ConfidentialityConfidentiality involves a set of rules or a promise usually executed through confidentiality agreements that limits the access or places restrictions on certain types of information. Privacy law By law, lawyers are often required to keep confidential anything pertaining to the representation of a client. The duty of confidentiality is much broader than the attorney–client evidentiary privilege, which only covers communications between the attorney and the client.
Lattice (order)A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection.
Information sensitivityInformation sensitivity is the control of access to information or knowledge that might result in loss of an advantage or level of security if disclosed to others. Loss, misuse, modification, or unauthorized access to sensitive information can adversely affect the privacy or welfare of an individual, trade secrets of a business or even the security and international relations of a nation depending on the level of sensitivity and nature of the information. This refers to information that is already a matter of public record or knowledge.
Classified informationClassified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, and mishandling of the material can incur criminal penalties. A formal security clearance is required to view or handle classified material. The clearance process requires a satisfactory background investigation.
Modular latticeIn the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition, Modular lawa ≤ b implies a ∨ (x ∧ b) = (a ∨ x) ∧ b where x, a, b are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. This phrasing emphasizes an interpretation in terms of projection onto the sublattice [a, b], a fact known as the diamond isomorphism theorem.
Information securityInformation security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthorized or inappropriate access to data or the unlawful use, disclosure, disruption, deletion, corruption, modification, inspection, recording, or devaluation of information. It also involves actions intended to reduce the adverse impacts of such incidents.
Distributive latticeIn mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is—up to isomorphism—given as such a lattice of sets. As in the case of arbitrary lattices, one can choose to consider a distributive lattice L either as a structure of order theory or of universal algebra.
Lattice of subgroupsIn mathematics, the lattice of subgroups of a group is the lattice whose elements are the subgroups of , with the partial order relation being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union, and the meet of two subgroups is their intersection. The dihedral group Dih4 has ten subgroups, counting itself and the trivial subgroup. Five of the eight group elements generate subgroups of order two, and the other two non-identity elements both generate the same cyclic subgroup of order four.
Word problem (mathematics)In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well. A deep result of computational theory is that answering this question is in many important cases undecidable. In computer algebra one often wishes to encode mathematical expressions using an expression tree. But there are often multiple equivalent expression trees.
Scheme (mathematics)In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise "Éléments de géométrie algébrique"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).
