The application of Fully Homomorphic Encryption (FHE) to privacy issues arising in inference or training of neural networks has been actively researched over the last few years. Yet, although practical performances have been demonstrated on certain classes of neural networks, the inherent high computational cost of FHE operators has prevented the scaling capabilities of FHE-based encrypted domain inference to the large and deep networks used to deliver advanced classification functions such as image interpretation tasks. To achieve this goal, a new hope is coming from TFHE functional bootstrapping which, rather than being just used for refreshing ciphertexts (i.e., reducing their noise level), can be used to evaluate operators which are difficult to express as low complexity arithmetic circuits, at no additional cost.

In this context, the team at CEA has proposed ComBo (Composition of Bootstrappings), a new full domain functional bootstrapping method with TFHE for evaluating any function of domain and codomain the real torus T by using a small number of bootstrappings. This result improves on previous approaches: like them, it allows for evaluating any functions, but with significantly lower error rates. This new methods has been presented and published in the proceedings of AFRICACRYPT’23.

As it allows to perform two bootstrappings in parallel, ComBo may come without additional computational cost compared to the other full domain methods which are intrinsically serial. As such, the method appears especially well adapted to benefit from the SIMD instruction sets available in modern processors. Following this, the subject of this project will be to propose an optimized implementation of the method taking advantage of the AVX SIMD processor on Intel processors. The students will first have to analyze and understand the method, then research ways of implementating it in an SIMD fashion and then produce experimental results illustrating the improved performances. It is expected that this work may lead to a publication.