Circuit Bootstrapping: Faster and Smaller

We present a novel circuit bootstrapping algorithm that outperforms the state-of-the-art TFHE method with 9.9 \(\times \) speedup and 15.6 \(\times \) key size reduction. These improvements can be attributed to two technical contributions. Firstly, we redesigned the circuit bootstrapping workflow to operate exclusively under the ring ciphertext type, which eliminates the need for conversion between LWE and RLWE ciphertexts. Secondly, we improve the LMKC+ blind rotation algorithm by reducing the number of automorphisms, then propose the first automorphism type multi-value functional bootstrapping. These automorphism-based techniques lead to further key size optimization, and are of independent interest besides circuit bootstrapping. Based on our new circuit bootstrapping we can evaluate AES-128 in 26.2 s (single thread), achieving 10.3 \(\times \) speedup compared with the state-of-the-art TFHE-based approach.