Paper 2026/1447

Faster NTRU-based Bootstrapping with Extended and Sorting-based Techniques

Abstract

NTRU-based bootstrapping offers a high-performance variant of FHEW-like bootstrapping schemes and is simpler than its RLWE-based counterparts. Nevertheless, it remains costly in terms of both memory and time. A key computational bottleneck arises from the constraint $q\mid 2N$ which links the LWE ciphertext modulus $q$ to the NTRU dimension $N$. In this work, we apply extended techniques to remove the limitation $q \mid 2N$. With a large modulus $q$, we are able to complete the bootstrapping algorithms using a relatively small $N$-dimensional ring, thereby improving both time and memory efficiency. Additionally, we employ sorting-based techniques to eliminate unnecessary operations, which further enhances time performance. We also extend this approach to improve the efficiency of NTRU-based multi-key bootstrapping algorithms. We implement our algorithms using the CHIFHE and MKFHE libraries. At the 128-bit security level, our sorting-based techniques (with factor $\eta=16$ ) accelerate single-key bootstrapping by factors of $1.82\times$ and $1.24\times$ over the FINAL scheme (ASIACRYPT 2021) and the key unrolling method (CHES 2024), respectively. For multi-key bootstrapping (with factor $\eta=4$), we achieve a $1.70\times$ speedup over the prior art (ASIACRYPT 2024). In addition, both single-key and multi-key algorithms reduce memory usage by a factor of $\eta$.