Paper 2024/1201

Designing a General-Purpose 8-bit (T)FHE Processor Abstraction

Abstract

Making the most of TFHE programmable bootstrapping to evaluate functions or operators otherwise difficult to perform with only the native addition and multiplication of the scheme is a very active line of research. In this paper, we systematize this approach and apply it to build an 8-bit FHE processor abstraction, i.e., a software entity that works over FHE-encrypted 8-bits data and presents itself to the programmer by means of a conventional-looking assembly instruction set. In doing so, we provide several homomorphic LUT dereferencing operators based on variants on the tree-based method and show that they are the most efficient option for manipulating encryptions of 8-bit data (optimally represented as two base 16 digits). We then systematically apply this approach over a set of around 50 instructions, including, notably, conditional assignments, divisions, or fixed-point arithmetic operations. We then conclude the paper by testing the approach on several simple algorithms, including the execution of a neuron with a sigmoid activation function over 16-bit precision. Finally, this work reveals that a very limited set of functional bootstrapping patterns is versatile and efficient enough to achieve general-purpose FHE computations beyond the boolean circuit approach. As such, these patterns may be an appropriate target for further works on advanced software optimizations or hardware implementations.