The Web Cryptology Game CODEBREAKERS.EU edition 2015

Transcription

1 Lecture 2, in which we look at the main methods of concealing information. We will learn that what used to be an unbreakable cipher can today be compared to a child play. We will also see how this children game can complicate the work of a codebreaker. In the present lecture we will devote our attention to the subject of the basic methods od concealing information. Probably we already can explain what steganography is and can tell the difference between codes and ciphers. It is time to look at how they work in reality. STEGANOGRAPHY Please take note of the word subject above: the letter t is written in a slightly smaller font than the other letters. You might have overlooked that while reading it for the first time. Now, however, knowing what you need to look for, you will find, in the first two sentences, several other characters that differ in size from the rest of the text. When you put these letters together they will form a phrase thisisthekey. The meaningful letters in a text can be made distinctive in many ways: by changing the font size, or type; by underlining or inserting an unexpected ápostrophe. Yet another method of transmitting information secretly consisted in formulating an apparently innocent message, in which only certain characters (plain to the receiver of the message) were meaningful. Let s take as an example the following sentence: Their gentlemanly spirits sagged almost tragically, taking out of every word only the third letter we get a secret message enigma. To compose a logical and unsuspicious masking text was a certain problem, however, dispatches of that kind were usually sent as trade correspondence, in which the use of e.g. a list of items or accepted abbreviations is natural. It was a Greek historian, Herodotus, who related the story of a Greek named Histiayos serving at the court of the great king of Persia. He decided once to send to his cousin in Miletus a message about a convenient moment to stir the uprising against the Persian rulers. He summoned one of his slaves, shaved his head and tattooed the text of warning on it. When the hair on the messenger s head grew back, he sent him to his country. These examples show that there is much reason behind hiding the fact of sending information. The point is that no one should know that the head of the slave (mentioned when the word steganography appeared in our course for the first time) has been tattooed. The guards of the Persian royal

2 road all too often had to search the messengers passing through, and might have failed to notice a message hidden under the hair - steganography thus fulfilled its role. In time, its methods became more sophisticated, as the users came to the conclusion that the fact of sending a courier or a parcel itself arouses suspicions of the enemy if no innocent and credible reason for sending them is provided. They would, therefore, send apparently innocent messages, hiding the proper message in their text or on their carrier. The illustration on the right is an example of such a situation. It was drawn by an insect researcher who happened to be a general in British army, Roberta Baden-Powell. As it turns out, the butterfly is an issue of secondary importance here, in reality the drawing presented the layout and distribution of guns of one of enemy s fortresses. A typical method of this kind was the use of the so-called invisible ink. The proper content of the message was written on a sheet of papyrus, parchment or paper with milk or lemon juice and then, after the invisible ink had dried, an ordinary letter, e.g. greetings for a cousin, was written on the same page with normal ink. Even during a detailed inspection the messenger could claim that he was transporting only some family correspondence. The addressee, later, heated the message over a burning candle or rubbed the sheet with a cloth soaked in an appropriate reagent, thus deciphering the hidden message. Just when it seemed that steganography would soon become a remnant of the past replaced by codes and ciphers, the era of computers has brought its unexpected revival. A substantial amount of information can be transmitted almost unnoticeably, without a visible or audible deterioration in the quality, in the graphic and music files sent via the Internet. MORE ABOUT CIPHERS Steganography has still not lost its significance, however, at the turn of our era cryptology made its comeback. It was largely due to Julius Caesar, who had to have at his disposal reliable methods to secretly pass on orders to the commanders of his military units. So he invented and used his own

3 cipher, eventually named after him. According to the contemporary standards the Caesar cipher was not very sophisticated. Each letter of the plaintext was replaced by a letter three positions down the alphabet. In this manner the letter A was replaced in the cipher message by D, B by E etc. The full modification in the cipher used by Caesar is shown below: plain alphabet: cipher alphabet: ABCDEFGHIKLMNOPQRSTUVXYZ DEFGHIKLMNOPQRSTUVXYZABC His own name, IULIUS CAESAR, thus became LXNLXV FDHVDU. For unclear reasons, or simply out of habit, Caesar would continue to use a shift of three. In other words, he encrypted his messages without changing the key, which is not a safe practice. Presumably, Caesar could feel confident as the tribes he fought were not aware of the existence of alphabets, let alone a cipher. If, however, he had to fight with some more civilised enemies, his cipher would have turned out dangerously weak. The structure of the cipher allowed for the use of merely 23 keys, corresponding to different shifts between the alphabets. To put it differently, the enemy, aware of the construction of the Caesar s cipher, would have to test only 23 possibilities to be able to break any message sent by Caesar. LET S BREAK THE FIRST CODE! It is a mystery why Caesar would never change the key to his cipher, which means that the letters were moved always by three positions. It was not the safest approach though safe enough as the tribes he fought were illiterate and therefore unaware of the existence of ciphers. How could then a potential literate enemy try to break Caesar s code? Let s assume a coded message of the following content: EXXEGOEXSRGI. We can check all possible moves by 1 letter (where A changes into B) up to the movement by the whole alphabet (where A changes into Z). Let s assume that the author has used the English alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ

4 If the author has moved by three letters forward - has changed A to D, in the coded message we have to move three letters backwards - from D to A. The table illustrates what messages we get by checking one by one each of the possible shifts. Because the message has already been deciphered there is no need to check further shifts. As you can see the messages are written with no spaces or punctuation marks. As you can see breaking the Caesar cipher has not caused any difficulty. There is, however, a simple way of making the Caesar cipher more secure, in reality - any cipher, and even now cryptologists make use of the opportunities it offers. If we have two relatively weak ciphers, we can increase the security level applying them to the plaintext one after another. There is a type of a word game that children from certain language circles like to play, in which the order of letters of a particular word is reversed in order to hide e.g. not a very favourable nickname of a teacher. In this manner LILLIPUT would change into TUPILLIL, LETTER into RETTEL, and SUPER into REPUS. In the early phase of the development of cryptology modifications of this type were taken quite seriously. We could, for instance, apply the child cipher with the reversed order to the word CAESAR first, and then encrypt the result with the classic Caesar cipher. Let s look at the process: plaintext: child cipher : Caesar cipher: CAESAR RASEAC UDVHDF Anyone trying to break this cryptogram by applying all of the possible keys of the Caesar cipher, would get a non-existent Latin word RASEAC. Whether he or she manages to discover the reversed word CAESAR in it depends on their intuition and ingenuity. MORE ABOUT THE CODES The reports related to the method used by Julius Caesar can indicate that ciphers developed as the second, after steganography, method of hiding information. Codes developed later.

5 Speaking of which, the language that we use on everyday basis is also a certain type of a code. In our early childhood we tend to give names to concepts using the language of the people surrounding us. Each word that we utter or a phrase we construct represents some concept, and that correlation is a matter of convention. After all people speaking languages foreign to us can understand each other perfectly well, even though the words that they use to represent the same concepts as we do are completely different. The analogy with foreign languages manifests the code nature of our language: people speaking a common language use one common code, allowing them to communicate. However, it is enough to use this code when speaking to a person of a different language circle to encounter an information barrier. Besides, there are particular variations of language the goal of which is to hide information from an unwelcome eye. Such are the prison or smugler slangs, as well as the language of most disciplines of science. In the first lecture we have already mentioned the subject of codes and the fact that during certain periods they were particularly popular as a practical tool for concealing information. In order to effectively hide the transmitted messages all that had to be done in this strategy was to assign a string of characters to words or even whole expressions. Below an example of a typical message: To staff. Company commander reports enemy movement noticed. It can be expressed in the following manner: In this case the numbers in the code would have the following meaning: 2133 TO STAFF, 3246 ENEMY MOVEMENT, 3452 COMPANY COMMANDER, 4354 REPORT, 9045 NOTICE,

6 It s easy to notice that this way of hiding information, although relatively easily applied, imposes certain restrictions. The code language is fairly rigid (and also of limited capacity) and therefore it was impossible to prepare codes for every situation. Because of that, a new code was invented in the period of the Renaissance, the so-called nomenclator. In its most typical form, it contained only the code equivalents of the notions most often used in correspondence and an accompanying simple cipher, which served to secure those fragments of the text for which there were no equivalents in the code. Here is an example of a simple nomenclator: COMPANY 8381 BATTALION 9211 REGIMENT 1153 DIVISION 0455 ATTACKING 9802 DEFENDING 6653 RETREATING 1388 DELIVER AMMUNITION 9077 SEND REINFORCEMENTS 6615 ABCDEFGHIJKLMNOPQRSTUVWXYZ CIPHERABDFGJKLMNOQSTUVWXYZ a report: Third company attacking. Deliver ammunition encrypted with the use of the nomenclator above will look as follows: TBDQH This short theoretical introduction will let you have a deeper insight into the issues related to cryptology, as well as solve the tasks accompanying the present lecture. Good luck!