Overview
This chapter outlines the methodology used to conduct the research presented in this thesis. It provides insight into how the research questions identified in Chapter I will be answered. The research objectives will be accomplished by conducting a literature review, an independent study, model development, model validation and verification, and experimentation as explained in the sections that follow.
Literature Review
The literature review presented in Chapter II provided salient background information related to systems engineering, model based systems engineering, quantum key distribution, photon number splitting attacks, and the decoy state protocol. The material presented in the literature review answers several of the stated research questions and is required to understand and guide the research presented in this thesis.
Independent Study
An initial study will be conducted to explore both the theory and application of QKD systems using the decoy states protocol. The purpose of the study is to develop a detailed understanding of the operational aspects of the decoy state protocol so that a preliminary experiment using the qkdX notional architecture can be designed and executed using selected MBSE PMTs. The results of this study will be captured in a journal article submission to the Journal of Defense Modeling and Simulation, which is included as Chapter IV of this thesis. Elements of experimental design not included in this article will be included in Appendix A. Beam Splitter Experiment (BSE). Several MBSE artifacts will be created and define the “As-Is” state of the QKD system notional architecture discussed in Chapter II. The “As-Is”
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DoDAF artifacts will be described in Chapter VI and use cases will be identified in Appendix C. Decoy State Enabled QKD System Use Cases.
Model Development
While the existing qkdX notional architecture was developed with the intent of being capable of implementing the Decoy State protocol, this capability was not fully developed [95]. During this research effort, MBSE will be used to define the requirements for the decoy state enabled QKD model development. This portion of the research shall begin by revising the “As-Is” MBSE artifacts into products that define the “To-Be” architecture. Lessons learned from the preliminary experiment will shape this effort and to produce updated use cases from which requirements can be derived.
Once the relevant behaviors are identified and captured using MBSE PMTs, implementation will begin. A combination of the incremental development process, the SE Vee model, and Banks et al.’s simulation process will be employed. Figure 14 is a depiction of this combined process as a flow chart.
Requirements and use cases will be captured, elaborated, and refined through steps 1-4. Once the use cases are reviewed by Subject Matter Experts (SMEs), the model translation, i.e., implementation, will begin. Once the model is completed and verified, an experiment will be conducted to perform validation.
The experimental design is fully described in Appendix B. Decoy State Enabled QKD Experiment. The results of the experiment will be captured in Chapter VI.
A summary, outlining the development process of transitioning the “As-Is” architecture into the
“To-Be” model, will be submitted as an article to INCOSE’s Systems Engineering journal and included as Chapter V. Details of the process and results which are not included in the article will be described in Chapter VI.
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Figure 14. Tailored Simulation Model Development Process.
Model Requirements, Verification and Validation
As discussed, the SE verification process intends to confirm that system conforms to specified requirements and validation confirms that system meets the needs of the stakeholders [36]. For this research study, the primary method of verification and validation of requirements and stakeholder needs will involve observation or analysis of the simulation’s output and output data. Thus, it will be necessary to capture (and refine) measureable requirements during the course of the study.
The majority of existing notional qkdX architecture components will undergo verification in parallel with the research that will be conducted in this paper. The results of the component verification
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will be used to gain confidence in the results of the simulation’s output. However since this effort may not conclude in time, analytical analysis will be performed as necessary to verify the output of the “To-Be”
decoy state enabled QKD simulation. For example, signal and decoy gain can be calculated using the equations described in Chapter II. Expected results can be estimated prior to performing simulation runs and therefore shape measureable requirements that can be evaluated against simulation results. Initial and refined requirements will be captured respectively in Appendix E. Initial Requirements and Appendix F:
Requirements. This analytical method will be combined with the results of the component verification to perform simulation model verification.
As discussed in Chapter II, validation confirms whether the model correctly represents the real system. Thus, if the decoy state enabled QKD system model is configured similarly to a realized system, the outputs of the model and system should be similar. This idea will shape the experimental design and link the experimental results to the MBSE process of validation. Elements of the requirements, verification, and validation processes will be discussed in the article included as Chapter V.
Experiment Design
The results of this experiment will be used for three purposes: 1) to establish baseline performance of the system in the absence of a photon number splitting (PNS) attack, 2) validate the model’s security performance against empirical data and, 3) verify the model’s ability to detect an eavesdropper performing a PNS attack. The baseline performance, i.e. yield tolerances, will be established by finding the mean and variance of single- and multi-photon signal and decoy yields over the course of a statistically significant number of simulation runs. The model’s security performance, i.e., signal gain, will be compared the results reported by Chen et al. [94]. Once the baseline performance is established, the PNS attack will be performed and the model will attempt to detect the attack using the established tolerances. The details of the experimental design and the results will be respectively captured in Appendix B. Decoy State Enabled QKD Experiment and Chapter VI.
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