Public-Key Cryptography

Abstract

In this chapter, we will explore some computational aspects of modular arithmetic, which we studied in Chapter 6. We will be concerned about how to compute certain numbers in a most efficient way. There is a whole field at work here, of which we barely scratch the surface, called computational complexity. For example, in Section 6.4 we introduced the concept of greatest common divisor (gcd). You might wonder how quickly one could compute the gcd of two, say, 1000-digit integers. As another example, we now discuss how to quickly compute a ^b modulo c for given positive integers a, b, and c.