International Association
for Cryptologic Research

Fully homomorphic encryption is a promising solution for privacy-preserving computation. For BFV, BGV, and CKKS, three state-of-the-art fully homomorphic encryption schemes, the so-called key switching is one of the primary bottlenecks when evaluating homomorphic circuits. While a large body of work explores optimal selection for scheme parameters such as the polynomial degree or the ciphertext modulus, the realm of key switching parameters is relatively unexplored.

This work closes this gap, formally exploring the parameter space for BGV-like key switching. We introduce a new asymptotic bound for key switching complexity, thereby providing a new perspective on this crucial operation. We also explore the parameter space for the recently proposed double-decomposition technique by Kim et al. [24], which outperforms current state-of-the-art only in very specific circumstances. Furthermore, we revisit an idea by Gentry, Halevi, and Smart [19] switching primes in and out of the ciphertext and find novel opportunities for constant folding, speeding up key switching by up to 50% and up to 11.6%, respectively.