factoring large prime numbers

As I am sure many people who follow this list know, the Subject issue is a the juncture of number theory and computer science.

I found the article about this on Slashdot called Factorization of a 768-Bit RSA Modulus.

Also you may be aware that this is related to security, cryptography and its "strength".

Of course all security, including the lock on your front door is not perfect. It is not designed to be either. It is only designed to "hard" to break.

As technology and our knowledge of mathematics increases, what is "hard" has to be pushed out. Even this factorization took many years. But for the guys trying to break into NASA and the Department of Energy, this is not a long time.

As I was reading this I was thinking about how I know about "public key crytography" but my explanation to a layman about what this really is and why this is important is probably not so good.

Slashdot is really great for "bit-heads" and with the posting I found the excellent explanation below.

Regards..
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Re:Can someone explain this to me?

by Mini-Geek writes: on Thursday January 07, @12:52PM

What they did was factor a 768-bit number, like one that could be used as a 768-bit RSA public key. e.g. to factor 15, you need to find that it is equal to 3*5, which can be easily done by dividing the first few primes and finding that 3 divides 15. To factor a very large number, like a 768-bit number that is semiprime with the two factors both about the same size, (as is the case with RSA public keys) is a very difficult task. It is currently best done by the General Number Field Sieve (GNFS). For more info on any of these concepts, use Wikipedia.

This demonstrates the possibility of breaking any given 768-bit RSA key by factoring the public modulus, and shows how much work that takes. Note, however, that it is still very difficult, and in this case took multiple years of calendar time and hundreds of years of CPU time to crack.

This does not mean that every 768-bit RSA key can be cracked any more easily than it could before, it just demonstrates that we have the ability to crack any 768-bit RSA key (given the time and resources).