Cryptography and Network Security

Chapter 2

Mathematics of Modern Cryptography

2.1 Basic Number Theory

Number theory is the process of learning the integers and the properties of objects made out of integers (for example, rational numbers) or generalizations of the integers. Number theory plays a vital role in the field of security, memory management, authentication and coding theory. Because, in many cryptographic algorithms used in the field of security, authentication and coding theory, the messages are represented as integer numbers. These integer numbers are converted into some other format before sending it to receiver side. Fermat’s theorem provides a good example of the importance of the number theory. Fermat asked a question that, can prime p be written as the sum ...