International Association
for Cryptologic Research

Amortized bootstrapping offers a way to refresh multiple ciphertexts of a fully homomorphic encryption scheme in parallel more efficiently than refreshing a single ciphertext at a time. Micciancio and Sorrell (ICALP 2018) first proposed this technique to bootstrap n LWE ciphertexts at a time, reducing the total cost from \tilde{O}(n^2) to \tilde{O}(3^\epsilon n^{1+1/\epsilon}) for arbitrary \epsilon > 0. Several recent follow-up works have further improved the asymptotic cost. Despite these amazing progresses in theoretical efficiency, none of these works have demonstrated the practicality of batched LWE ciphertext bootstrapping. Moreover, most of these works only support limited functional bootstrapping, i.e., they only allow evaluating a specific type of function when bootstrapping. In this work, we propose a construction that is not only asymptotically efficient (requiring only \tilde{O}(n) polynomial multiplications for bootstrapping of n LWE ciphertexts) but also concretely efficient. We have our scheme implemented as a C++ library and show that it takes <5ms per LWE ciphertext to bootstrap for a binary gate, which is an order of magnitude faster than the state-of-the-art C++ implementation on LWE ciphertext bootstrapping in OpenFHE. Furthermore, our construction supports batched arbitrary functional bootstrapping. For a 9-bit messages space, our scheme takes ~6.7ms per LWE ciphertext to evaluate an arbitrary function with bootstrapping, which is about two to three magnitudes faster than all the existing schemes that achieve a similar functionality and message space.