain about the tracking of purchases to give them targeted ads and deals. Every website can record the details of the visitor's browser and computer settings that often make up a unique fingerprint. Only the most paranoid try to block such data collection, and they do so only with inconvenience.

Cellphone providers can track our location to an increasingly high level of accuracy, and maintain such data in our call records, to presented to the authorities when warranted. We make purchases at the supermarket, the supermarket company tallies what we buy, and gives us customized sales coupons. Effectively everything we do online is traceable, with more of our lives going online all the time, and there's not much we can do to keep it under wraps. Every purchase or other "trusted transaction" that we perform online is necessarily accessible to the authorities, since the law is the ultimate enforcer of trusted transactions.

Sure, we could take more measures to maintain privacy, but people on the remote end don't have to cooperate; websites have a perfect right to refuse access if we have an ad blocker running in our web browser. We are generally cooperative with surveillance by websites, even when we are aware that it's going on. It's just a nuisance to try to defy surveillance, and for law-abiding citizens, there's not much reason to: we like our targeted ads and coupons.

To be sure, only those with a legitimate "need to know" and legal authorization should have access to data on such transactions, but there will be no preventing them from obtaining it. Even if we try to maintain anonymity, it's it's easily penetrated with data-mining; if the authorities want to figure out who's doing what online, all they have to do is put the pieces together.

* The bottom line is that we know that when we go online, we're open to the world, to a substantial degree. The fact that the authorities can track our activities is worrisome; but not half as worrisome as the fact the Black Hats can, too. If we're going to conduct trusted transactions online, we need them to be secure; there is a particular need for a secure online identification scheme that eliminates the need to mail documents back and forth for signature -- a scheme that is not only antiquated and cumbersome, but hardly secure.

On the whole, the internet is not too secure; it is not secure enough. Malicious hackers break into corporate and government databases on a regular basis -- sometimes only too easily, by exploiting the incompetence and laziness of their targets. Western spymasters are beginning to concede the inevitable and admit that it is too late to suppress secure encryption, and that it would cause more harm than good even if it could be. The suspicious wonder if such concessions are a smokescreen, that the spooks have developed means of readily breaking secure encryption.

BACK_TO_TOP

[12.3] QUANTUM COMPUTING & CODEBREAKING

* Current ciphers such as RSA or AES are extremely difficult to break by brute-force methods. To be sure, there is no such thing as an "unbreakable" cipher, since if a cipher can't be broken by analytical means, there are other links in the chain where it can be attacked. For example, Eve could write a software virus or even a modified version of PGP and slip it unnoticed onto Alice's computer. When Alice tries to encrypt a message, Eve's "stealth" software could obtain the key or the plaintext, and then sneakily send it on to Eve over the Internet later.

Such trickery does not appeal to most cryptanalysts, who would really like to be able to crack a strong cipher such as RSA by analytic means. That means factoring a very large number in some period of time hopefully much shorter than the age of the Universe. There is a approach known as "quantum computing" that might be able to do the trick, if anybody can figure out how to make it work.

Modern computers are based on simple logic operations that are easily understood, though their elaborations may become very complicated. Quantum computing, in contrast, is based on operations that even those who are working on quantum computing not only admit, but insist, cannot be understood at an intuitive level.

Quantum computing is based on quantum physics, the branch of modern physics that deals with the often bizarre laws of nature at the microscale. One of the best-known experiments in quantum physics, an experiment very relevant to quantum computing, is the "two-slit light interference paradox", or "two-slit paradox" for short. This paradox is based on the phenomenon of light interference, which has been understood for over two centuries, and for most of that time did not seem paradoxical at all.

In 1803, the English polymath Thomas Young published a paper on experiments he had conducted on light. In one such experiment, he shined a light onto a screen through two parallel slits, spaced a short distance apart. The strip of light cast through the two slits was not a broad swath of light, but alternated from dark to bright to dark to bright across the swath. This could be explained if light were assumed to be a type of wave phenomenon. The dark positions in the swath occurred where the pathlengths of light from the two slits were such that the light from one was shifted by a half-wavelength from the other, and so the light canceled out. The bright positions in the swath occurred where the pathlengths resulted in the light from the two slits being in the same phase, and so the light from the two slits added up. There had long been a controversy among physicists over whether light was a particle or wave phenomenon. Young's experiments seemed to conclusively prove that it was a wave phenomenon, and light was accepted as a wave for over a century.

However, in the 20th century, light was proven to have behaviors clearly characteristic of particles as well. Quantum physics was able to reconcile, uncomfortably, the mutually conflicting ideas of light as a particle and light as a wave through a concept known as "wave-particle" duality, which said essentially that an experiment on a subatomic particle that was intended to show wavelike properties would show wavelike properties, and an experiment that was intended to show particle properties would show particle properties.

Light is now known to travel as individual particles called "photons". The two-slit interference pattern observed by Thomas Young can be seen as the result of countless photons pouring through the two slits, building up the interference pattern one photon at a time. This is a bit puzzling, since if light were simply a particle the photons would simply pile up in front of each slit, establishing maximum brightness at those locations and fading at locations farther away from the slits. There would be no interference pattern. However, wave-particle duality does allow the wave interference pattern to occur.

What is much more puzzling is that the interference pattern will build up over time even if only one photon is emitted at a time. This sounds perfectly crazy: if only one photon goes through at a time, what could it possibly be interfering with to build up the pattern? Although a photon absolutely has a wavelength, any one photon seems to be a point particle; there's nothing particularly "wavy" about it in itself.

One of the important features of the sub-microscopic world is that a measurement cannot be taken on a particle without seriously affecting it. This is known as the "uncertainty principle". According to traditional quantum physics, by a further implication of the uncertainty principle, nothing can be said about the properties of a particle, or its "state", until a measurement is made on it. This might not seem to be much of a condition, since intuitively it seems obvious that the particle is in some state before we measure it, even though the measurement will alter that state.

Intuition is wrong. Before a measurement is taken, nothing can be said about the properties of the particle; it is "indeterminate". It is not a question of the particle being in one of the particular states available to it before the particle is measured, and not knowing what that state is; the particle exists in all the states at the same time. If no measurement is taken to see which slit the particle goes through, it could go through either slit, and goes through both of them. This principle is called "superposition of states", and the existence of the photon in these multiple states is known as "coherent superposition". Once the photon is measured, the superposition of states "collapses" into a measured event, a process known as "decoherence".

This traditional view of quantum physics, known as the "Copenhagen interpretation", has its critics and a number of alternative interpretations have been proposed. None of them sound much less outrageous and there's no good reason to discuss them here, but all the interpretations agree on the existence of the concepts of quantum indeterminacy and superposition of states. These notions are observables, not arbitrary theoretical contraptions, with the interpretations simply representing a struggle to explain the observed reality. When a student told famed American physicist Richard P. Feynman that he didn't believe in superposition of states, Feynman replied: "Well, go do the experiments until you do believe it."

* Just because superposition of states violates common-sense logic does not mean that it's useless. In 1985, following up on hints provided by Feynman a few years earlier, a British physicist named David Deutsch of the University of Oxford published a paper that suggested that superposition of states could be put to use in a "quantum computer".

A conventional computer encodes a bit, a 1 or 0, as the presence or absence of a voltage. A quantum computer, in contrast, uses a quantum-physical property of a particle to encode a 1 or 0, for example the spin axis of an electron (which is either "up" or "down" but nothing in between) or the polarization of a photon. In either case, calculations will be performed on a group of bits, say 32 bits, at one time. 32 bits can be arranged in a total of 4,294,967,296 different ways, allowing them to encode that number of different numbers. Suppose a conventional computer were to perform a calculation requiring a test of all possible values that can be represented by 32 bits. It would have to loop through every single value, one at a time.

In contrast, if a 32-bit value were represented by the spin states of 32 electrons or the polarization states of 32 photons, by the principle of superposition of states, all possible 32-bit values would be present at the same time! A quantum computer operating on these 32 particles could test all 4,294,967,296 values in a single calculation, without going in a loop.

While adding another bit doubles the number of loops for a conventional computer, even if another bit is added to the calculation in a quantum computer, the calculation would still be done at one time and would take no longer than before. The hardware would have to get bigger, but the computation time would remain the same.

Since the use of the spin state of an electron or polarization state of a photon to represent a bit has vastly different properties from the use of a voltage level to represent a bit, in a quantum computer the bits are referred to as "quantum bits" or "qubits".

* This was a completely mind-boggling idea. It was also a purely abstract proposal, similar to Diffie's conceptual invention of public-key cryptography. Deutsch was in a worse situation, however, since not only did he not know how to implement a quantum computer, he didn't really know what could be specifically done with such a technology even if it existed. All he had was a marvelous "what if?" scenario. For this reason, quantum computing remained little more than an exotic theoretical toy for almost a decade. Researchers figured out examples of tasks that a quantum computer could execute, but these tasks were trivial and of little practical value.

That changed in 1994, when Peter Shor of the AT&T Bell Laboratories in New Jersey came up with a practical algorithm that could be implemented with a quantum computer: fast factoring of large numbers. Two years later, his colleague Lov Grover, working from Shor's research, came up with a second practical algorithm: a fast technique for searching for the location of a specific value in an unsorted list of values. Grover announced an even more efficient scheme in the summer of 2000.

Neither of these algorithms actually got a result in a single step using a quantum computer, but they were far more efficient than comparable calculations performed on a conventional computer. For example, while the average number of searches to find a specific entry in a list of N items is no better than N/2 with a conventional sequential search, with Shor's scheme is SQRT(N). Cryptographers quickly realized that the first two practical algorithms to be devised for a quantum computer were not merely useful to cryptanalysis but of central importance to it. A fast factoring algorithm could crack RSA. A fast value-search algorithm could crack DES and other block ciphers. Interest in quantum computing increased significantly.

* A quantum computer is very high on the wishlist of cryptanalysts and the black organizations that hire them. However, nobody's figured out how to build a quantum computer yet. Controlling individual particles or small groups of particles is very difficult, and to make matters worse the qubits have to be isolated from the environment to achieve a superposition of states. This problem gets more difficult as more qubits are used at one time.

Researchers are painfully nailing down the technological steps pieces needed to build a quantum computer. Much recent research has focused on using atoms or molecules to implement qubit storage. For example, in 2000 a team from IBM and Stanford University announced that they had developed a quantum computer that used a five-atom fluorine molecule to perform a two-qubit quantum calculation. The qubit value was encoded by the spin states of the atoms in the molecule, with the spin states ultimately sensed by nuclear magnetic resonance (NMR) measurements. Two of the atoms were used for qubit storage, while the other three were used to evaluate the operation.

An actual quantum computer will require thousands of qubits to be useful, including a large number of bits simply for error correction. Nobody believes that the approach of sensing the spin states of molecules with NMR is useful for much more than demonstrating that quantum computing is possible, but other schemes are being investigated, based on semiconductor micromechanical systems implementing sets of single-ion traps; single photons fed through optical elements; single-electron transistors; oscillations of current across superconducting junction elements; or manipulation of magnetic flux states in superconducting loops.

So far, all demonstrations of quantum computing techniques have been just that, demonstrations, and a long way from practical technology. Some critics have compared quantum computing to "cold fusion", suggesting it has very little basis in reality. Others have more generously suggested it's more like "hot fusion", meaning that it's possible in principle, but there's no reason to believe that it will ever be practical.

BACK_TO_TOP

[12.4] QUANTUM CRYPTOGRAPHY

* Although quantum technology may provide means to crack any existing cipher, it may also be used to produce a cipher that even a quantum computer can't crack.

In the late 1960s Stephen Weisner, at that time was a graduate student at Columbia University, came up with an unusual idea for "quantum money" that couldn't be counterfeited. Weisner's quantum money was based on the physics of light photons. One of the ways in which light is wavelike is in that it can be "polarized". It has a wave motion at a right angle to its direction of travel. Relative to the axis of travel, that wave motion could be oriented vertically, horizontally, or any direction in between. A "Polaroid" lens can be used to screen for light of a given polarization. Such lenses are made of plastic with all the polymer molecules oriented in the same direction. If they are all oriented vertically, photons with vertical polarization can pass through, but photons with horizontal polarization cannot.

To explain Weisner's quantum money, let's assume that we have filtered light so that we end up with photons polarized in only four directions: vertically, horizontally, +45 degrees, and -45 degrees. We'll designate these four polarizations as "V", "H", "P" (plus), and "M" (minus).

Suppose we try to send photons with these four polarizations through a vertically-polarized Polaroid lens. A V photon will pass through and an H photon will be blocked, as expected. However, the concept of quantum indeterminacy applies to the polarization of photons. What this means in practice is that a P photon has a 50:50 chance of passing through or being blocked, as does an M photon; if a P or M photon does pass through the vertically polarized lens, it will be vertically polarized and will be indistinguishable from a V photon. Similarly, if a P or M photon is passed through a horizontally polarized lens, it will have a 50:50 chance of being blocked; if it is passed through, it will be horizontally polarized and will be indistinguishable from an H photon.

Weisner's quantum money, as he envisioned it, included 20 "light traps", which were devices that could capture and store a photon. Each trap could be loaded with a single photon with V, H, P, or M polarization. The polarization sequence of the 20 photons would be unique for each bill. Each bill would also have a printed serial number, and a record could be kept of serial numbers and the corresponding polarization sequence loaded into each and every bill. To forge the bill, a counterfeiter would have to copy a legitimate serial number, which is trivial, and copy the polarization pattern for the bill with that serial number, which is not.

The problem arises because of the ambiguity in reading photon polarizations. If the counterfeiter uses a vertically polarized filter, it would pass V photons and block H photons. But what about the P and M photons? On the average, half the time they would be passed, with the counterfeiter interpreting them as V photons, and the other half of the time they would be blocked, and the counterfeiter interpreting them as H photons. The counterfeiter could use a Polaroid lens with an orientation of +45 degrees to discriminate between P and M photons, but then will be confounded by the V and H photons. Since the photons can only be released from the traps to be measured once, the counterfeiter cannot use a trial-and-error method to determine the polarization sequence.

The bank can reliably read the polarization sequence because the information describing the sequence has been recorded and so the proper filters can be used. To be sure, there is some ambiguity even for the bank, since M and P photons could be misinterpreted as V and H photons or the reverse, but the likelihood of properly testing all 20 photons by accident is very small. Of course, the bill has to be "reinitialized" with the recorded polarization sequence after it has been read, since the original is destroyed by reading it.

* Even Weisner didn't think that quantum money was a practical idea; he just found it an interesting theoretical toy. Nobody else was interested, and all the papers he wrote on it were rejected by scientific publications.

One person who did find it interesting was his friend Charles Bennett, who kept tinkering with the idea over a period of several years. In the early 1980s, when Bennett was working for IBM, he got to talking with a computer scientist from the University of Montreal named Gilles Brassard, and the two realized that the quantum money concept had applications in cryptography. In particular, it offered the possibility of a cipher that could not be broken analytically.

Suppose Alice wants to send Bob an enciphered message in binary code. She could transmit each bit of the message using the polarization of photons: a V photon could represent a 1, while an H photon could represent a 0. Alternatively, she could use a P photon to send a 1, and a M photon to send a 0.

For purposes of this argument, we can call the V-H scheme the "rectilinear" scheme and designate it with a "+", and we can call the P-M scheme the "diagonal" scheme and designate it with an "x". Alice, being devious, decides to use the rectilinear scheme and the diagonal scheme interchangeably, at random. For example, if she wants to send the binary string "10111001110001", she could send it like this:

   1 0 1 1 1 0 0 1 1 1 0 0 0 1
   + + x + x x + + x + + x + x
   V H P V P M H V P V H M H P

What makes this devious is that if Eve tries to intercept the message, just as with the quantum-money counterfeiter, she has no way of knowing what polarization filter to use to sense the polarization of a particular bit of the message, and she will get the wrong bit value about half the time. Eve simply can't read the message.

Of course, Bob can read the message reliably if he knows the pattern of polarization schemes that Alice is using. However, this leads straight back to the classic key-distribution problem, with Alice trying to think of a secure way to get the pattern of polarization schemes to Bob. Alice and Bob could use RSA to transfer the key, but then we would have a scheme that would be no more and no less secure than RSA. Bennett and Brassard chewed on this problem at length and finally came up with an answer in 1984. The result was quantum cryptography.

* A quantum cryptography session involves a set of preliminary initialization steps:

STEP 1: Alice sends Bob a purely random sequence of a given number of bits, using a purely random sequence of the two polarization schemes.

STEP 2: Bob has no idea what bits are being sent and no idea which of the two polarization schemes are being used for each bit. On his end, he tries the two polarization filters at random, sometimes getting the correct result, sometimes not.

STEP 3: Now Alice phones Bob, on an ordinary insecure line, and tells him what sequence of polarization schemes she used, but not what the bit values were. Bob then replies and tells Alice which of the bits he read using the correct filter, meaning he got the correct values, but does not tell her what those results were.

STEP 4: The actual values of the bits that were read correctly can then be used as a completely unbreakable one-time pad cipher key. Alice's message can then be sent, using one or the other of the polarization schemes but not both at random, and will be completely secure.

STEP 5: Eve, the eavesdropper, is in the same position of using randomly-chosen filters to read Alice's sequence, but the likelihood of Eve using the same sequence of filters as Bob is vanishingly small. Eve cannot obtain the full cipher key by intercepting the transmission.

To illustrate, using an unrealistically short binary sequence:

   Alice's random bit sequence:   1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0
   Alice's random polarizations:  + + + + x x + + + x x + x + + x x + x + x
   Bob's random filters:          x + + x + x + + x x x + x x x + + + x + +
   Correctly read bits:           - 0 0 - - 1 0 1 - 0 0 1 0 - - - - 0 1 1 -

   Resulting key sequence:        001010010011

   Eve's random filters:          + x x + + x + x + + + x + x x x + + x + +
   Correctly read bits:           1 - - 0 - 1 0 - 1 - - - - - - 0 - 0 1 1 -

   Eve's reconstruction of key:   ??10?????011

Eve is actually in a worse position than this scenario shows. Since only single photons are being sent between Alice and Bob, if Eve intercepts them she will affect their polarization, for example converting P photons to V photons, and this will corrupt Alice and Bob's encryption. If Bob tries to decrypt the message and gets gibberish, he knows someone's been listening in.

Since the measurement of photon polarizations is tricky, it is possible that Bob will make errors in measurement. Bob can perform a little error-checking by actually telling Alice some subset of the bit values he received, with Alice confirming that they matched. If they don't, they construct another key. If they do, they simply discard the bits Bob told Alice, on the presumption that Eve was listening in, and use the remainder.

For example, they could build a key of 1,100 bits, use 100 of those bits as an error check, and then use the remaining 1,000 bits as a key. An alternative that would not throw away bits and would be as easy to do would be for Alice to simply tell Bob what the "parity" of a number of bits selected from the key would be, or in other words indicate if there were an even or odd number of "1" bits in that random selection. Less than 20 such parity comparisons would be enough to ensure that the key hadn't been tampered with by eavesdropping.

Quantum cryptography promised to make the absolutely secure one-time pad cipher useful for common use. Cipher users could produce an absolutely random keystream for every individual message, and communicate it between each other with little fear of interception.

* The cryptography community was fascinated by the idea of quantum cryptography, but many doubted it could be made to work in practice. However, in 1988, Bennett and one of his students, John Smolin, managed to send a quantum-encrypted message between two personal computers, appropriately named "Alice" and "Bob", and read it properly. The distance between the two computers was only 30 centimeters (a foot), but other researchers have been steadily increasing the distance between transmitter and receiver.

By late 2008, the technology had advanced to the level where a quantum cryptography system had been implemented as a demonstration in Vienna, Austria, with six sites linked over the city's fiber-optic communications network. However, so far none of the systems have been perfectly secure. Sending and receiving single photons is very difficult, so current technologies use pulses of polarized photons instead. This opens the possibility that Eve could use a half-silvered mirror, set at an angle to the line of transmission of the pulse, to divert part of the pulse and let the rest through. Eve could then test the polarization of the diverted portion of the pulse without disturbing the portion of the pulse that went through the mirror. The probability that Eve can successfully sample the pulse in this way increases with the size of the pulse, and at some size of pulse, the security of the system is lost completely. On the other hand, reducing the size of the pulse reduces the range over which it can be sent.

Progress is being made towards development of a true quantum cryptography system. A number of firms have developed "light emitting diodes (LEDs)" that could emit single photons, providing a critical element for a quantum cryptography system. It is unclear how far a single photon might be transmitted, but the length of a system could be multiplied by adding "repeaters" at intervals. The photon itself can't be regenerated by the repeater without measuring it and corrupting the quantum cryptography scheme, but the message could be securely enciphered and deciphered between each set of repeaters, with the full transmission consisting of a chain of such sessions. Work is now underway towards development of experimental communications satellites featuring quantum encryption technology in hopes of creating a long-distance quantum-encrypted communications system.

* Other approaches are being considered for quantum cryptography. An alternate scheme, based on what is known as "quantum entanglement (QE)", has been proposed by Artur Ekert of Oxford University in the UK.

QE is based on a quantum-physical quandary, the "Einstein-Podolsky-Rosen (EPR) paradox", which has been known since the 1930s. The EPR paradox imagines the generation of two photons from an event that creates them with, say, polarizations at right angles to each other, and sends them in opposition directions. In quantum physics terms, the two photons are said to be "entangled". Entangled photons with a right-angle relationship can be generated, for example, by shining a laser beam through certain types of optically-active crystals.

However, according to quantum indeterminacy, until the polarization of at least one of the photons is measured, the polarization of both photons remains indeterminate. Once the polarization of one photon is measured and "resolved", then the polarization of the other "entangled" photon is also implicitly resolved, even though it is far away by that time.

Now suppose Alice generates pairs of entangled photons, storing her half of the pairs in some kind of optical "trap" and sending the other half to Bob, who also stores his in an optical trap. When Alice wants to send an enciphered message to Bob, she calls him, and the two then perform measurements on the trapped photons with filters, much as with the quantum cryptography scheme outlined previously. The beauty of the scheme is that if Eve gets her hands on any of the entangled photons they do her no good, since she can't duplicate them without resolving them and making them absolutely useless for the procedure. They can be delivered to Bob or to Eve, but not both. Alice and Bob can even use the same filter sequence -- all "+" for example, or all "x" -- and eliminate the guesswork, at least as long as Alice is certain she is talking with Bob.

Some starflight enthusiasts have jumped to the conclusion that QE permits instantaneous communications. In fact, Einstein and his colleagues came up with the EPR paradox just to show how absurd quantum physics is, since instantaneous communications are impossible in terms of relativistic physics. The joke was on them, of course, since the EPR paradox turned out to be provably true, but the joke cut both ways. Without non-instantaneous communications between Alice and Bob about the proper filter orientations, there's no way to get a useful interpretation of the results of their measurements. Quantum physics has a quirky tendency to cheat on classical physics, but in a way that can't really be detected or used, at least directly. The Creator does have a sense of humor.

* Or, in other words, what quantum physics gives, quantum physics takes away, and this applies at a higher level as well. Quantum computing will be able to crack any existing cipher, but quantum cryptography will result in ciphers that even quantum computers won't be able to crack. A question that will remain when quantum computing and cryptography become practical: Is the cryptographic game over? Or will it just move on to a new and even more devious level?

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