Finite Field Arithmetic

Finite Field Arithmetic

Arithmetic in a finite field is different from standard integer arithmetic. There are a limited number of elements in the finite field; all operations performed in the finite field result in an element within that field.

While each finite field is itself not infinite, there are infinitely many different finite fields; their number of elements (which is also called cardinality) is necessarily of the form pn where p is a prime number and n is a positive integer, and two finite fields of the same size are isomorphic. The prime p is called the characteristic of the field, and the positive integer n is called the dimension of the field over its prime field.

Finite fields are used in a variety of applications, including in classical coding theory in linear block codes such as BCH codes and Reed–Solomon error correction and in cryptography algorithms such as the Rijndael encryption algorithm.

Read more about Finite Field Arithmetic:  Effective Polynomial Representation, Addition and Subtraction, Multiplication, Arithmetic Example (where The Characteristic Is Not 2)

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