Research Papers

sFEA: A Secure Finite Element Analysis Technique

[+] Author and Article Information
Siva C. Chaduvula, Jitesh H. Panchal

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907

Mikhail J. Atallah

Department of Computer Science,
Purdue University,
West Lafayette, IN 47907

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received September 14, 2018; final manuscript received January 25, 2019; published online March 18, 2019. Assoc. Editor: Mahesh Mani.

J. Comput. Inf. Sci. Eng 19(3), 031004 (Mar 18, 2019) (10 pages) Paper No: JCISE-18-1242; doi: 10.1115/1.4042695 History: Received September 14, 2018; Revised January 25, 2019

Designers need a way to overcome information-related risks, including information leakage and misuse by their own collaborators during collaborative product realization. Existing cryptographic techniques aimed at overcoming these information-related risks are computationally expensive and impractical even for moderate problem sizes, and legal approaches such as nondisclosure agreements are not effective. The computational practicality problem is particularly pronounced for computational techniques, such as the finite element analysis (FEA). In this paper, we propose a technique that enables designers to perform simulations, such as FEA computations, without the need for revealing their information to anyone, including their design collaborators. We present a new approach, the secure finite element analysis approach, which enables designers to perform FEA without having to reveal structural/material information to their counterparts even though the computed answer depends on all the collaborators' confidential information. We build secure finite element analysis (sFEA) using computationally efficient protocols implementing a secure codesign (SCD) framework. One of our findings is that the direct implementation of using SCD framework (termed as naïve sFEA) suffers from lack of scalability. To overcome these limitations, we propose hybrid sFEA that implements performance improvement strategies. We document and discuss the experiments we conducted to determine the computational overhead imposed by both naïve and hybrid sFEA. The results indicate that the computational burden imposed by hybrid sFEA makes it challenging for large-scale FEA—our scheme significantly increases the problem sizes that can be handled when compared to implementations using previous algorithms and protocols, but large enough problem sizes will swamp our scheme as well (in some sense this is unavoidable because of the cubic nature of the FEA time complexity).

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Fig. 1

Different collaboration scenarios between two enterprises (say A and B) that amplify the risk of information leakage

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Fig. 2

Design of a 2D plate: problem formulation for sFEA

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Fig. 3

Different possibilities of mesh configurations for the same connectivity matrix (C)

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Fig. 4

Illustration of the sFEA technique using SAPAS protocols. Each SAPAS protocol requires inputs from designers (Alice and Bob). For simplicity, we have shown the additive splits of inputs and outputs that belong to Alice (denoted by subscript 1).

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Fig. 5

The mesh configuration with triangular elements results in a band structure for global stiffness matrix (K)

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Fig. 6

Comparison of the average time (in milliseconds) taken by the hybrid sFEA simulation and naïve FEA for a mesh with four triangular elements

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Fig. 7

Comparison of amount of data transfer required (in kB) by the hybrid sFEA simulation and naïve FEA for a mesh with four triangular elements

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Fig. 8

Mesh configuration used for the generation of FEM results listed in Table 3

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Fig. 9

Comparison of average total time taken (in seconds) by the hybrid sFEA simulation and open FEA using triangular mesh elements

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Fig. 10

Comparison of average total time taken (in seconds) by the hybrid sFEA simulation and open FEA using triangular mesh elements



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