Unfortunately for those of us who enjoy stories of codes and ciphers, future books on this topic are likely to have only a historical focus. That 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, the doctors involved in this new work are slaves to government agencies that are unlikely to allow disclosure. That’s too bad, because the chances of mischief in government are generally reduced if there is some public involvement and oversight.
“In the modern age,” writes Stephen Pincock in code breaker“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 Britain’s General Communications Headquarters (GCHQ), keep information about codebreaking and cryptography secret, making the prediction of future developments be a fool’s game.”
Even historical texts on ciphers and codes can lead us down alleys that require intellectual perseverance to read and understand. In fact, writing and reading anything is an abstraction, an abstraction we take for granted when we leave grade school. Writing in English, as I’m doing here, makes it possible for anyone who encounters my text to read these black scribbles in print and grasp meaning that isn’t inherently in the ink or on the page (or on the screen!). It has a look that is almost metaphysical. Yet understanding ensues, whether you are a thousand miles away, dead or alive, or indeed dead for a thousand years.
And with a modest effort, my words can be translated into Finnish, Swahili or Tagalog.
Translation into a foreign language is a simple analogue to codes and ciphers, a wonderfully intuitive way to understand the process. However, the art of creating codes and ciphers takes this process of abstraction to a higher level and in a different direction. Through the use of codes and figures, we can cover up instead of 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.
That is the gist of the process in both codes and figures, although they differ in a technical sense. “Ciphers are systems for disguising the meaning of a message by replacing each of the individual letters in a message with other symbols,” Pincock explains, while “codes, on the other hand, place more emphasis on meanings than characters.” , and tend to replace entire words or phrases according to a list contained in a codebook.” But this is a detail that should not worry us.
Codes and figures are explicitly and inherently difficult to understand because at their heart is the desire No It will be understood. And doesn’t that also end the enjoyment of it?
Codebreaker, The history of codes and ciphers, from the ancient pharaohs to quantum cryptography, (New York: 2006), Walker & Company, is Stephen Pincock’s short and clever coffee-table account of the subject. This book would grace any living room or library. It is printed on heavyweight coated paper and is packed with high-resolution photographs. It is not a textbook. Quite the contrary: it is a book for the amateur. It gracefully and lightly touches on its many facets without delving too deeply into any of its enticing nooks and crannies. For the young at heart, he also offers examples of various codes and ciphers that one can try to see if there is 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 training is in biology and chemistry, not code-breaking. However, this is a fascinating book that will provide hours of entertainment for those who are already fans.
Stephen Pincock, a 1991 graduate of the University of New South Wales, is a biochemist by training. Since 2008 he is deputy editor of australian doctor. He is a former editor of the scientist magazine and writes occasionally for Nature, the weekly science magazine. He has written several books on scientific subjects. He divides his time between Sydney and London.
The two areas of this book I enjoyed the most were the discussion of the German Enigma encryption machine in World War II and how a group of Polish mathematicians cracked it, with the later help of Alan Turing and a platoon of British cryptanalysts at Bletchley Park. In England. ; and second, I learned a lot from Pincock’s layman’s exposition of the complex mathematics used to factor large prime numbers, and how a breakthrough in that area by any bright teenager could jeopardize current encryption methods.
Arthur Scherbius, a Frankfurt native electrical engineer, invented the Enigma encryption machine for commercial use in the early 1920s. Thinking of protecting his British trade rights, he filed his patents in London, as well as Vienna and Berlin, a favor unwanted to Churchill’s war cabinet happily exploited twenty years later.
The Nazis greatly improved on Scherbius’s initial design, which simply used three wheels with the alphabet inscribed on them to encode input into output. Readable text went in, encoded gibberish came out that could then be transmitted securely wirelessly without fear of being understood without an Enigma machine with its wheels turned precisely into positions identical to the input device. It was actually a bit more complicated than that, involving a few extra layers of coding, but essentially that’s all Enigma did.
The Enigma device itself was housed in a varnished wooden box and looked very much like a terribly ugly typewriter, and was about the same size, easy to transport, although it did require an electrical power supply.
Like any mechanical device, the Enigma was prone to failure, and it was these failures, along with the carelessness of its human users, that made it possible for the Poles and the British to crack the Enigma and read the most secret communications from the German High Command. . Those patent plans in London didn’t hurt either.
Pincock tells this story very well, with great enthusiasm and a page-turning intensity. Historians still debate the actual influence that the breaking of Enigma had on the course of the war, but we must not forget Winston Churchill’s words to King George VI after his victory: “It was thanks to Ultra [the British code term for the intelligence gleaned from breaking the Enigma cipher] that we won the war.”
That’s a definitive answer, at least for this reader.
A more modern problem has to do with the way we use computers and the Internet to securely transmit private information like credit card numbers and health care data. Cryptology is no longer just a military concern. Today, encryption is routinely employed every time you use your Blackberry or order flowers online. And so it has to be done with great speed and without a lot of human intervention, and it also has to be much, much more secure than Enigma ever was.
Modern encryption techniques are based on a quirk of some real numbers, that big category can only be divided by themselves and 1. You learned about them in high school: we call these numbers ‘prime’ or ‘prime numbers’.
Here are some of them, the first five, in fact: 2, 3, 5, 7 and 11.
The list goes on to infinity. There are much larger primes, including for example this one: 7,427,466,391. The two largest primes discovered so far (in 2013) have more than seven million digits each. No larger prime has been found, for the good reason that there is no larger prime. There will always be a larger prime than the largest prime found so far. 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 a ‘module’. The wonderful thing about multiplying two primes to create a modulus is that it can be done very quickly, almost instantly on a computer. However, the opposite is not true.
If I give you modulo 35 and ask you to tell me which two prime numbers are multiplied together 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 cousins that make it up? That’s a harder problem (hint, one of the two prime numbers is the larger one I gave you earlier).
Supercomputers may need five months of continuous operation to factor a large modulus into its two prime numbers. Even larger numbers are believed to require thirty years of continuous computer calculations to factor. Some may not even be deciphered during the lifetime of our galaxy.
So if I want to create unbreakable code, I can safely stream the module to my receiver on the other as open text, in ‘clear’ to use the term of art. I don’t care if everyone knows about the module, including thieves and spies, because as long as the two prime numbers that make it up remain hidden, my code is safe. Unless my opponent has a few thousand years of free computer time at his disposal, he won’t crack my code.
And yet, and yet!
Consider this from Stephen Pincock: “As a result…of the increasingly complex mathematical methods needed to find solutions, today’s codebreaking is beyond the realm of the interested hobbyist and is instead proprietary.” exclusive to mathematicians.But the tantalizing possibility remains that there could be a chink in the armor of the cipher that uses the difficulty of factoring large numbers.
“Although the factoring methods that have been discovered so far are mathematically complex, a simpler way may still exist. After all, the mathematics involved in Einstein’s theory of relativity is terrifyingly complex, yet out of complexity arose the beautiful and simple equation E = mc2 Therefore, code breakers around the world are concentrating their efforts on finding simple factoring methods. If they find them… “then, crack the current codes used by credit cards and governments can crumble very quickly.
And this is where the brilliant high school student comes in. Mathematics is first and foremost the arena of the young and talented.
So watch out and watch out. We may still need new and better ways to protect our money and our secrets.
