[Anonymouse]

Originally Posted by BadPhormula

I don't think anyone should worry too much about super computers trying to break crypto systems.

(OT for a bit) Don't worry about it at all, because even if you have a supercomputer, you're not going to break public-key encryption this side of the Sun going nova, at least not until someone proves the Riemann Hypothesis* - and trust me, that ain't gonna happen any time soon because no-one on this planet has the slightest idea as to how to prove it, or even disprove it (it's believed to be true, and mathematicians are praying to God that it is true, because a number of major theorems are based on the assumption that it is!). They can spend as much dosh on it as they like, and waste years of computer time (that's computer-years, not man-years) - the difficulty in breaking encryption is mathematically fundamental.

The only known method of deriving the prime factors is to systematically check all the possibilities, because there is zero correlation between them (that is, neither prime tells you anything about the other) - and there are so many possibilities that the power or speed of the computer is entirely irrelevant. Without a proof of the Riemann Hypothesis, there's no known way to derive a faster method, so there aren't any shortcuts - mathematics doesn't work that way. They really are wasting their time and money; the reason you never hear of public keys being broken is that it simply does not happen. Planting a trojan is cheating and can be prevented in any case by a) decent AV software, b) not using an administrator account so the damn trojan can't install in the first place, and c) being careful - but that is not breaking encryption. I don't know offhand how many 60-digit primes there are, but I recall reading that there are enough to see us through several million years without repeating even once. The computer does not exist that can crack that problem in the time available, i.e. approx. 5,000,000,000 years.

If it could be done, it would have been by now and the news would have been all over the world in less than an hour. Encryption per se is perfectly safe unless some unsung mathematical genius turns up. Bear in mind that it takes over 300 pages of symbolic logic, starting from first principles, just to prove 1 + 1 = 2.


* If you're into recreational mathematics and/or popular science, you've probably heard of it and might even understand it. If not - to borrow from Arthur Dent, don't ask me how it works or I'll start to whimper...