Cryptography and Network Security Principles and Practice, 8th Edition - Pearson

CHAPTER 5

Finite Fields

 

5.1 Groups

Groups

Abelian Group

Cyclic Group

 

5.2 Rings

 

5.3 Fields

 

5.4 Finite Fields of the Form GF(p)

Finite Fields of Order p

Finding the Multiplicative Inverse in GF(p)

Summary

 

5.5 Polynomial Arithmetic

Ordinary Polynomial Arithmetic

Polynomial Arithmetic with Coefficients in Z_p

Finding the Greatest Common Divisor

Summary

 

5.6 Finite Fields of the Form GF(2ⁿ)

Motivation

Modular Polynomial Arithmetic

Finding the Multiplicative Inverse

Computational Considerations

Using a Generator

Summary

 

5.7 Key Terms, Review Questions, and Problems

 

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

• ◆ Distinguish among groups, rings, and fields.
• ◆ Define finite fields of the form GF(p).
• ◆ Explain ...