finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite...

mathematics, finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) contrary to arithmetic in a field with an...

quasi-finite field is a generalisation of a finite field. Standard local class field theory usually deals with complete valued fields whose residue field is...

s ) / K {\displaystyle K(s)/K} is not finite, the field K ( s ) {\displaystyle K(s)} is isomorphic to the field of rational fractions in s {\displaystyle...

be simply finite if it is a finite extension; this should not be confused with the fields themselves being finite fields (fields with finitely many elements)...

Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The theory of fields proves that angle trisection and squaring...

supercomputers. The simplest and the original implementation, later formalized as Finite Field Diffie–Hellman in RFC 7919, of the protocol uses the multiplicative group...

In field theory, a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field. In other words, α ∈ GF(q) is called...

pseudo-finite field F is an infinite model of the first-order theory of finite fields. This is equivalent to the condition that F is quasi-finite (perfect...

a finite field Fp is, in some sense, a generating function assembling the information of the number of points of E with values in the finite field extensions...

mathematics, a hyper-finite field is an uncountable field similar in many ways to finite fields. More precisely a field F is called hyper-finite if it is uncountable...

(field) norm is a particular mapping defined in field theory, which maps elements of a larger field into a subfield. Let K be a field and L a finite extension...

conjecture could be carried over to the Euclidean case. Finite Field Kakeya Conjecture: Let F be a finite field, let K ⊆ Fn be a Kakeya set, i.e. for each vector...

for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization...

{\displaystyle S} can be represented as an element a 0 {\displaystyle a_{0}} of a finite field G F ( q ) {\displaystyle \mathrm {GF} (q)} (where q {\displaystyle q}...

an algebraic function field (often abbreviated as function field) of n variables over a field k is a finitely generated field extension K/k which has...

the characteristic of any field is either 0 or a prime number. A field of non-zero characteristic is called a field of finite characteristic or positive...

field: A finite extension of Q {\displaystyle \mathbb {Q} } Global function field: The function field of an irreducible algebraic curve over a finite...

{\displaystyle X,} finite unions, and finite intersections. Fields of sets should not be confused with fields in ring theory nor with fields in physics. Similarly...

propositions required for completely determining the Galois groups of a finite field extension is the following: Given a polynomial f ( x ) ∈ F [ x ] {\displaystyle...

the field trace is a particular function defined with respect to a finite field extension L/K, which is a K-linear map from L onto K. Let K be a field and...

Desarguesian planes. When K is a field, a very common case, they are also known as field planes and if the field is a finite field they can be called Galois...

refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phrase...

valuation v and if its residue field k is finite. In general, a local field is a locally compact topological field with respect to a non-discrete topology...

higher finite inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector spaces over a finite field; the affine...

given on fields k in which computation (including equality testing) is easy and efficient, that is the field of rational numbers and finite fields. Searching...

over the integers, the rational numbers, finite fields and finitely generated field extension of these fields. All these algorithms use the algorithms...

In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical...

A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of...

The Itoh–Tsujii inversion algorithm is used to invert elements in a finite field. It was introduced in 1988, first over GF(2m) using the normal basis representation...