For the NIST RBAC standard, we can define the general role hierarchy as follows: RH is a subset of Roles X Roles is a partial order on Roles called the inheritance relation, written as >=, where r1>=r2 only if all permissions of r2 are also permissions of r1, and all users of r1 are also users of r2. Define the set of authorized_permissions(ri) to be the set of all permission associated with rolei. Define the set of authorized_users(ri) to be the set of all users assigned to rolei. Finally, node r1 is represented as an immediate decendant of r2 by r1 >> r2, if r1 >= r2, but no role in the role hierarchy lies between r1 and r2. a. Using the preceding definitions, as needed, provide a formal definition of the general role hierarchy. b. Provide a formal definition of a limited role hierarchy.
For the NIST RBAC standard, we can define the general role hierarchy as follows:
RH is a subset of Roles X Roles is a partial order on Roles called the inheritance relation, written as >=, where r1>=r2 only if all permissions of r2 are also permissions of r1, and all users of r1 are also users of r2. Define the set of authorized_permissions(ri) to be the set of all permission associated with rolei. Define the set of authorized_users(ri) to be the set of all users assigned to rolei. Finally, node r1 is represented as an immediate decendant of r2 by r1 >> r2, if r1 >= r2, but no role in the role hierarchy lies between r1 and r2.
a. Using the preceding definitions, as needed, provide a formal definition of the general role hierarchy.
b. Provide a formal definition of a limited role hierarchy.
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