SCOTT SIMON, host:
Many students who don't exactly take to math will ask, but, like, when will we actually ever need to know this? Well, there's a new answer — because it could be a matter of national security.
Last week, a prominent cryptographer warned that a mere math error could have dangerous consequences. Our math guy Keith Devlin joins from Stanford University. Keith, thanks very much for being with us.
Dr. KEITH DEVLIN (Director, Center for Study of Language and Information, Stanford): Hi, Scott. Good to be here again.
SIMON: Now, the cryptographer is a very imminent mathematician named Adi Shamir.
DR. DEVLIN: Correct.
SIMON: And tell us what triggered his concern and what he said?
DR. DEVLIN: Okay. So we have to realize that Shamir, together with a couple of colleagues — Ron Rivest and Leonard Adelman who were then all at MIT back in the '70s — they came up with what's now the standard method for encrypting messages sent over the Internet. It's called the RSA System, after their initials of Rivest, Shamir and Adelman, and the clever thing about this system is it allows two computers that have never been in communication before to establish a secure communication link.
And Here's essentially how it works. Supposing I wanted to go online and order something from the Car Talk Web site using my credit card. My computer would send…
SIMON: I would never use my credit card on the Car Talk Web site of all Web sites.
DR. DEVLIN: (Unintelligible)
SIMON: Yeah, exactly. But go ahead, forgive me. Yeah.
DR. DEVLIN: This is hypothetical.
SIMON: Yeah, yeah.
DR. DEVLIN: So I give my credit card to my computer, my computer connects with Click & Clack's computer and gets from them a public encoding key for encoding messages. My credit card details are then encoded, sent over the Internet. When that message arrives at Click & Clack's Car Talk computer, they use a secret key that only their computer knows to decode that message. And anybody that picks up the message on transit - and lots of people will pick it up or can pick it up in transit - won't be able to decode it because they might have access or they can have access to the public encoding key, but the decryption key is a secret one that's different from the encoding key. This means computers can communicate securely even though they've never previously been in communication.
SIMON: What's Mr. Shamir worried about then?
DR. DEVLIN: Okay. So…
SIMON: Dr. Shamir probably.
DR. DEVLIN: Right. Well, the weird thing about this system, the thing that was surprising when it was first proposed in the 1970s was the number you used to unlock the message is not the same as the number you use to lock it. And people first thought, well, how can that be? Because with a physical padlock, the same key that locks it unlocks it because you just turn the key the other way.
However, it turns out to be different when you're using mathematical keys. The keys in this case are large numbers. The secret decoding key that each computer generates consists of two very large prime numbers of the order of a hundred or more digits. The public encoding key that anybody can get hold of or anybody's computer can get hold of is the product of those prime numbers.
Now, in principle, given a large 200-digit number, which is made up by multiplying two large prime numbers, in principle, you could find what those prime factors are. However, the fastest computers in the world would take hundreds of years to solve that one problem, so the system is secure not because you can't, in principle, find the key to unlock the message, but it would take the fastest computer hundreds of years to do so; that's the system security.
There are two dangers to this system. One is that some smart mathematician, probably here at Stanford, would one day come up with a very, very fast method of finding prime factors. Now, that hasn't been done, and the experts believe that it won't be done, but it's a possibility.
Shamir has pointed out that there's a much more likely danger out there. If there is a new computer chip that comes out that has a single arithmetical flaw in it so that for two numbers - when it multiples them together - it gives the wrong answer, then using that information, a hacker could crack any RSA cryptogram system in any computer anywhere in the world. In fact, the hacker could simultaneously crack millions of computer security systems - unlock all of the credit card and banking information for millions of customers. All it would take is one arithmetical error in one computer chip, and the game is over as far as Internet security is concerned.
SIMON: Now that you've said it, it could be an intentional mistake.
DR. DEVLIN: It's always possible. I mean, when you consider that we - you know, computer chips are manufactured all over the world. You know, if there's a simple mistake in one - either intentional or accidental - where there is an arithmetical problem, then, as I said, the game is over for Internet security, and it's not clear how the world would get over that hiccup.
SIMON: Keith, I think you have just ruined Christmas for Amazon and eBay and all other online retailers.
(Soundbite of laughter)
DR. DEVLIN: I - that was certainly not my aim.
SIMON: Lots of luck getting a research grant, Dr. Devlin.
DR. DEVLIN: Keith Devlin, who's executive director of the Center for Study of Language and Information at Stanford, thanks so much.
SIMON: Okay. My pleasure, Scott. And be careful with that credit card.
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