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If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, ...

A lattice-ordered set is a poset (L,<=) in which each two-element subset {a,b} has an infimum, denoted inf{a,b}, and a supremum, denoted sup{a,b}. There is a natural ...

An ordered pair representation is a representation of a directed graph in which edges are specified as ordered pairs or vertex indices. The ordered pairs representation of a ...

An algorithm for determining the order of an elliptic curve E/F_p over the finite field F_p.

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

A map f:R^n|->R which assigns each x a scalar function f(x).

An extremely fast factorization method developed by Pollard which was used to factor the RSA-130 number. This method is the most powerful known for factoring general numbers, ...

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

A two-dimensional affine geometry constructed over a finite field. For a field F of size n, the affine plane consists of the set of points which are ordered pairs of elements ...

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...