The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title:	Towards practical homomorphic encryption and efficient implementation
Author:	Sahu, Gyana R.
View Online:	njit-etd2020-097 (xv, 173 pages ~ 1.2 MB pdf)
Department:	Department of Computer Science
Degree:	Doctor of Philosophy
Program:	Computer Science
Document Type:	Dissertation
Advisory Committee:	Rohloff, Kurt (Committee chair) Polyakov, Yuriy S. (Committee member) Tang, Qiang (Committee member) Khreishah, Abdallah (Committee member) Di Crescenzo, Giovanni (Committee member)
Date:	2020-08
Keywords:	Bootstrapping Fully homomorphic encryption GPU Lattice based cryptography Proxy re-encryption
Availability:	Unrestricted
Abstract:	Cloud computing has gained significant traction over the past few years and its application continues to soar as evident from its rapid adoption in various industries. One of the major challenges involved in cloud computing services is the security of sensitive information as cloud servers have been often found to be vulnerable to snooping by malicious adversaries. Such data privacy concerns can be addressed to a greater extent by enforcing cryptographic measures. Fully homomorphic encryption (FHE), a special form of public key encryption has emerged as a primary tool in deploying such cryptographic security assurances without sacrificing many of the privileges of working with data in cleartext. In brief, a FHE scheme allows for computation of arbitrary functions on encrypted data stored on cloud and retrieve results in encrypted form. In this dissertation, construction of various Proxy Re-encryption (PRE) schemes based on FHE schemes are presented and their parameter selection leading to secure instantiation discussed. PRE is a valuable cryptographic primitive that enables users to exchange information in an untrusted environment via a proxy. In the second line of work, bootstrapping algorithms for FHE schemes and their efficient implementation in PALISADE lattice cryptography software library is presented. Originally proposed by Gentry, bootstrapping plays a central role in extending a somewhat homomorphic encryption (SHE) scheme towards full homomorphism. Several novel techniques to extend bootstrapping algorithms for larger secret key bounds, plaintext modulus and other FHE parameters are discussed. Despite several advances and nearly a decade of research, efficiency of FHE schemes still remains one of the primary concern in deploying them in real-life applications. These concerns are addressed in the last line of work by demonstrating practical implementation of PRE schemes and bootstrapping algorithms on various heterogeneous GPGPU computing platforms. Since FHE schemes fall into the category of "embarrassingly parallel" computing workloads, the massive computing power of GPUs consisting of multiple processors can be leveraged to result in multiple order of improvement in performance. To aid this effort, parallel NTT algorithms are designed and various other optimizations suitable for CPU architectures discussed.