A Summary of the FV Homomorphic Encryption Scheme and the Average-Case Noise Growth

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Date
2021-09-20Author
Perrin, Derek
ORCID
0000-0001-5496-7055Type
ThesisDegree Level
MastersMetadata
Show full item recordAbstract
Homomorphic encryption is a method of encryption that allows for secure computation of
data. Many industries are moving away from owning expensive high-powered computers and
instead delegating costly computations to the cloud. In an age of data breaches, there is an
inherent risk when putting sensitive data on the cloud. Homomorphic encryption allows one
to securely perform computations on the cloud without allowing the host or any other party
access to the raw data itself. One application being explored is encrypting health data on
low-powered embedded devices, uploading it to a cloud application, performing computations
to assess health risks, and send the results back to the user’s device for decryption and
interpretation. Another application being explored is digital voting.
This thesis aims to provide a summary of the current state-of-the-art of homomorphic
encryption. We will begin by providing the reader with sources for the current main im-
plementations and schemes they are based on. We will then present the mathematical
background used in existing schemes. This includes a background on lattices, cyclotomic
fields, rings of integers, and the underlying believed-to-be-hard problems existing schemes
take advantage of. We will then shift our attention to the FV scheme which is based on the
ring-LWE problem and is one of the main schemes used today. We will then briefly discuss
some optimizations used in FV implementations. Finally, we will look at some probabilistic
experiments which suggest the noise growth in FV is significantly lower than the theoretical
maximum in the average case, and will explore some of the benefits that can be gained.
Degree
Master of Science (M.Sc.)Department
Mathematics and StatisticsProgram
MathematicsSupervisor
Franc, CameronCommittee
Rajchgot, Jenna; Rayan, Steven; Osgood, NathanielCopyright Date
September 2021Subject
cryptography
homomorphic encryption
lattice cryptography
ideal lattices