Abstract: Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, the last 

few years have witnessed dramatic progress on designing more efficient homomorphic encryption

schemes, and some of them have been implemented for applications. The main bottlenecks are in

bootstrapping and large cipher expansion (the ratio of the size of ciphertexts to that of messages).

Ducas and Micciancio (2015) show that homomorphic computation of one bit operation on LWE

ciphers can be done in less than a second, which is then reduced by Chillotti et al. (2016, 2017) to

13ms. This paper presents a compact fully homomorphic encryption scheme that has the following

features: (a) its cipher expansion is 6 with private-key encryption and 20 with public-key encryp- tion;

(b) all ciphertexts after any number (unbounded) of homomorphic bit operations have the same size

and are always valid with the same error size; (c) its security is based on the LWE and RLWE

problems (with binary secret keys) and the cost of breaking the scheme by the current approaches

is at least 2160 bit operations. The scheme protects function privacy and provides a simple solution

for secure two-party computation and zero knowledge proof of any language in NP. 

Bio: Shuhong Gao received his BS (1983) and MS (1986) from Department of Mathematics, Sichuan

University, China, and PhD (1993) from Department of Combinatorics and Optimization, University of

Waterloo, Canada.  From 1993 to 1995, he was an NSERC Postdoctoral Fellow in Department of

Computer Science, University of Toronto, Canada. He joined Clemson University in USA in 1995 as an

assistant professor in Mathematical Sciences, and was promoted to associate professor in 2000 (with

early tenure) and to full professor in 2002.  Professor Gao's research interests include coding theory,

cryptography, symbolic computation, computational number theory and computational algebraic

geometry.  More information about his research and  teaching can be found at Applicable

Algebra Lab: https://www.ces.clemson.edu/aca/