COSIC seminar 'Full Domain Functional Bootstrapping Towards Practical Fully...' (Leonard Schild)

COSIC seminar "Full Domain Functional Bootstrapping Towards Practical Fully Homomorphic Encryption" (Leonard Schild)

Computation on ciphertexts of all known fully homomorphic encryption (FHE) schemes induces some noise, which, if too large, will destroy the plaintext. The bootstrapping technique that re-encrypts a ciphertext and reduces the noise level remains the only known way of building FHE schemes for arbitrary unbounded computations. The bootstrapping step is also the major efficiency bottleneck in current FHE schemes. A promising direction towards improving concrete efficiency is to exploit the bootstrapping process to perform useful computation while reducing the noise at the same time. Building upon the GINX/TFHE bootstrapping scheme, we show a bootstrapping algorithm, which embeds a lookup table and evaluates arbitrary functions of the plaintext while reducing the noise. As we impose no limitations on the function, we can employ the additive homomorphism of Regev encryptions with basically no restrictions, making our algorithm particularly suitable for the evaluation of arithmetic circuits composed of additions, scalar multiplications and univariate functions. Furthermore, depending on the choice of parameters, the resulting homomorphic encryption scheme may be either an exact FHE or homomorphic encryption for approximate arithmetic.