ringbaserte

Ringbaserte is a Norwegian term meaning "ring-based" and is used to describe concepts, constructions, or methods that are built upon the mathematical notion of a ring. In mathematics, a ring is a set equipped with two binary operations—addition and multiplication—that satisfy ring axioms: closure, associativity, distributivity of multiplication over addition, and the existence of an additive identity; many rings also have a multiplicative identity and may be commutative or noncommutative. Ring theory studies such structures, including examples like the integers, polynomial rings, matrix rings, and quotient rings formed by ideals.

In computer science and cryptography, ring-based approaches employ ring structures to define algorithms and security assumptions. A prominent example is Ring-LWE, a lattice-based hardness assumption that uses polynomial rings to build efficient public-key cryptosystems. Another widely discussed area is ring signatures, a type of digital signatures enabling a signer to authenticate a message on behalf of a defined ring of possible signers without revealing the actual signer.

The term is used in technical literature, tutorials, and discussions to distinguish methods that rely on rings from those based on other algebraic structures such as fields or groups. Ring-based constructions can offer computational efficiency and compact representations but require careful parameter choices to ensure security.