SFEA: A Secure Finite Element Analysis Technique

Abstract

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).