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Codes and Codecracking Intrude Increasingly In Our Daily Lives
Unfortunately for those of us who like stories of codes and numbers, future books on this subject will probably only have a historical focus. This is so because the evolution of cryptology takes it into areas of mathematics and quantum physics that are inaccessible to almost all of us. And, more likely than not, PhDs engaged in this new work are in the grip of government agencies unlikely to allow disclosure. It’s a shame, because the chances of wrongdoing in government are generally reduced if there is some public involvement and oversight.
“In the modern age”, writes Stephen Pincock in Descrambler“the field of cryptology is largely in the hands of physicists and mathematicians [and] most of what is happening is undoubtedly happening behind closed doors. Government agencies, such as the US National Security Agency (NSA) and the UK’s General Communications Headquarters (GCHQ), keep information about decoding and cryptography secret, making predicting future developments a fool’s game. »
Even historical texts on numbers and codes can lead us down paths that require intellectual perseverance to read and understand. Indeed, writing and reading anything is an abstraction, an abstraction that we take for granted when we leave primary school. Writing in English, as I do here, allows anyone who comes across my text to read those printed black squiggles and pick up meaning that isn’t inherently in the ink or on the page (or screen!). It has an almost metaphysical aspect. Yet understanding occurs whether I am thousands of miles away, or alive or dead, or, in fact, dead for a thousand years.
And with modest effort, my words can be translated into Finnish, Swahili or Tagalog.
Translating into a foreign language is a simple analog to codes and numbers, a wonderfully intuitive way to grasp the process. Yet the art of cipher and code creation takes this process of abstraction to the next level and in a different direction. Through the use of codes and numbers, we to hide rather than revealing the meaning of the dialogues and texts we express, using those same scribbles we learned in elementary school, and we do it in such a way that only someone with a “key” can reveal the hidden meaning and read the text.
This is the essence of the process in codes and numbers, although they differ technically. “Ciphers are systems for disguising the meaning of a message by replacing each of the individual letters of a message with other symbols,” explains Pincock, while “codes, on the other hand, put more emphasis on meanings than on characters, and tend to replace whole words or phrases according to a list contained in a codebook.” But this is a detail that should not concern us.
Codes and numbers are explicitly and inherently not easy to understand because their core is desire not to be understood. And doesn’t that also lend to their pleasure?
Codebreaker, The History of Codes and Ciphers, From Ancient Pharaohs to Quantum Cryptography, (New York: 2006), Walker & Company, is Stephen Pincock’s short and succinct account of the subject. This book would beautify any living room or library. It is printed on thick coated paper and is packed with high resolution photographs. It is not a manual. On the contrary: it is an amateur’s book. It gracefully and lightly touches its many facets without delving too deeply into any of its enticing nooks and crannies. For the young at heart, it also offers examples of several codes and ciphers one can try their hand at to see if there’s a real cryptanalyst inside. However, do not plan to use this book as a guide to passing the CISSP Certified Information Systems Security Professional exam. Pincock’s background is in biology and chemistry, not codebreaking. Still, it’s a captivating 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. Since 2008, he has been deputy editor of australian doctor. He is a former editor of The scientist magazine and writes occasionally for Nature, the weekly journal of science. He wrote several books on scientific subjects. He divides his time between Sydney and London.
The two areas of this book that I enjoyed the most were the discussion of the German Enigma cipher machine during WWII, and how a group of Polish mathematicians broke it, with later help from Alan Turing and a platoon of British cryptanalysts at Bletchley Park in England. ; and second, I learned a great deal from Pincock’s lay exposition of the complex mathematics used to factor large primes, and how a breakthrough in this area by any bright teenager could jeopardize current encryption methods .
Arthur Scherbius, an electrical engineer from Frankfurt, invented the Enigma cipher machine for commercial use in the early 1920s. Thinking of protecting his British commercial rights, he registered his patents in London as well as Vienna and Berlin, a favor involuntary to Churchill’s war cabinet happily exploited twenty years later.
The Nazis greatly improved on Scherbius’ initial design, which simply used three wheels with the alphabet inscribed on them to scramble entry to exit. In readable text, a jumbled gibberish emerged which could then be transmitted safely wirelessly without fear of being understood without an Enigma machine with its wheels precisely turned in positions identical to the input device. It was actually a bit more involved than that, involving a few extra layers of scrambling, but in essence that’s all Enigma did.
The Enigma device itself was housed in a varnished wooden box and looked a lot like a terribly ugly typewriter, and was about the same size, easily transportable, although it required a power supply.
Like any mechanical device, the Enigma was prone to failure, and it was these failures, coupled with the negligence of its human users, that allowed the Poles and the British to crack the Enigma and read the top secret communications of the German high command. . Those patent projects in London didn’t hurt either.
Pincock tells this story very well, with great excitement and page-turning intensity. Historians still debate the actual influence of the destruction of Enigma on the course of the war, but one should not forget the words of Winston Churchill to King George VI after his victory: “It is thanks to Ultra [the British code term for the intelligence gleaned from breaking the Enigma cipher] that we have won the war.”
That’s a definitive answer, at least for this reader.
A more modern issue concerns how we use computers and the Internet to securely transmit private information such as credit card numbers and health data. Cryptology is no longer just a military concern. Today, encryption is commonly used whenever you use your Blackberry or order flowers online. And so it has to be done with great speed and without too much human intervention, and it also has to be much, much safer than Enigma ever was.
Modern encryption techniques rely on an oddity of certain real numbers, this large category can only be divided by themselves and 1. You learned them in high school: we call these numbers “primes” or “prime numbers”.
Here are a few, the first five in fact: 2, 3, 5, 7 and 11.
The list goes on ad infinitum. There are much larger primes, including, for example, this one: 7,427,466,391. The two largest prime numbers ever discovered (as of 2013) have over seven million digits each. The greatest prime has not been found – for the compelling reason that there is no greatest prime. There will always be a greater prime number than the greatest prime number ever found. So who cares?
Well, it turns out that you can do some interesting things with prime numbers that lend themselves to secret communication. They can be multiplied together. For example, (5 times 7) generates a product, in this case 35, which cryptographers call a “module”. The wonderful thing about multiplying two prime numbers to create a modulus is that it can be done very quickly, almost instantly on a computer. However, the reverse is not true.
If I give you modulus 35 and ask you to tell me which two prime numbers are multiplied to create it, it will take you a few seconds or minutes to figure it out by trial and error.
Now let me give you this module: 440 191 461 900 225 377 727. And I ask you to tell me the two prime numbers that compose it? This is a harder problem (hint, one of the two primes is the very big one I gave you earlier).
Supercomputers can take five months of continuous operation to fit a large modulus into its two primes. Even larger numbers are believed to require thirty years of continuous computer calculations to account for. Some may not even be crackable for the lifetime of our galaxy.
So if I want to create an unbreakable code, I can safely pass the module to my receiver to the other as open text, in “plain” to use the art term. I don’t care if the whole world knows about the module, including thieves and spies, because as long as the two prime numbers that compose it remain hidden, my code is secure. Unless my adversary has a few thousand years of computer time available, he won’t crack my code.
And yet, and yet!
Consider this from Stephen Pincock: “Because of…increasingly complex mathematical methods needed to find solutions, modern codebreaking is now beyond the domain of the interested hobbyist and is instead the preserve of mathematicians. But the tantalizing possibility remains that there could be a crack in the armor of encryption that uses the difficulty of factoring large numbers.
“Although the methods of factorization that have been discovered so far are mathematically complex, a simpler method may yet exist. After all, the mathematics involved in Einstein’s theory of relativity is horribly complex, but of this complexity was born the beautifully simple equation E=mc2 So decryptors around the world focus their efforts on finding simple factorization methods. If they find them…” then crack the current codes used by credit cards and governments can collapse very quickly!
And that’s where the brilliant high school student comes in. Mathematics is first and foremost the arena of the young and gifted.
So pay attention and stay tuned. We may still need new and better ways to protect our money and our secrets.
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