Special Sub-Topic: Introduction to Cryptography and its History
|One of the first cyphers used in the world was the so-called "Caesar cypher". In this cypher, each letter is replaced by the letter 3 after it in the alphabet, so A would become D, B would become E, and so on, until X became A, Y became B, and Z became C. Using this cypher, how would you encrypt the message "jinx"?|
mlqa. J is replaced by m since m is three letters after j. Similarly, i is replaced by l and n by q. To go three letters after x, we loop around and get back to a.
|Now you receive a message encoded in the caesar cypher which states "Vrphergb khos ph". What is the decoded message?|
Somebody help me. If you encode a message by going 3 letters later in the alphabet, you decode it by undoing that and going back 3 letters. V goes back to S, R goes back to O and so on. To go back 3 letters from B, you wrap back around the alphabet.
|The problem with the caesar cypher is that anyone who wants to, can decode it. One possibility to counteract this is to make the method of coding more secret, for example to translate all the letters forward by an unknown number of letters (known to you and the recipient, but not to anyone who intercepts the message in route. It could be 3 letters (like the caesar cypher), or it could be 25. Knowing this, what might the message "Aol mvya pz bukly haahjr" be decoded as?|
The fort is under attack. The key is to look at one of the short words ... trying some common three letter words as aol, we see that if "the" is moved forward 7 letters, we get aol. After that, decryption is fairly easy.
|Even using the method above, there are only 26 possible ciphers to be used (one of which doesn't even encrypt the message). A spy intercepting the message could just try all 26 and be done. To counteract this, some cryptologists suggested a code where the letters were rearranged entirely. Each letter would be assigned one other (possibly the same) letter, and every occurence of the original letter would be replaced by the new letter. "Good", for example, could be enciphered as "abbc", "pmma", "baad", or any other similar structure. Using this method, how many possible different ciphers could be used? |
about 4 times 10 to the 26th (400 septillion American, 400 quadrillion European). Obviously, it is no longer possible for the enemy to simply try every possible method of decoding the message. Nevertheless... (see next answer)
|True or False? Because there are so many possible combinations for such a code (a "simple substitution cypher"), the code is virtually unbreakable.|
f. This may seem surprising, until you think about it. The key is to use what is called frequency analysis. Some letters are used more in any language than others are (In english, for example, e is used more often than any other letter). If e is always replaced by the same letter, than the letter which occurs most often in the coded message is probably the one that e is replaced by. Many letters don't appear as double letters, further narrowing things down. Finally, if a 3 letter word appears 25 or 30 times a page, odds are its "the".
|You receive 400 pages of a secret document encoded by the method in 4. Looking at it, you notice that in the coded message the letter "C" appear 50 times in the 400 pages. Furthermore, all 50 times the "C" is immediately followed by a "M" in the coded message. What letter does the "M" probably represent?|
U. It is likely that C represents the letter Q, both because it occurs so rarely and because it is always followed by the same letter. Given that, the M simply has to represent the U. This code isn't nearly as secure as it seems at first glance! To counteract this, some mathematicians in the 15th to 16th century created codes which change over the course of a message. M may represent U in one sentence, but it may represent T in the sentence after it. This makes the code much more difficult to break, though not impossible.
|One of the triumphs of modern cryptanalysis was the breaking of what cipher used by German U-Boats during World War II?|
Enigma. This also marked one of the first uses of (primitive) computers to break codes ... Alan Turing was one of the chief mathematicians on site. Even though the British knew a method of breaking the code, the Germans were able to thwart their efforts somewhat by changing the code slightly each day. It would take the British and their computers half a morning (or sometimes more) to break the new code, so messages were safe ... for an hour or two, at least.
|Although computers have made breaking codes much easier, they also have opened up horizons to many new ways of breaking codes. One of the codes used today, RSA, is based on computers being able to carry out operations with extremely large numbers. RSA's security is based upon the inability of an outsider to factor a large number into two of what kind of smaller numbers, numbers which cannot be written as the product of two numbers smaller than themselves?|
Prime Numbers. Basically RSA works as follows: Each person published what is known as a public key, a number that is known to everyone. Messages are converted to series of numbers, and each number is taken to the power of the public key. The only (practical) way to undo this operation is to take the numbers in the coded message to a certain other power. The only way you can know this number is by knowing the factorization of the public key. What makes this code special is that even the person who encodes this message doesn't know how to decode it. It is (for now) secure in that even eavesdroppers can't decode it.
|Even RSA cryptography may not be safe. The mathematician Peter Shor has devised a way to factor large numbers incredibly quickly. Unfortunately, his method is as of yet impossible to implement, because it relies on the use of what kind of computer?|
Quantum Computer. Quantum computers were first suggested by Richard Feynmann (of "Surely you're joking!" and bongo drum fame). Shor's method relies on a quantum computer being able to store much more information at a time (as a superposition of a large number of what are known as "Quantum states"). All is not lost, however. Other people have suggested methods of using quantum mechanics to create even more secure codes. The battle goes on!
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