Fully Homomorphic Encryption: A Mathematical Introduction

Sara Logsdon

Paper 2023/1402

Fully Homomorphic Encryption: A Mathematical Introduction

Sara Logsdon, University of Georgia

Abstract

This paper offers a mathematical introduction to fully homomorphic encryption, a concept that enables computation on encrypted data. We trace the historical development of FHE, describe Fully Homomorphic Encryption over the Torus (TFHE) and how it performs certain mathematical operations, and explore bootstrapping and the possibility for adjusting computational depth. This paper equips readers with a brief understanding of FHE's evolution and the essential mechanisms facilitating practical implementation.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Fully Homomorphic Encryption TFHE Bootstrapping Computational Depth
Contact author(s): sara logsdon @ uga edu
History: 2023-09-24: approved; 2023-09-18: received; See all versions
Short URL: https://ia.cr/2023/1402
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1402,
      author = {Sara Logsdon},
      title = {Fully Homomorphic Encryption: A Mathematical Introduction},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1402},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/1402}},
      url = {https://eprint.iacr.org/2023/1402}
}