Paper 2026/732

Faster Logical Operations from Discrete CKKS

Abstract

We study non-arithmetic operations for BFV with arbitrary plaintext moduli and for large-modulus GBFV. Existing approaches either rely on interpolation over large plaintext spaces or use digit representations that are efficient for logic but poorly matched to native arithmetic. We build conversions between BFV/GBFV and Discrete CKKS, so that radix-based integer computation in Discrete CKKS can be used as a reusable backend. For fixed radix base, comparison uses $O(\log p \log\log p)$ bootstrappings for BFV with plaintext modulus $p$ and $O(\log\log p)$ bootstrappings for GBFV with associated modulus $p=b^\ell+1$.