Galois field

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• Galois/Counter Mode — GCM mode (Galois/Counter Mode) is a mode of operation for symmetric key cryptographic block ciphers. It is an authenticated encryption algorithm designed to provide both authentication and privacy. GCM mode is defined for block ciphers with a… …   Wikipedia

• Galois-Feld — Ein endlicher Körper oder Galoiskörper ist eine Menge mit einer endlichen Anzahl von Elementen, auf der die Grundoperationen Addition, Subtraktion, Multiplikation und Division definiert sind. Die Bezeichnung Galoiskörper leitet sich vom Namen des …   Deutsch Wikipedia

• Galois-Körper — Ein endlicher Körper oder Galoiskörper ist eine Menge mit einer endlichen Anzahl von Elementen, auf der die Grundoperationen Addition, Subtraktion, Multiplikation und Division definiert sind. Die Bezeichnung Galoiskörper leitet sich vom Namen des …   Deutsch Wikipedia

• Galois theory — In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory,… …   Wikipedia

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

• Galois module — In mathematics, a Galois module is a G module where G is the Galois group of some extension of fields. The term Galois representation is frequently used when the G module is a vector space over a field or a free module over a ring, but can also… …   Wikipedia

• Field arithmetic — In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a ql|field (mathematics)|field and its absolute Galois group.It is an interdisciplinary subject as it uses tools from algebraic number… …   Wikipedia

• Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …   Wikipedia

• Galois group — In mathematics, a Galois group is a group associated with a certain type of field extension. The study of field extensions (and polynomials which give rise to them) via Galois groups is called Galois theory. The name is for Évariste Galois.For a… …   Wikipedia

• Galois connection — In mathematics, especially in order theory, a Galois connection is a particular correspondence between two partially ordered sets (posets). Galois connections generalize the correspondence between subgroups and subfields investigated in Galois… …   Wikipedia

• Galois extension — In mathematics, a Galois extension is an algebraic field extension E / F satisfying certain conditions (described below); one also says that the extension is Galois. The significance of being a Galois extension is that the extension has a Galois… …   Wikipedia