Selim G. Akl

Cryptographic solution to a problem of access control in a hierarchy

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.

Views for Multilevel Database Security

Because views on relational database systems mathematically define arbitrary sets of stored and derived data, they have been proposed as a way of handling context-and content-dependent classification, dynamic classification, inference, aggregation, and sanitization in multilevel database systems. This paper describes basic view concepts for a multilevel-secure relational database model that addresses the above issues. All data entering the database are labeled according to views called classification constraints, which specify access classes for related data. In addition, views called aggregation constraints restrict access to aggregates of information. All data accesses are confined to a third set of views called access views.

The principal continuation and the killer heuristic

An algorithm is presented for obtaining the <italic>principal continuation</italic> in trees searched by two-person game playing programs based on the <italic>Alpha-Beta algorithm</italic>. Moves saved while determining the principal continuation are shown to be good candidates for killer moves when the <italic>killer heuristic</italic> supplements the Alpha-Beta search.

On Some Properties and Algorithms for the Star and Pancake Interconnection Networks

The star and pancake networks were proposed recently as attractive alternatives to the popular hypercube for interconnecting processors on a parallel computer. In this paper, we present a number of results in connection with these two networks. In particular, we examine their graph theoretic properties and derive algorithms for solving several problems on them.

Optimal Parallel Merging and Sorting Without Memory Conflicts

A parallel algorithm is described for merging two sorted vectors of total length N. The algorithm runs on a shared-memory model of parallel computation that disallows more than one processor to simultaneously read from or write into the same memory location. It uses k processors where l ¿ k ¿ N and requires O(N/k + log k × log N) time. The proposed approach for merging leads to a parallel sorting algorithm that sorts a vector of length N in O(log2 k + N/k) log N) time. Because they modify their behavior and hence their running time according to the number of available processors, the two new algorithms are said to be self-reconfiguring. In addition, both algorithms are optimal, for k ¿ N/log2 N, in view of the ¿(N) and ¿(N log N) lower bounds on merging and sorting, respectively.

Optimal communication algorithms on star graphs using spanning tree constructions

Abstract In this paper we consider three fundamental communication problems on the star interconnection network: the problem of simultaneous broadcasting of a message from every node to all other nodes, or multinode broadcasting, the problem of a single node sending distinct messages to each one of the other nodes, or single-node scattering, and finally the problem of each node sending distinct messages to every other node, or total exchange. All of these problems are studied under two different assumptions: the assumption that each node can transmit a message of fixed length to one of its neighbors and simultaneously receive a message of fixed length from one of its neighbors (not necessarily the same one) at each time step, or single-link availability, and the assumption that each node can exchange messages of fixed length with all of its neighbors at each time step, or multiple-link availability. In both cases communication is assumed to be bidirectional. The cases where the originating processor wishes to send only one or more than one message to each one of the other processors are distinguished when necessary. Lower bounds are derived for these problems under the stated assumptions, and optimal algorithms are designed in terms of both time and number of message transmissions. Although the algorithms derived for the first two problems require the minimum amount of the above resources, the algorithm designed for the total exchange problem is optimal only to within a multiplicative factor. All the communication algorithms presented in this paper are based on the construction of spanning trees with special properties on the star graph to fit different communication needs. A special framework is developed to facilitate the construction of these trees. The scheduling disciplines that lead to optimal results in each case are described.

A parallel algorithm for computing Fourier transforms on the star graph

The n-star graph, denoted by S/sub n/, is one of the graph networks that have been recently proposed as attractive alternatives to the n-cube topology for interconnecting processors in parallel computers. We present a parallel algorithm for the computation of the Fourier transform on the star graph. The algorithm requires O(n/sup 2/) multiply-add steps for an input sequence of n! elements, and is hence cost-optimal with respect to the sequential algorithm on which it is based. This is believed to be the first algorithm, and the only one to date, for the computation of the Fourier transform on the star graph. >

MATRIX OPERATIONS USING ARRAYS WITH RECONFIGURABLE OPTICAL BUSES

This paper examines the possibility of implementing matrix operations on an array with reconfigurable optical buses (AROB). The AROB combines some of the advantages and characteristics of reconfigurable meshes and meshes with optical pipelined buses. This model is extremely flexible, as demonstrated by its ability to efficiently simulate CREW PRAMs and reconfigurable networks. A number of applications arc investigated and it is shown that many matrix operations can be implemented efficiently, reducing the time complexity and/or the cost of existing algorithms which are given for other models of parallel computation.

Fundamental algorithms for the star and pancake interconnection networks with applications to computational geometry

The star and pancake networks were recently proposed as attractive alternatives to the hypercube topology for interconnecting processors in a parallel computer. However, few parallel algorithms are known for these networks. In this paper, we present several data communication schemes and basic algorithms for these two networks. These algorithms are then used to develop parallel solutions to various computational geometric problems on both networks. Computational geometry is just one area where the algorithms proposed here can be applied. Indeed, we believe that these algorithms are interesting and important in their own right and are fundamental to the design of solutions on the star and pancake networks to a host of other problems.

Cryptographic Solution to a Multilevel Security Problem

A scheme based on cryptography is proposed for enforcing multilevel security in a system where hierarchy is represented by a partially ordered set (or poset). Straightforward implementation of the scheme requires users highly placed in the hierarchy to store a large number of cryptographic keys. A time-versus-storage trade-off is then described for addressing this key management problem.