So I’m considering a paper on the topic of visual cryptography in art. Here’s a short abstract I wrote, I would love any feedback anyone would have.

The intention of this paper is to explore the potential uses of visual cryptography in the arts. Cryptography has typically been the playground of mathematicians and computer scientists and the lifeblood of the financial industry and secretive organizations. In 1994 Moni Noar and Adi Shamir developed a novel method of encryption that splits an image into shares which when layered can recreate the original image. Alone the shares are just static and their original image can’t be deciphered through pattern analysis. This concept has obvious potential uses in the arts to hide a message either to protect the author, the content or simply to make a statement through the process. This paper will explore how cryptography has been used in art thus far and suggest potential methods and applications of visual cryptography in art practice.

There is no way to summarize succinctly the incredible story of the Enigma Machine and the drama that surrounded the machine in this blog post, so I highly recommend reading some of the many wonderful books on the subject or reading the excellent chapter on the machine in Simon Singh’s book as I am.

With that said, I will try to give you an overview of how it is the Enigma Machine was developed and how it worked, as well as how it was finally cracked.

Arthur Scherbius, a German inventor and engineer developed the Enigma around the end of the first world war and tried at first (unsuccessfully) to sell it to commercial companies to help them protect their communications from competitors.

The device looked like a typewriter with a keyboard in the middle, a plug board below it and a set of lights that were associated with letters in the alphabet above the keyboard. The keyboard sent an electrical signal through a plug board which allowed the user to customize the wirings of letters, mapping the A key to the P key for example, the signal would then continue to a set of three scrambling cylinders that would take the signal and output it to another position. This process would be repeated two more times scrambling the signal through three levels of the rings and then into a reflector at the end which would then send the signal back up through another path on the scramblers. The signal would then finally terminate at the lights, illuminating the cipher text which corresponded with the original keypress.

What made the machine complicated was the fact that on top of the customizations available (the plug board settings, the scrambler settings and the scrambler order) the machine would then automatically rotate the scramblers with every key press creating a new scrambling order and developing a new cipher for every sequential key.

After many attempts to decipher the messages being enciphered by the Enigma most cryptanalysts simply gave up, believing the system was impregnable. At the same time many governments were shuttering their cryptanalysis bureaus because of the new sensibility that couldn’t permit the eavesdropping and spy craft necessary.

This was not the case in Poland, the young nation was terrified of its neighbors and when faced with the challenge of the Enigma Machine they adapted and persevered. The Polish Biuro Szyfrów began recruiting German-speaking mathematicians into their ranks to take a stab at deciphering the Enigma and when coupled with some excellent spy craft that gave them the scrambler wiring configurations a mathematician named Marian Rejewski was able to deduce a weakness in their system.

To understand the weakness you have to understand the process used to encrypt and send messages. The Germans utilized a set of code books that were developed and distributed every month to all of the hundreds of Enigma operators. The code books detailed day codes to be used by all operators that set the plug board order, the scrambler order and the scrambler settings. This was the greatest weakness they realized. If the code books fell into enemy hands it could be conceivable that the enemy could simply plug-in the settings and intercept all of the orders being broadcasted by all the Enigma operators.

To combat this the Germans instituted a message key system that the message senders used to make unique encryptions for each message. After setting the Enigma to the day code, the operators were instructed to pick a random three-letter combination for a new message key and transmit that twice in the day code setting, and then reset their machines to the new message key settings and finally transmit the entire message. The weakness was the repetition. As you remember, repetition is the enemy of security, and when Rejewski realized this fatal error he exploited it ruthlessly.

Through tedious experimentation he was able to deduce that in order for a message key such as ABR, when repeated ABRABR, and enciphered TWEVZP, to become this unintelligible mess the rotors of the scramblers had to have turns 6 times. Since the first and fourth letters, as well as the second and fifth letter and the third and sixth letters were identical, the process of scrambling had in fact been revealed. If you could track how the scrambler had to have turned in order for the letter to be enciphered one way initially and another way in just three steps then you can deduce how the scramblers were set up.

With this information Rejewski and the team at Biuro Szyfrów were able to monitor almost all German communications even as their allies were blind. Unfortunately, this wasn’t able to save Poland, as just before the war broke out Germany added several layers of complexity to the Enigma machine by adding additional scrambler configurations and extra plug board inputs. The Polish then decided to share what they knew with other allied forces just two weeks before Germany invaded Poland.

Utilizing what Rejewski and the Biuro had managed to do, the teams of cryptanalysts in Britain’s Bletchley Park were able to decipher the now more complex Enigma messages up until the German’s stopped broadcasting the repeated message keys. At this point however, a brilliant mathematician named Alan Turing had begun work on a slightly varied way of exploiting the numerical structure of the Enigma cipher.

Turing is widely acknowledged to have developed a formal framework for the modern computer as a young academic before taking up his secretive role at Bletchley Park. Utilizing this system of computing, Turing thought of a way of mechanizing the process of deciphering the day codes through exploiting yet another human error: the error of being predictable. The cryptanalysts realized at some point that the German operators often wrote messages the same way again and again. For example the weather reports would often start one way. If you could reasonable assume that a message included a specific text (this was called a crib), then you can play with this piece of cipher text and run through the various permutations of scramblers until the code was revealed.

Turing built this machine and after a few iterations had a series of these machines to descramble the day codes in hours if the cribs were accurate. This wouldn’t always work, but it worked well enough to provide a huge advantage to the Allied forces as they intercepted German assault boats and convoys as well as troops and reinforcements. The German’s never suspected their Enigma had been cracked.

So I decided to take a break from Simon Singh’s book which I mentioned in my last two posts to take a look at some practical applications of modern cryptography in Cristof Paar and Jan Pelzl’s Understanding Cryptography: A Textbook for Students and Practitioners. The book is surprisingly informative and so far easy to read, even though it deals with a set of mathematics and code that I haven’t worked with.

The book starts of general enough, with a condensed introduction to cryptography and cryptanalysis. The authors give a brief overview the state of modern cryptography and the avenues an interested party can take to crack the codes being utilized today. One that I had briefly heard of before and would be interested in researching more about later is a side channel attack, where an attacker uses the system’s physical properties to circumvent the encryption by gleaming a little about the process. This can include anything from tapping the actual processor to read the electrical currents flowing through, to analyzing the sounds a keyboard makes when a user types in their keyphrase. Interesting as this is, it isn’t what I wanted to post about today, modulus arithmetic is.

Modulus arithmetic is more commonly known as remainder arithmetic or “clock arithmetic.” In code, the modulus operator is signified by the “%” symbol and when applied to two numbers X and Y will simply give the remainder of the two when X is divided by Y.

As Paar and Pelzl explain, even in early caesar cipher’s, all cipher text is created out of a finite set of objects. Modulus math can be used to tell us where in the set of numbers a digit/character lays after being ciphered and deciphered. What’s more, modulus arithmetic has certain fascinating properties, such as equivalency sets.

Now equivalency sets took me a while to understand completely since the concept was a bit foreign to me. Take for example 12 % 9… for the most part the answer we see and use is 3. But according to modulus arithmetic, there is an equivalency set made up of all other numbers that would also have the same remainder, that is {…, -6, 3, 12, 21, … }. This equivalency allows us to do some math with the other numbers in the set which can be very useful as we get more involved in public key cryptography.

I’ve been reading Simon Singh’s Code Book which reads as part cryptography lesson and part historical thriller. The last time I updated we read about the cipher of Mary Queen of Scots and how it was broken through excellent spy craft and cryptanalysis. Even though most us mere mortals wouldn’t be able to break her cipher, to a trained analyst like those who served Queen Elizabeth and Walsingham her spy master, the cipher was easily broken.

Mary was at the time under house arrest in England, watched over by a stern guardian who monitored all of her communication. As Singh tells the story, Mary thought herself forgotten by the world until a young catholic named Gilbert Gifford offered his services as a courier between Mary and a young radical named Babington. It turns out that Gifford was in fact a double agent who was asked by Walsingham (Queen Elizabeth’s spymaster) to become the courier. Needless to say during the entire time he was ferreting letters back and forth between Babington and Mary, he was letting Walsingham copy the letters character by character, giving Walsingham and his cryptanalysts time to decipher them, all the while leaving Babington and Mary to believe they were communicating securely. These encrypted letters which later decrypted by Walsingham, condemn Mary Queen of Scots to death for her role in the Babington Plot against Queen Elizabeth.

Now what Singh fails to mention is of critical importance here. Singh fails to mention how Babington and Mary, who had never met and as we know never really had a secure channel of communications, were able to coordinate their initial cipher. The challenge nowadays in cryptography is that initial handshake, how did Mary and Babington manage to overcome this problem?

Around the same time another cipher was developed that Singh suggests would have saved Mary’s life had she used it, the Vigenère cipher. Vigenére was a mathematician and cryptographer who developed a new cipher that used more than one caesar cipher alphabet. According to Singh, no one really thought to use the cipher until decades later, but the polyalphabetic cipher were considerably more difficult to crack than the monoalphabetic cipher. The problem that monoalphabetic ciphers like Mary’s had was that they were susceptible to frequency analysis. Polyalphabetic ciphers were also susceptible as Charles Babbage later proves.

Babbage is more famously known for his ingenious designs that predicted the computer over a century before the first transistor was invented at Bell Labs. Babbage saw the Vigenére cipher as a challenge and used mathematics and statistics, much like before the earlier cryptanalysts did when using frequency analysis against monoalphabetic ciphers, but this time around the mathematics gets considerably more complicated.

As we can see from Babbage and the Vigenére cipher, math is becoming more and more important in cryptography. Babbage’s Victorian-era story, the story of the “father of computing” tackling a challenging puzzle of mathematics and linguistics only to break yet another cryptographic protocol foreshadows our contemporary story of hackers and cryptopunks constantly tweaking away at the systems that secure the internet and our data.

I’ve always been fascinated and terrified by encryption algorithms. They’re the backbone of our web based economy and provide companies and users with some level of privacy. Of course nothing is fool proof, not even the most advanced of our encryption algorithms. It seems day after day we hear about hacker collectives that exploit a flaw in a system and extracted hashed and encrypted data that everyone fears might be cracked. I say fears, because most no one understands how these encryption algorithms work and how they really protect our data. Where are they weak and how do they shine?

For my research studio on algorithms I’ve decided to concentrate on understanding and implementing some encryption and decryption algorithms as well as playing around with some advanced mathematics, just so I can get a better idea of what it is we need in applications and to protect ourselves in an increasingly open (to spy on) world.

It was surprising to learn that the origins of cryptanalysis can be traced to the Muslim world after the birth of Islam. Considering the other numerous breakthroughs in the areas of arts, science and mathematics pioneered by those early Muslims, this shouldn’t have been a surprise but it was.

Hoping to find many more pleasant little surprises in the history and the code before I’m done.