How To Fit A Table Through A Door Math Problms Codes and Codecracking Intrude Increasingly In Our Daily Lives

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Codes and Codecracking Intrude Increasingly In Our Daily Lives

Unfortunately for those of us who enjoy stories of codes and ciphers, future books on the subject may have only a historical focus. This is so because the evolution of cryptology is taking it into the realms of mathematics and quantum physics that are inaccessible to almost all of us. And, most likely, these newly engaged PhDs are thrilled to government agencies unlikely to allow publication. That’s too bad, because public participation and oversight generally reduces the potential for mischief in government.

“In the Modern Age,” writes Stephen Pincock Code Solver“The field of cryptology is largely in the hands of physicists and mathematicians [and] Much of what is happening is no doubt happening behind closed doors. Government agencies, such as America’s National Security Agency (NSA), and Britain’s General Communications Headquarters (GCHQ), keep information about codebreaking and cryptography tight, making predictions of future developments a fool’s game.”

Even historical texts about ciphers and codes can lead us down alleyways that require intellectual persistence to read and understand. Indeed, writing and reading anything is an abstraction, an abstraction we take for granted by the time we leave primary school. Writing in English, as I do here, anyone can read these printed black squiggles over my text and understand a meaning that is not inherent in ink or on the page (or screen!). It has an aspect that is almost metaphysical. Yet understood, I am a thousand miles away, or alive or dead, or, indeed, dead for a thousand years.

And with moderate effort, my words can be translated into Finnish, Swahili or Tagalog.

Translation into a foreign language is a simple analog of codes and ciphers, a surprisingly intuitive way of understanding the process Yet the art of ciphers and code-making takes this process of abstraction to a higher level and in a different direction. Through the use of codes and ciphers, we to conceal Instead of revealing the meaning of the conversations and texts we publish, we use the same squiggles we learned in elementary school and we do it in such a way that only anyone with the ‘key’ can reveal the hidden meaning and read the text. .

This is the essence of the process in both code and cipher, although they are technically different. “Cyphers are systems of disguising the meaning of a message by replacing each individual letter of a message with other symbols,” explains Pincock, while “codes, on the other hand, emphasize meaning more than letters and tend to replace” entire words, according to a list in a code-book. or phrase.” But that is a detail we need not concern ourselves with.

Codes and ciphers are not easy to understand clearly and intuitively because at their heart is desire no Must understand. And doesn’t it lend them enjoyment?

Codebreakers, the history of codes and ciphers, from ancient pharaohs to quantum cryptography, (New York: 2006), Walker & Company, Stephen Pincock’s chic, concise, coffee table content. This book will grace any living room or library. It is printed on heavyweight coated stock and is full of high-resolution photographs. This is not a textbook. Quite the opposite: this is a book for amateurs. It touches on its many facets very nicely and lightly without getting too deep into any of its terrifying nooks and crannies. For the young at heart, it also provides several examples of codes and ciphers that one can try to see if a true cryptanalyst has one. However, do not plan to use this book as a guide to pass the CISSP Certified Information Systems Security Professional exam. Pincock’s training was in biology and chemistry, not codebreaking. Still, it’s a fascinating book that will provide hours of entertainment for those who are already aficionados.

Stephen Pincock, a 1991 graduate of the University of New South Wales, is a biochemist by training. He has been its deputy editor since 2008 Australian doctor. He is its former editor Scientist Writes for magazines and occasionally the nature, Weekly Journal of Science. He has written many books on science. He divides his time between Sydney and London.

The two areas of this book that I enjoyed most are the discussion of the German Enigma ciphering machine in World War II, and how a team of Polish mathematicians broke it, later with the help of Alan Turing and a platoon of British cryptanalysts at Bletchley Park, England. ; And second, I learned a lot from Pincock’s layered exposition of the complex math used to factor large primes, and how a breakthrough in that area by any brilliant teenager could jeopardize current methods of encryption.

Arthur Scherbius, an electrical engineer in Frankfurt, invented the Enigma ciphering machine for commercial use in the early 1920s. Mindful of protecting his British commercial rights, he filed his patents in London as well as Vienna and Berlin, an unintended favor of Churchill’s War Cabinet that was gleefully exploited twenty years later.

The Nazis improved greatly on Scherbius’s early design, which simply used three wheels with alphabets to scramble the input to the output. In readable text, came scrambled gobbledygook that could then be safely transmitted by wireless without fear of it being deciphered without an enigma machine whose wheels turned into precisely identical positions on the input device. It was actually a bit more complicated than that, involving a few extra layers of scrambling, but that’s what Enigma did in its essence.

The Enigma device itself was housed in a varnished wooden box and looked very much like a hideously ugly typewriter and was about the same size, easily portable, although it required an electrical power supply.

Like any mechanical device, the Enigma was prone to breakdowns, and it was these breakdowns, combined with the sloppiness of its human users, that enabled the Poles and British to break the Enigma and read the German High Command’s most secret communications. . Those patent plans in London didn’t hurt either.

Pincock tells this story very well, with great tension and a page-turning intensity. Historians still debate whether Enigma’s true impact broke during the war, but we should not forget Winston Churchill’s words to King George VI after the victory: “It was thanks Ultra [the British code term for the intelligence gleaned from breaking the Enigma cipher] That we won the war.”

This is a definitive answer, at least for this reader.

A more modern issue relates to the way we use computers and the Internet to securely transmit personal information such as credit card numbers and healthcare data. Cryptology is no longer just a military concern. Today, encryption is routinely used whenever you use your BlackBerry or order flowers online. And so it has to be done very quickly and without much human intervention, and it has to be much more secure than Enigma.

Modern encryption techniques rely on some number of real numbers, large divisions that can only be divided by themselves and 1. You learned about them in high school: we call these numbers ‘primes’ or ‘prime numbers’.

Here are a few of them, the first five, actually: 2, 3, 5, 7, and 11

The list goes on and on. There are many large primes, for example, including: 7,427,466,391. The two largest primes discovered so far (in 2013) each contain more than seven million numbers. Largest prime not found — forced because there is no largest prime. There will always be a larger prime than the largest prime yet found. So, who cares?

Well, it just so happens that one can do interesting things with prime numbers that lend themselves to secret communication. One can multiply them together. For example, (5 times 7) produces a product, in this case 35, which cryptographers call the ‘modulus’. The wonderful thing about multiplying two primes to produce a modulus is that it can be done very quickly, almost instantaneously, on a computer. Yet the reverse is not true.

If I give you the modulus 35 and ask you to tell me which two primes are multiplied to produce it, it will take you seconds or minutes to figure it out by trial and error.

Now, I give you this modulus: 440,191,461,900,225,377,727. And I tell you that the two primes that make it? This is a hard problem (clue, one of the two primes is the great big one I gave you earlier).

Super-computers can operate continuously for five months to factor a large modulus into its two primes. Still larger numbers are thought to factor in thirty years of continuous computer calculations. Some may not be crackable in the lifetime of our galaxy.

So, if I wanted to create an unbreakable code, I could safely transmit the modulus to my receiver as plain text to others, ‘in the clear’ to use the term of the industry. I don’t care if the whole world knows the modulus, including thieves and spies, because as long as the two primes that make it up are hidden, my code is secure. Unless my adversary has several thousand years of spare computer time, he won’t crack my code.

And yet, and yet!

Consider this from Stephen Pincock: “Requiring increasingly complex mathematical methods to find solutions, modern-day codebreaking is now mostly outside the realm of interested amateurs and instead the preserve of mathematicians. It remains that encryption may have a chink in its armor that factorizes large numbers.” using difficulty.

“Although the factorization methods discovered so far are mathematically complex, a simple way may still exist. After all, the mathematics involved in Einstein’s theory of relativity is terrifyingly complex, yet out of the complexity emerges the beautifully simple equation E=mc2. Thus codebreakers around the world are focusing their efforts on simple On finding factorization methods. If they find them…” then breaking the current codes used by credit cards and governments can break down really fast!

And this is where the brilliant high school student comes in. Mathematics is first and foremost the field of the young and gifted.

So be careful and stay tuned. We may still need new and better ways to protect our money and our privacy.

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