Solving the Digit Encryption from Summer Wars?

How would one go about getting a sentence from a 2056 digit sequence? In the movie Summer Wars, Kenji manages to solve said encryption. The only useful site I found was the e're reliable *coughs* Wikipedia, and that still doesn't help me. Does anyone have any non-trolling ideas?

 

Didja click the hypertext at all? it hypered Wikipedia. After a bit more searching, I found this article, again from the e're trusty *cough* wikipedia. i cant fully understand it, i might go to one of the math profs and see if they can dumb it down for me at all. still, anyone know how to put it in layman's terms?

 

That about sums RSA up. To explain it in more depth, it works by having two numbers everyone knows, the encryption exponent and the modulus. If you don't know what modulus is, it's the remainder after a division. Anyway, so you have some series of numbers that make up your message, and you raise it to the exponent, and then "mod" it by your modulus. To break it, you use Euler's totient function and get the totient of the modulus. Then you use Euclid's GCD algorithm, and find the inverse of the exponent (mod totient of your modulus). Finding the totient of the modulus is near impossible for a large modulus. You have to prime factor it. How would you efficiently factor a number that's 100 or so digits long? Although there are simpler ways than just checking every single number beneath it to see if it's a factor (checking the prime numbers only, checking up to the square root of the number, to name a few), it's not efficient enough.
Finding the inverse of a number mod some other number is a complicated process to explain. I'm sure you can find various explanations of it. That process is actually fairly efficient (if you get big-O notation, it's a logarithmic complexity, I think).
Anyway, once you have your inverse exponent, you raise the encrypted message to the inverse exponent (and mod it by the original modulus, I think). That gives you back your original series of digits.
As for how to make a series of words into some digits, just substitute 01 = a, 02 = b, and so on. If you're trying to break the encryption, you can't always guarantee that the other person will do that. It's likely they're using some other rules for turning words into numbers and numbers into words.

 

Let the 14 year old blonde girl solve it, she did computing once at school. And don't worry about those pesky velociraptors chasing you, the T-Rex will eat them.

 

The Solution is
"The magic words are squeamish ossifrage to know is to know that you know nothing That is the true meaning of knowledge"

 

as they showed in Summer Wars