Faster Bootstrapping With Multiple Addends

As an important cryptographic primitive in cloud computing and outsourced computing, fully homomorphic encryption (FHE) is an animated area in modern cryptography. However, the efficiency of FHE has been a bottleneck that impeding its application. According to Gentry’s blueprint, bootstrapping, which is used to control the noise propagation in ciphertexts, is the most important process in FHE. However, bootstrapping is also the most expensive process that affects the scheme’s efficiency. This paper has made three improvements to accelerate the bootstrapping. Firstly, as hundreds of serial homomorphic additions take most of the time of bootstrapping, we constructed the logical expression using truth table to reduce the amount of serial homomorphic additions by two-thirds and thus proposed an efficient FHE scheme with bootstrapping within 10 ms. Secondly, the most expensive parts in our bootstrapping, enhanced homomorphic constant multiplication and homomorphic addition, can be implemented in parallel, which may accelerate the bootstrapping. At last, we proposed a set of more efficient combinations of parameters. Analysis shows that our scheme’s security level is 128 bits and the correctness is improved compared with CGGI16 scheme in ASIACRYPT 2016. Experiments show that the running time of bootstrapping in this paper is within 10 ms, which is only 52% of CGGI16, and is less than CGGI17 in ASIACRYPT 2017.