Finished Projects
Security Architecture and Modeling
A Mathematics for Reasoning About Systems
Problem
Critical systems have traditionally achieved limited Information
Assurance (IA) through special purpose development and through isolation
from the rest of the world. The need for IA is rapidly increasing, but,
at the same time, new factors have greatly increased the difficulty of
achieving meaningful IA. These factors include the fact that today?s
systems are dramatically more complex and interconnected with other
systems that span a variety of IA capabilities and that it is typical
for cost reasons to employ COTS components in such systems. COTS
components provide functionality but usually have very weak IA
properties. To transform building systems with critical IA properties
from an art to an engineering discipline, a scientific basis for system
prediction, analysis, and reproducibility is needed. Such a scientific
basis requires a mathematics for reasoning about systems and their IA
properties in (preferably) closed form expressions.
Solution
Under DARPA funding, SPARTA ISSO is developing a body of mathematics
(Information Assurance Mathematics -- IAM) for analysing systems,
components, IA policies, and their compositions. This work builds upon
and extends prior research in the mathematical fundamentals of
ultra-large-scale systems known as the WDL theory. These fundamentals
include a large number of proved theorems governing ultra-large-scale
system component interactions.
The figure below illustrates a basic interaction between two components A and B. Information from A is input to B. Usually there is no assurance that A?s interpretation of the information it sends matches B?s interpretation of the information it receives. The illustration is deceiving since the information from A is depicted as being the "same" as that input to B.
IAM is intended to model components, component policies, and their composition to form systems and system polices. The IAM approach includes capturing the subtle interactions that are possible when components and policies are combined.
Objective
The objective of the IAM research effort is to build upon and extend the
existing WDL theory of component and component policy composition. These
ideas, concepts, and approaches are currently in the domain of
ultra-large-sale systems and systems modelling. This is the modelling
domain that deals with high-level views of systems, focusing primarily
on issues of architecture and interface definition. It does not deal
with internal behavior or software architecture or design. While
providing insight for composing components and component policies, the
WDL theory is not complete nor does it provide much detailed guidance
for software architects and engineers. With IAM we intend to complete
the WDL theory at the systems modelling level and extend it to the
software modelling level. The goal of such extensions will be to provide
and maintain consistency of models across IA-critical systems and
software. The consequence of such extensions will be to increase
information assurance for both IA-critical systems and software.
The figure below graphically depicts just one aspect of the complexity of modelling a combination of two components. The information from A is input to B. The figure shows that the information from A is interpreted differently from the information input to B. The basic information is the same. This is depicted by four dots on the arrow from A to B. However, the respective interpretations of that information by A and B are not the same. The IAM composition operator will permit expression of this subtlety as a closed-form mathematical expression. This allows computation of expressions that represent models of component combination without the distraction of extraneous details. This property is vital for ease of use of IAM in system and software analysis and design.
Research Focus
Two Fundamental Challenges
Our research is focusing on two fundamental challenges for developing
IAM:
- How to complete the existing mathematical theory as a mathematical basis for systems modelling ; and
- How to extend this mathematical systems theory to a mathematical theory for modelling software systems. To complete the existing theory, our research will investigate operators on components and policies and properties of combinations of such components and policies under these operators. In particular, there are two properties, closure and transitivity, that are important for describing IA properties of combinations of components and policies.
To extend the mathematical systems theory to a mathematical theory for modelling software systems we will investigate the properties of mappings from systems level concepts to software level concepts. We expect that the operators on systems models will need to be extended to operators on software models. We also expect that the systems properties of closure and transitivity will need to be appropriately extended to concepts that are meaningful for software properties of components and their policies.
Additional Information
For additional technical information regarding Information Assurance
Mathematics (IAM), contact us at 443-430-8000.