Access structure
Encyclopedia
Access structures are used in the study of security system where multiple parties need to work together to obtain a resource. Groups of parties that are granted access are called qualified. In set theoretic
terms they are referred to as qualified sets. In turn, the set of all such qualified sets is called the access structure of the system. Less formally it is a description of who needs to cooperate with whom in order to access the resource. In its original use in cryptography
, the resource was a secret shared
among the participants. Only subgroups of participants contained in the access structure, are able to join their shares to recompute the secret. More generally, the resource can also be a task that a group of people can complete together, such as creating a digital signature
, or decrypting an encrypted message.
It is reasonable to assume that access structures are monotone
in the sense that, if a subset S is in the access structure, all sets that contain S as a subset should also form part of the access structure.
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
terms they are referred to as qualified sets. In turn, the set of all such qualified sets is called the access structure of the system. Less formally it is a description of who needs to cooperate with whom in order to access the resource. In its original use in cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
, the resource was a secret shared
Secret sharing
Secret sharing refers to method for distributing a secret amongst a group of participants, each of whom is allocated a share of the secret. The secret can be reconstructed only when a sufficient number of shares are combined together; individual shares are of no use on their own.More formally, in a...
among the participants. Only subgroups of participants contained in the access structure, are able to join their shares to recompute the secret. More generally, the resource can also be a task that a group of people can complete together, such as creating a digital signature
Digital signature
A digital signature or digital signature scheme is a mathematical scheme for demonstrating the authenticity of a digital message or document. A valid digital signature gives a recipient reason to believe that the message was created by a known sender, and that it was not altered in transit...
, or decrypting an encrypted message.
It is reasonable to assume that access structures are monotone
Monotone
Monotone refers to a sound, for example speech or music, that has a single unvaried tone.Monotone or monotonicity may also refer to:*Monotone , an open source revision control system*Monotone class theorem, in measure theory...
in the sense that, if a subset S is in the access structure, all sets that contain S as a subset should also form part of the access structure.