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Cryptography
High Performance Encryption Methods Ever notice when you're shopping online how as you enter that secure cash register zone where you give the merchant your credit card, your connection to the Internet seems to slow down? That's because the information you're sending back and forth is encrypted using public-key cryptography. Now a modern computer can perform the several complicated mathematical operations on 128-digit numbers necessary for ordinary public-key cryptography in about 1/100th of a second. That seems fast, but a server computer on a busy merchant's site has to reply to thousands of requests every minute. Those hundredths of a second add up pretty quick when you're waiting for your real-time stock quotes. The merchant can't compromise the security of the transaction. He either has to buy more servers or let the customers wait. So the challenge for the cryptographers at Microsoft Research is to strike a balance between speed and security. The fewer steps in an algorithm, the faster it works. The question then becomes, does a fast encryption message provide enough security for the data? That's always a judgment call. Cryptographers Peter Montgomery, Kristin Lauter and Ramarathnam Venkatesan are pursuing a promising high-speed encryption method called elliptic curve cryptography. Elliptic curves are simple mathematical functions, cubic equations like y2 = x3 - 3x - 5. When these equations are plotted on a graph, they form a curve that looks something like this:
Montgomery, Venkatesan and colleague Dan Simon are working on a mathematical analysis of performance versus speed. They adapt existing tricks and invent new ones, searching for a way to make things like digital signatures shorter and easier to process without sacrificing security. "That is the big question," says Simon. "What is secure enough?" |
The equations that
describe elliptic curves work as one-way functions: you can take two points on a
the curve, draw a straight line through them and find a third point where this
line re-intersects the curve, but that third point leaves no clue as to the
identity of the first two. These equations can be used to build public key
cryptosystems with keys that are smaller than the keys in traditional
Rivest-Shamir-Adleman or Diffie-Hellman systems, and take the computer less time
to encode and decode messages. Even better, the best available algorithms for
breaking elliptic curve systems are slower than the best available algorithms
for breaking RSA, so it appears that elliptic curve systems may be more secure.
