Paper 2024/2032

Carousel: Fully Homomorphic Encryption from Slot Blind Rotation Technique

Abstract

Fully Homomorphic Encryption (FHE) enables secure computation of functions on ciphertexts without requiring decryption. Specifically, AP-like HE schemes exploit an intrinsic bootstrapping method called blind rotation. In blind rotation, a look-up table is homomorphically evaluated on the input ciphertext through the iterative multiplication of monomials. However, the algebraic structure of the multiplicative group of monomials imposes certain limitations on the input and output plaintext space: 1. only a fraction of the input plaintext space can be bootstrapped, 2. the output plaintext space is restricted to subsets of real numbers. In this paper, we design a novel bootstrapping method called slot blind rotation. The key idea of our approach is to utilize the automorphism group instead of monomials. More specifically, the look-up table is encoded into a single polynomial using SIMD (Single Instruction Multiple Data) packing and is rotated via a series of homomorphic multiplications and automorphisms. This method achieves two significant advantages: 1. the entire input plaintext space can be bootstrapped, 2. a more broad output plaintext space, such as complex numbers or finite field/rings can be supported. Finally, we present a new HE scheme leveraging the slot blind rotation technique and provide a proof-of-concept implementation. We also demonstrate the the benchmark results and provide recommended parameter sets.