ABSTRACT
This chapter considers some topics from modern algebra that have important uses in cryptography. We begin with group theory. Many cryptographic functions are computations in groups. Then we study rings, which generalize the structure of the integers modulo m. We consider fields, which generalize the integers modulo a prime p . We investigate polynomials and then make a brief incursion into algebraic number theory, which we need to describe the number field sieve integer factoring algorithm. Other books that cover the same material as this chapter are [78] and [53].
