A study on implementing the BLAS interface in the MPC context

Linear Algebra (LA) plays a significant role in fields where computation on sensitive data is performed, like Machine Learning (ML), for example, and where privacy of the computation is a desirable property. Basic Linear Algebra Subprograms (BLAS) is an interface for the most commonly used Linear Algebra functions. It enables hardware vendors to provide implementations that are optimized for their selling hardware and also for the operating system running on it. Secure Multi-Party Computation (MPC/SMPC) is a class of interactive cryptographic protocols that enable multiple participants to securely evaluate arbitrary public functions on their private inputs, thus achieving a privacy-preserving computation. In this article, we explore the requirements and the current possibilities of implementing the BLAS interface in the context of MPC, to achieve privacy for the computation process and its probably sensitive data input. Our focus is on setting the requirements for providing an almost drop-in replacement for the CBLAS interface, the BLAS interface for the C programming language, which is the interface most commonly used today. We believe that implementing such a crucial part of modern frameworks that process sensitive data, in terms of MPC, will have an impact on the world of privacy. Next, we review how some of the most popular MPC frameworks do not fulfill our purpose. Using the most suitable frameworks from our evaluation, we implement and benchmark all the Level-1 CBLAS interface functions. This is the maximum possible subset of the interface that could be implemented on the basis of existing MPC frameworks, while satisfying the most crucial of our requirements. Finally, we highlight the gaps that exist in current MPC protocols and framework implementations that forbid us from implementing the complete CBLAS interface and discuss probable solutions that can be examined in future work, that will help fill those gaps.