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Safety in Numbers

Safety in Numbers

You may not know it, but you depend on math for security - at least as far as protecting information is concerned. We'll talk with a mathematician about secret codes - after this on Earth and Sky.


DB: This is Earth and Sky, on the mathematics of secret codes.

JB: The main problem in code-making is to come up with something unbreakable. One coding system often used in the banking world - known as the "RSA cryptosystem" - relies on a certain property of numbers for its strength. For some reason, it's just easier to multiply numbers together than it is to do the reverse - to divide a number up, or "factor" it.

DB: So if you wanted to crack the RSA cryptosystem, you'd basically have to factor apart really huge numbers, say two hundred digits long. No one's been able to crack it so far. But it's possible that the code isn't as strong as it seems. That's because it's possible that dividing apart or "factoring" large numbers isn't as hard as it seems. Dr. Joe Buhler of Berkeley's Mathematical Sciences Research Institute told us more:

(Tape 0:12:38-0:13:20) It seems basically very unlikely that computers will get fast enough to be able to routinely factor large integers. However, it's possible that factoring isn't nearly as hard a problem as it looks. Namely, one of the best arguments that this is in fact a strong cryptosystem is that so far nobody's been able to factor large numbers. But there's no reason that somebody might have a very clever idea and come up with a procedure, an algorithm, to factor large numbers. If that happens, the RSA cryptosystem is probably out the window.

JB: Thanks to Dr. Joe Buhler for speaking with us. And with thanks to the National Science Foundation, we're Block and Byrd for Earth and Sky.

Author: Beverly Wachtel

Thanks to the following individual who aided in the preparation of this


Dr. Joe Buhler
Deputy Director
Mathematical Sciences Research Institute
Berkeley, CA

If you enjoyed this program, you may be interested in the following websites:

Mathematical Sciences Research Institute:

RSA Data Security homepage:





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