ABSTRACT
R epresentation of numbers is an important topic in the study ofnumber theory. Expressing a number in terms of a continued fraction is of particular interest among the different ways of representing numbers. It provides knowledge of the nature and properties of numbers from a new perspective. Combined with other methods, continued fractions have been used in solving many difficult problems arising from the course of understanding numbers. From examples, continued fraction methods play important roles in the rational approximation of real numbers, finding roots of quadratic equations, and solving Diophantine equations and congruence equations. These provide useful ideas and methods for the development of number theory. In this chapter, we introduce basic knowledge of continued fractions and an application in cryptography, that is, a method of attacking the Rivest, Shamir, and Aldeman (RSA) encryption algorithm using continued fractions.
