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1 Wendy: We be free o' our pursuers, cap'n!
2 Long Tom: That be good. Now, let's be seein' what we can be makin' o' this map.
3 Long Tom: Hmmm. It be writ in an ancient hand, usin' a long forgotten secret pirate cipher, but I can be readin' some o' it.
4 Wendy: How so, cap'n?
4 Long Tom: I be studyin' arrrchaic languages!
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To illustrate: If you wanted to send the message "The treasure is in Tortuga" in a code, you'd need a codebook with pre-agreed encodings of the ideas of "treasure" and "Tortuga" at the very least. If "treasure" maps to "bananas" and "Tortuga" maps to "the moon", then your encoded message would be "The bananas are on the moon". The person receiving your coded message would need to know that the bananas refer to treasure, and the moon refers to Tortuga. Anyone who didn't know those mappings would have no idea what the message was really about, and no conceivable way to discover the meaning from the message itself. (To break such a code, you basically need to steal the codebook or interrogate someone who knows it.)
On the other hand, if you wanted to send the same message by a cipher, you'd apply some sort of pre-agreed mapping to the letters in the message. An example might be to reverse the words and replace each letter with the next letter of the alphabet, which yields: "fiu fsvtbfsu tj oj bhvuspu". Ciphers may look less comprehensible, but they are more liable to be broken using no information but that contained in the message itself. In this case, the letter "f" appears several times. The most common letter in English text is "e", so we might guess that "f" represents "e" - which in this case is true. A variety of such techniques can crack pretty much any cipher invented before about 1950 and the advent of computer cryptography.
At one level, computer algorithms can scramble text so thoroughly (and unscramble it correctly assuming you have the correct key) that unaided humans have essentially no hope of cracking the encryption manually. However, with the help of computers themselves, some of these algorithms can be broken and messages decrypted.
Moving up a level, there are some types of cryptographic algorithms that rely on computational properties of mathematics so that messages can be encoded and decoded (if you have the key), but are more or less impervious to any sort of cryptanalysis other than the brute force method of trying every possible key. These are the sorts of encryption schemes in common use today for encrypted Internet connections, email, and banking transactions. But here's where things get interesting, because the number of possible keys that you can try in a given time depends on the speed of your computers. As computers keep getting faster and faster, old cryptographic schemes that used to be effectively secure can become more and more easily broken. The advent of quantum computers threatens to speed up this sort of encryption cracking by vast amounts, rendering most traditional encryption schemes useless.
But moving up yet another level, we can also harness the power of quantum stuff to make quantum cryptography - which goes a step beyond mathematics and uses properties of physics to encode messages securely. To crack quantum encodings, you basically need to change the laws of physics, so it'll be impervious to anything short of Chief Engineer Montgomery Scott.
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