SFEA: A Lightweight, Scalable, and Secure Finite Element Analysis Technique

Abstract

Designers need a way to overcome information related risks, including information leakage and misuse from their own collaborators during a collaborative product realization process. Existing cryptographic techniques aimed at overcoming these information related risks are computationally expensive and slow even for moderate problem sizes, and legal approaches (e.g., the use of non-disclosure agreements) are not effective. The computational practicality problem is particularly pronounced for simulation computations like finite element analysis (FEA), that involve both a geometric partitioning (meshing) and computations of cubic time complexity. In this paper, we propose a technological approach that enables designers to perform simulations, such as FEA computations, without the need for revealing their information to anyone, including their design collaborators. We demonstrate our approach using secure finite element analysis (sFEA) 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 sFEA using computationally efficient protocols implementing a secure co-design framework. One of our findings is that the most natural implementations of sFEA, using existing protocols, suffer from limited scalability. To overcome these limitations, we propose strategies that help improve the scalability of sFEA. We document and discuss the experiments we conducted to determine the computational overhead imposed by sFEA. The results indicate that the computational burden imposed by 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). This work is another step towards opening up new avenues for improving the way information is exchanged in collaborative simulation computations such as FEA.