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Functional Model

A subject is a human or machine user agent interacting with a secured software application.

s ∈ S

A credential is a secret that uniquely identifies a subject.

c ∈ C

An authentication domain is a function Fd from credentials C subjects S.

Fd: C ⟶ S

In particular an authentication domain can be represented by a set D := {(c, s) | Fd(c) = s}, where D ⊂ P(C x S).

Any fundamental authentication operation should be expressed in the context of authentication domains, to be able to explicitly represent side effects.

Operations

Authenticate

The authenticate operation checks whether a given credential c identifies a subject s. This operation could possibly modify a given authentication domain: for example, in the OTP use case, a credential must be used only once.

Fa: D x C ⟶ D x S

Register

The register operation adds a new association (c, s). This means that the subject s can be identified by the credential c.

Fr: D x C x S ⟶ D

Unregister

The unregister operation removes any associations (c, s) for any given subject s. This means that s will not be identifiable in the authentication domain.

Fu: D x C ⟶ D

For greater flexibility we can also define a companion operation that allows to remove a single association (c, s). This means that s will not be identifiable by c in the authentication domain.

Fu': D x C ⟶ D

Exchange

The exchange operations allows to use multiple authentication domains and different credential types to implement complex authentication workflows. The Token Based Authentication, for example, involves the use of login credentials which can generate temporary access tokens.

Fx: Da x Db x Ca x Cb ⟶ Da x Db