Date of Award
12-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Shuhong Gao
Committee Member
Ryann Cartor
Committee Member
Felice Manganiello
Committee Member
Hui Xue
Abstract
Homomorphic encryption allows for computations on encrypted data without exposing the underlying plaintext, enabling secure and private data processing in various applications such as cloud computing and machine learning. In this thesis, we conduct a comprehensive worst-case noise analysis for three prominent leveled homomorphic encryption schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski-Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS). We propose modifications to these schemes and their residue number system (RNS) variants, ensuring fresh encryption noise falls under a constant bound. For BFV and BGV, we design and prove parameter conditions which guarantee certain homomorphic circuit evaluations return ciphertexts containing noise within a fixed bound. For CKKS, we design and prove parameter conditions which guarantee some amount of precision accuracy. We consider all these designs and analyses with both original and RNS variants of the schemes. We also conduct our own security analysis and recommendations for parameters with guaranteed homomorphic computation and precision accuracy.
Recommended Citation
Yates, Kyle, "Leveled Homomorphic Encryption Schemes: Noise and Precision Control" (2025). All Dissertations. 4174.
https://open.clemson.edu/all_dissertations/4174