Field Instruction Multiple Data

Khin Mi Mi Aung, Enhui Lim, Jun Jie Sim, Benjamin Hong Meng Tan, Huaxiong Wang, Sze Ling Yeo

Abstract: Fully homomorphic encryption (FHE) has flourished since it was first constructed by Gentry (STOC 2009). Single instruction multiple data (SIMD) gave rise to efficient homomorphic operations on vectors in \((\mathbb {F}_{t^d})^\ell \), for prime \(t\). RLWE instantiated with cyclotomic polynomials of the form \(X^{2^N}+1\) dominate implementations of FHE due to highly efficient fast Fourier transformations. However, this choice yields very short SIMD plaintext vectors and high degree extension fields, e.g. \(\ell < 100, d > 100\) for small primes (\(t = 3, 5, \dots \)).

External IDs:doi:10.1007/978-3-031-06944-4_21