PARAMETER SELECTION IN FULLY HOMOMORPHIC ENCRYPTION SCHEMES AND FHE APPLICATIONS
Tez Türü: Doktora
Tezin Yürütüldüğü Kurum: New Jersey Institute of Technology, College of Computing, Computer Science, Amerika Birleşik Devletleri
Tez Danışmanı: Kurt Rohloff
Tezin Onay Tarihi: 2022
Tezin Dili: İngilizce
Desteklendiği Program: Diğer
Özet:
Quantum computing has been gaining momentum as a result of recent technological
advances. Existing cryptographic systems rely on the di cult problems that can be
solved by su ciently powerful quantum computers. As the quantum age approaches,
the desire to discover new di cult problems that cannot be solved by quantum
systems has increased. Lattice-based cryptography is a prominent tool for the
post-quantum era that facilitates the implementation of encryption systems for
practical applications.
The Learning with Error (LWE) and Ring-LWE problems introduce new lattice
hardness assumptions that have been incorporated into public-key cryptosystems
to facilitate the implementation of numerous privacy-enhancing applications. Fully
homomorphic encryption (FHE) is the crown jewel of lattice-based cryptography
under the hardness assumptions of LWE and RLWE. FHE provides computation
on encrypted data without revealing the actual data and private key. FHE is a
versatile tool for privacy-preserving technologies, also known as the \Holy Grail of
data privacy". Existing FHE schemes have a number of issues, including parameter
selection, noise growth, and performance.
Parameter selection is an open problem for the FHE schemes. The initial step
of this thesis focuses on the parameter selection problem on FHE. To provide security,
accuracy, and e cacy, FHE parameters must be carefully chosen. Otherwise, it results
in security failure, incorrect results, or ine cient computations. The introduction of
a method for parameter selection will increase the pace of FHE schemes in real-
world applications and make it easier for non-experts to apply FHE in their own applications. This work employs BFVrns, a prominent lattice-based FHE scheme, as
the primary and building block scheme for FHE applications. This study introduces
a novel parameter selection model for the BFVrns scheme that is based on a hybrid
principles-based approach that combines theoretical and experimental analyses.
With the advent of new technologies such as cloud computing and the Internet
of Things (IoT), the demand for privacy-enhancing technologies has increased.
Private information retrieval (PIR) and secure multiparty computation (MPC) are fundamental tools for new technologies that ensure the security and confidentiality
of cloud-based data. PIR enables a user to retrieve data privately from a public
database. This signi es that neither the database operator nor any other third party
knows which entry the user is querying. PIR is an innovative solution for a wide range
of applications, including online patents, real-time stock data, and search engines.
FHE is referred to as the \Swiss army knife of cryptography" because it is utilized as
a building block in numerous privacy-preserving technologies, such as computational
PIR (cPIR) schemes. This study introduces three FHE-based cPIR protocols that
are e cient in terms of communication and computation.
Secure MPC is another cryptographic tool that enables a number of distinct
parties to perform a joint computation of a function while maintaining the con -
dentiality and accuracy of each party's data. Due to the sensitivity of the data in
certain applications, such as medical and nancial data, it is essential for the systems
that users encrypt their data before sending it to a third party (e.g., cloud). In this
scenario, the cloud must perform computations on encrypted data encrypted with
di erent keys. Secure MPC is a competent solution for such systems, which are
utilized in a wide variety of commercial applications, including blockchain, mobile
computing, and cryptographic voting schemes. This work proposes three distinct
FHE-based secure MPC protocols that improve the number of rounds and the
performance and communication effciency.