Running head: Finite Fields1Finite FieldsNameCourseTutorDateFinite Fields2Finite FieldsField in mathematics is a set of numbers that can be subtracted, added, divided andmultiplied together, and the result exists in the sets of numbers. Therefore, finite field inmathematics is a field which consists of finite numbers of elements. Finite field also have thecharacteristics of field in that it is a set on which operations of subtraction, addition, division andmultiplication are defined and their results are found in the sets of numbers. Finite fields arecritical in several areas of computer science and mathematics, which includes coding theory,finite geometry, algebraic geometry and number theory. The minimum of once which sum tozero is called the characteristic of finite fields, which must be a prime number. Since finite fieldshas prime characteristic, therefore it contains fields isomorphic to FP for some prime number p.Hence, it is a finite dimensional vector space over range Fp. Finite field which is also calledGalois Field is an important factor in understanding a cryptography. Finite fields have severalterms which comprises of groups, polynomial arithmetic, finite fields of form GF(p) finite fieldsof the form GF(2n) and rings fields. These terms are illustrated and exemplify below.Group is a term in finite field which is a set of elements M= {g, h, j} and addition forwhich the followings decorum holds:1) Associative law which state that f ...

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