Public-key Cryptography: Theory and Practice

2.9. Finite Fields

Finite fields are seemingly the most important types of fields used in cryptography. They enjoy certain nice properties that infinite fields (in particular, the well-known fields like , and ) do not. We concentrate on some properties of finite fields in this section. As we see later, arithmetic over a finite field K is fast, when char K = 2 or when #K is a prime. As a result, these two classes of fields are the most common ones ...