math

Quanta Crypto: cool but useless

business, security / /

From Bruce Schneier’s “Quantum Cryptography” (Crypto-Gram: 15 November 2008):

Quantum cryptography is back in the news, and the basic idea is still unbelievably cool, in theory, and nearly useless in real life.

The idea behind quantum crypto is that two people communicating using a quantum channel can be absolutely sure no one is eavesdropping. Heisenberg’s uncertainty principle requires anyone measuring a quantum system to disturb it, and that disturbance alerts legitimate users as to the eavesdropper’s presence. No disturbance, no eavesdropper — period.

…

While I like the science of quantum cryptography — my undergraduate degree was in physics — I don’t see any commercial value in it. I don’t believe it solves any security problem that needs solving. I don’t believe that it’s worth paying for, and I can’t imagine anyone but a few technophiles buying and deploying it. Systems that use it don’t magically become unbreakable, because the quantum part doesn’t address the weak points of the system.

Security is a chain; it’s as strong as the weakest link. Mathematical cryptography, as bad as it sometimes is, is the strongest link in most security chains. Our symmetric and public-key algorithms are pretty good, even though they’re not based on much rigorous mathematical theory. The real problems are elsewhere: computer security, network security, user interface and so on.

Cryptography is the one area of security that we can get right. We already have good encryption algorithms, good authentication algorithms and good key-agreement protocols.

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DRM fails utterly

business, law, tech in changing society / /

From John Siracusa’s “The once and future e-book: on reading in the digital age” (Ars Technica: 1 February 2009):

Nuances aside, the big picture remains the same: DRM for digital media distribution to consumers is a mathematically, technologically, and intellectually bankrupt exercise. It fails utterly to deliver its intended benefit: the prevention of piracy. Its disadvantages, however, are provided in full force: limiting what consumers can legally do with content they have legitimately purchased, under threat of civil penalties or criminal prosecution.

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How to open a physicist’s briefcase

security, technology / /

From John D. Barrow and John K. Webb’s "Inconstant Constants: Do the inner workings of nature change with time?" (Scientific American: 23 May 2005):

One ratio of particular interest combines the velocity of light, c, the electric charge on a single electron, e, Planck’s constant, h, and the so-called vacuum permittivity, 0. This famous quantity … called the fine-structure constant, was first introduced in 1916 by Arnold Sommerfeld, a pioneer in applying the theory of quantum mechanics to electromagnetism. It quantifies the relativistic (c) and quantum (h) qualities of electromagnetic (e) interactions involving charged particles in empty space (0). Measured to be equal to 1/137.03599976, or approximately 1/137, has endowed the number 137 with a legendary status among physicists (it usually opens the combination locks on their briefcases).

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The Cold War as game theory

history, politics, science / /

From Charles Platt’s “The Profits of Fear” (August 2005):

Game theory began with the logical proposition that in a strategic two-player game, either player may try to obtain an advantage by bluffing. If the stakes are low, perhaps you can take a chance on trusting your opponent when he makes a seemingly fair and decent offer; but when the penalty for being deceived can be nuclear annihilation, taking a chance is out of the question. You work on the principle that the person you are dealing with may be utterly ruthless, unethical, and untrustworthy, no matter how peaceful his intentions may seem. You also have to assume that he may be smart enough to use game theory just like you; and therefore, he will assume that _you_ are ruthless, unethical, and untrustworthy, no matter how peaceful _your_ intentions may seem. In this way a supposedly rational system of assessment leads to a highly emotional outcome in which trust becomes impossible and strategy is based entirely on fear. This is precisely what happened during the decades of the Cold War.

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Hear someone typing & know what was written

security, writing ideas / /

From Edward Felten’s “Acoustic Snooping on Typed Information“:

Li Zhuang, Feng Zhou, and Doug Tygar have an interesting new paper showing that if you have an audio recording of somebody typing on an ordinary computer keyboard for fifteen minutes or so, you can figure out everything they typed. The idea is that different keys tend to make slightly different sounds, and although you don’t know in advance which keys make which sounds, you can use machine learning to figure that out, assuming that the person is mostly typing English text. (Presumably it would work for other languages too.) …

The algorithm works in three basic stages. First, it isolates the sound of each individual keystroke. Second, it takes all of the recorded keystrokes and puts them into about fifty categories, where the keystrokes within each category sound very similar. Third, it uses fancy machine learning methods to recover the sequence of characters typed, under the assumption that the sequence has the statistical characteristics of English text. …

The only advantage you have is that English text has persistent regularities. For example, the two-letter sequence “th” is much more common that “rq”, and the word “the” is much more common than “xprld”. This turns out to be enough for modern machine learning methods to do the job, despite the difficulties I described in the previous paragraph. The recovered text gets about 95% of the characters right, and about 90% of the words. It’s quite readable.

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Pi to unfathomable places

cool stuff, science / /

From “Man recites pi from memory to 83,431 places“:

A Japanese psychiatric counselor has recited pi to 83,431 decimal places from memory, breaking his own personal best of 54,000 digits and setting an unofficial world record, a media report said Saturday.

Akira Haraguchi, 59, had begun his attempt to recall the value of pi – a mathematical value that has an infinite number of decimal places – at a public hall in Chiba city, east of Tokyo, on Friday morning and appeared to give up by noon after only reaching 16,000 decimal places, the Tokyo Shimbun said on its Web site.

But a determined Haraguchi started anew and had broken his old record on Friday evening, about 11 hours after first sitting down to his task, the paper said. …

Pi, usually given as an abbreviated 3.14, is the ratio of the circumference to the diameter of a circle. The number has fascinated and confounded mathematicians for centuries.

Aided by a supercomputer, a University of Tokyo mathematician set the world record for figuring out pi to 1.24 trillion decimal places in 2002.

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The history of =

commonplace book, history, science / /

From "The History of the Equals Sign", at The Science Show:

In 1543, [Robert] Record published The Ground of Arts, the first ever maths book in English, which ran through over fifty editions … Until 1557, mathematicians had finished off a calculation by laboriously writing out the words, is equal to, which was sometimes abbreviated to AE or OE from the Latin word for equal, aequalis. But Record had a better idea, why not use a symbol, he said, to avoid, as he put it, the tedious repetition of these words he proposed the use of a pair of parallel lines. Using this simple device that we now call the equals sign released an enormous logjam in the efficient handling of numbers and the implications extended far beyond pure maths.

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