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-BOL quote: "...and Blogger..."-

No particularly interesting dreams this week -- it strikes me once again that dreams generally deal with very ordinary situations, but with limited ability for your brain to manipulate them in order to see what would happen if x or y happened and you reacted in z way.

I'm surprised that, as the years go by, less and less people seem interested in cryptography. In world war eras, sure, there was that sort of umbrella fascination with spies, which included cryptography, but now crypto is mostly associated with day-to-day data encryption. While this is an extremely important field, it's also a lot less awesome than spies, I must admit.

What makes crypto unique, in my opinion, is that it is one of the few "practical" jobs in which theoretical mathematicians can participate. Both the public and private sectors are always looking for new encryption schemes that are more difficult to crack, and this process actually requires mathematical research, if you can wrap your mind around that phrase.

Many of the encryption schemes deal with prime numbers, a concept which is still surprisingly mysterious to modern mathematics. Prime numbers have the advantage that, since they are not divisible by other numbers, there won't be duplicate "keys" that unlock the same encrypted message. For example, if each digit in a passcode multiplied the numbers in the encrypted message (which wouldn't be particularly secure, but as an example), you would have to guard against situations in which you could use either "41" or "22" to unlock the same message. Naturally, you'd want only the one correct key to unlock it to make it harder for someone to hit a working key by accident. If the numbers were restricted to primes, then neither 4 nor 1 would be allowed, and only 22 could unlock the message.

Another important area for cryptos to keep track of is letter usage frequency. If a person is looking at a poorly encrypted document and sees 12 times as many $'s on it as anything else, he could guess straight away that "$" means "e". The way around this problem is to give frequently-used letters multiple representations, while keeping the representations of rarely-used letters proportionately low. If "e" is now represented by "$", "&" and "*", it's harder for a person ignorant of their meanings to notice the huge streaks of the letter in the document, but decoding the document is essentially just as easy as before for people who do know the relationships.

Reality check. For some more rigorous cryptomania fodder: http://www.mycrypto.net/encryption/crypto_algorithms.html