Don’t be mean: Reducing Approximation Noise in TFHE through Mean Compensation

Fully Homomorphic Encryption (FHE) allows computations on encrypted data without revealing any information about the data itself. However, FHE ciphertexts include noise for security reasons, which increases during operations and can lead to decryption errors. This paper addresses the noise introduced during bootstrapping in Torus Fully Homomorphic Encryption (TFHE), particularly focusing on approximation errors during modulus switching and gadget decomposition. We propose a mean compensation technique that removes the mean term from the noise equations, achieving up to a twofold reduction in noise variance. This method can be combined with bootstrap key unrolling for further noise reduction. Mean compensation can reduce the error probability of a standard parameter set from 2−73.77 to 2−130.21, or allows the selection of more efficient parameters leading to a speedup of bootstrapping up to a factor 2.06x. Compared to the state-of-the-art rerandomization technique, mean compensation requires no additional key material, and offers a fixed workflow. Furthermore, it removes the dependency between the noise variance and the Hamming weight of the secret key.