Efficient Fully Homomorphic Encryption Schemes

Shuhong Gao — Clemson University

As cloud computing, internet of things (IoT) and blockchain technology become  increasingly  prevalent, there is an urgent need to protect the privacy of massive volumes of  sensitive data collected or stored in distributed  computer networks  or cloud  servers,  as many of the networks or servers can be vulnerable to external and internal threats such as malicious hackers or curious insiders.   The Holy-Grail of cryptography is to have practical fully homomorphic encryption (FHE) schemes that allow any third party (including cloud servers, hackers, miners or  insiders) to perform searching or analytics of an arbitrary function on encrypted data without decryption, while no information on the original data is ever leaked. The breakthrough was made by Gentry in 2009  who discovered the first FHE scheme, and since then  many improvements have been made on designing more efficient homomorphic encryption schemes.  The main bottlenecks are in bootstrapping and large cipher expansion factor (the size ratio of ciphertexts over messages): the current best FHE schemes compute bootstrapping of one bit operation in 0.013 second and still have a cipher expansion factor of 10,000. In this talk, we present a compact  FHE scheme whose  bootstrapping speed is slightly slower but  whose cipher expansion factor  is  only 6  under private-key  encryption  and 20  under public-key encryption,  hence practical in term of storage.