(as given from an example here) has 2 products (other than 1 and itself), both of which are extremely large prime number. Clearly, this wouldn't be very easy number to factor quickly, even if you do have an entire list of prime numbers, and I'm guessing it isn't nearly as difficult as numbers that websites use for encryption.

Also, if you're interested, the website I linked to earlier has a challenge problem so you can try hacking a large prime number like the one above.

]]>As for credit card numbers: the security measures taken to protect credit card numbers comes not in the way that numbers are issued on cards, but rather how those numbers are transmitted from your computer to your vendor. This transmission involves an "encryption" phase where your credit card number is scrambled into unreadable gobblity-gook and a "decryption" phase where the transmitted gobbilty-gook is turned back into your credit card number. The security of the encryption, then, is in its ability to keep people who intercept the gobbilty-gook from being able to decrypt it back into your credit card number. Its in this encryption/decryption that number theory creeps in. Dan's got the right idea about how this stuff works, but we'll talk about it at length closer to the end of the term.

]]>The process was a few pages long in my notes so here's a link to a Wikipedia article that I used to clarify my notes (which includes how this system is used). I guess I should have looked at the book in the first place…chapter 8.2, page 233 is where the RSA stuff begins.

Well, even though it didn't really contribute to your questions specifically, this is a way prime number computation can be used in systems security. At the very least, it's an example that encompasses a lot of the things we've been learning so far!

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