Assume t h a t the users of a c o m p u t e r (or c o m m u n i c a t i o n ) s y s t e m are d iv ided in to a n u m b e r of d i s jo in t sets, /_}1, U2 . . . . . Un. T h e t e r m security class (or class, for short) is used to des igna te each of the Ui. A s s u m e fu r the r t h a t a b i n a r y r e l a t ion _< par t i a l ly orders the set S = ( U1, U 2 , . . . , /_7,} of classes. T h e m e a n i n g of Ui <Uj in the pa r t i a l ly ordered set (poset) (S, ~) is t h a t users in Ui have a security clearance lower t h a n or equa l to those in Uj. S i m p l y put , th is m e a n s t h a t users in Uj can have access to i n f o r m a t i o n he ld by (or de s t i ned to) users in Ui, while the opposi te is no t allowed. Le t xm be a piece of in fo rmat ion , or object, t h a t a cen t r a l a u t h o r i t y (CA) desires to s tore in (or b roadcas t over) the sys tem. T h e m e a n i n g of the subsc r ip t m is t h a t ob jec t x is accessible to users in class Urn. T h e par t i a l o rder on S impl ies t h a t xm is also accessible to users in all classes Ui such t h a t Um Ui. I t is r equ i r ed to design a sy s t em which, in add i t i on to sa t i s fy ing the above condi t ions , e n su r e s t h a t access to i n f o r m a t i o n is as decen t ra l i zed as possible. T h i s m e a n s t h a t au thor ized users shou ld be able to retrieve xm independent ly as soon as it is stored or broadcast by CA.

Cryptographic solution to a problem of access control in a hierarchy

Hierarchies arise in the context of access control whenever the user population can be modeled as a set of partially ordered classes (represented as a directed graph). A user with access privileges for a class obtains access to objects stored at that class and all descendant classes in the hierarchy. The problem of key management for such hierarchies then consists of assigning a key to each class in the hierarchy so that keys for descendant classes can be obtained via efficient key derivation.We propose a solution to this problem with the following properties: (1) the space complexity of the public information is the same as that of storing the hierarchy; (2) the private information at a class consists of a single key associated with that class; (3) updates (i.e., revocations and additions) are handled locally in the hierarchy; (4) the scheme is provably secure against collusion; and (5) each node can derive the key of any of its descendant with a number of symmetric-key operations bounded by the length of the path between the nodes. Whereas many previous schemes had some of these properties, ours is the first that satisfies all of them. The security of our scheme is based on pseudorandom functions, without reliance on the Random Oracle Model.Another substantial contribution of this work is that we are able to lower the key derivation time at the expense of modestly increasing the public storage associated with the hierarchy. Insertion of additional, so-called shortcut, edges, allows to lower the key derivation to a small constant number of steps for graphs that are total orders and trees by increasing the total number of edges by a small asymptotic factor such as O(log*n) for an n-node hierarchy. For more general access hierarchies of dimension d, we use a technique that consists of adding dummy nodes and dimension reduction. The key derivation work for such graphs is then linear in d and the increase in the number of edges is by the factor O(logd − 1n) compared to the one-dimensional case.Finally, by making simple modifications to our scheme, we show how to handle extensions proposed by Crampton [2003] of the standard hierarchies to “limited depth” and reverse inheritance.

Dynamic and Efficient Key Management for Access Hierarchies

Cryptographic implementation of a tree hierarchy for access control

The cryptographic key assignment problem is to assign cryptographic keys to a set of partially ordered classes so that the cryptographic key of a higher class can be used to derive the cryptographic key of a lower class. In this paper, we propose a time-bound cryptographic key assignment scheme in which the cryptographic keys of a class are different for each time period, that is, the cryptographic key of class C/sub i/ at time t is K/sub i, t./ Key derivation is constrained not only by the class relation, but also the time period. In our scheme, each user holds some secret parameters whose number is independent of the number of the classes in the hierarchy and the total time periods. We present two novel applications of our scheme. One is to broadcast data to authorized users in a multilevel-security way and the other is to construct a flexible cryptographic key backup system.

A time-bound cryptographic key assignment scheme for access control in a hierarchy

Refereed article: A cryptographic key generation scheme for multilevel data security

A cryptographic scheme for controlling access to information within a group of users organized in a hierarchy was proposed in [1]. The scheme enables a user at some level to compute from his own cryptographic key the keys of the users below him in the organization.

Taylor

Papers

An Optimal Algorithm for Assigning Cryptographic Keys to Control Access in a Hierarchy