29-09-2012, 02:44 PM
The RSA Implementation of Public Key Encryption and Digital Signatures
ABSTRACT
Typical encryption techniques use mathematical operations to transform a message (represented as a number or a series of numbers) into a ciphertext. Mathematical operations called one way functions are particularly suited to this task. A one way function is one which is comparatively easy to do in one direction but much harder to do in reverse. As a trivial example, it is comparatively easy to square a two digit number; with a little concentration, many people can probably multiply 24 by 24 without using a pencil and paper. One the other hand, calculating the square root of the number 576 is much harder, even with a pencil and paper.
The RSA system uses one way functions of a more complex nature. Specifically, the system uses modular arithmetic to transform a message (or pieces of the message, one piece at a time) into unreadable ciphertext. Modular arithmetic is often called "clock" arithmetic, because addition, subtraction, and the like, work like telling time. In a 12-hour system, four hours after 10:00 is not 14:00 (10 + 4 is not equal to 14); it is 2:00. This is because we subtract out 12 (or any multiples of 12) after doing the addition.