Using Category Theory and Data Flow Analysis for Modeling and Verifying Properties of Communications in the Process-Oriented Language Erasmus

Zhu, Muhua; Grogono, Peter; Ormandjieva, Olga; Kamthan, Pankaj

doi:10.1145/2641483.2641529

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…While cryptography asks how can we communicate securely, systems modeling and analysis asks how can we represent attacker actions over a behavioral and architectural model in a manner that is traceable, such that we can examine what mitigation strategies to implement in the design of the system. The same differentiation applies to secure design using dependent types [60] -which are often formalized categoricallyand categorical data flow analysis [61].…”

Section: Related Workmentioning

confidence: 99%

Yoneda Hacking: The Algebra of Attacker Actions

Bakirtzis¹,

Genovese²,

Fleming³

2021

Preprint

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Our work focuses on modeling security of systems from their component-level designs. Towards this goal we develop a categorical formalism to model attacker actions. Equipping the categorical formalism with algebras produces two interesting results for security modeling. First, using the Yoneda lemma, we are able to model attacker reconnaissance missions. In this context, the Yoneda lemma formally shows us that if two system representations, one being complete and the other being the attacker's incomplete view, agree at every possible test, then they behave the same. The implication is that attackers can still successfully exploit the system even with incomplete information. Second, we model the possible changes that can occur to the system via an exploit. An exploit either manipulates the interactions between system components, for example, providing the wrong values to a sensor, or changes the components themselves, for example, manipulating the firmware of a global positioning system (GPS). One additional benefit of using category theory is that mathematical operations can be represented as formal diagrams, which is useful for applying this analysis in a model-based design setting. We illustrate this modeling framework using a cyber-physical system model of an unmanned aerial vehicle (UAV). We demonstrate and model two types of attacks (1) a rewiring attack, which violates data integrity, and (2) a rewriting attack, which violates availability.

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Section: Related Workmentioning

confidence: 99%

Yoneda Hacking: The Algebra of Attacker Actions

Bakirtzis¹,

Genovese²,

Fleming³

2021

Preprint

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“…However, for the analysis of implementation of concurrent systems by process-oriented languages, not much research has been done yet with category theory. To explore this research area, a verification approach based on category theory and data flow analysis is proposed to check whether some properties of concurrent systems in the design are preserved in the implementation 14 . As an extension and a continual work, this paper keeps working on verification between design and implementation of concurrent systems by process-oriented languages.…”

Section: Category Theorymentioning

confidence: 99%

Using Category Theory to Verify Implementation Against Design in Concurrent Systems

Zhu

Grogono

Ormandjieva

2015

Procedia Computer Science

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The research has shown that process-oriented programming languages provide a suitable means for developing concurrent systems. However, in the development of a concurrent system, there is a challenge to manage consistency between design and implementation. To deal with such a challenge, we propose a new formal verification methodology and illustrate it by a running example. In this methodology, a concurrent system is designed using a process algebra, namely communicating sequential processes, and implemented in a process-oriented programming language, namely Erasmus. The consistency between the design and the implementation of such a concurrent system is verified formally using category theory.

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“…To deal with such a challenge, verification plays a crucial role in reducing, or even preventing, the introduction of errors in design and implementation of a concurrent system [5]. Research [6] [7] used category theory, dataflow and Traces in Communicating Sequential Processes (CSP) to explore approaches that may address the challenge. This paper is based on Category Theory, Galois connections and Failures in CSP.…”

Section: Introductionmentioning

confidence: 99%

Towards a Categorical Framework for Verifying Design and Implementation of Concurrent Systems

Zhu¹,

Li²

2018

JCC

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Process-oriented design and implementation of concurrent systems has important benefits. However, the inherent complexity of concurrent processes' communication imposes challenges such as verifying consistency between the process-oriented design and implementation of a concurrent system. To deal with such a challenge, we use Galois connections, Failures and Category Theory to construct a formal framework for designing, implementing, analyzing and verifying consistency of concurrent systems. For the purpose of illustrating the framework, a running concurrent system is designed by Communicating Sequential Processes, implemented by a process-oriented programming language Erasmus.

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Using Category Theory and Data Flow Analysis for Modeling and Verifying Properties of Communications in the Process-Oriented Language Erasmus

Cited by 5 publications

References 10 publications

Yoneda Hacking: The Algebra of Attacker Actions

Yoneda Hacking: The Algebra of Attacker Actions

Using Category Theory to Verify Implementation Against Design in Concurrent Systems

Towards a Categorical Framework for Verifying Design and Implementation of Concurrent Systems

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