ORCID

0000-0001-8656-5026

Keywords

Homomorphic Encryption, Cloud Computing, Matrix Multiplication, RAG

Abstract

Homomorphic encryption (HE) enables computation directly on encrypted data, offering strong privacy guarantees for sensitive applications. Despite its promise, the practical adoption of HE remains limited by high computational overhead and inefficient support for fundamental operations such as matrix multiplication, sparse computation, and secure retrieval.

This dissertation addresses these challenges by developing efficient and scalable methods for privacy-preserving computation under HE. First, it presents HEGMM, a framework for secure general matrix multiplication that reduces redundant computation and improves efficiency through optimized data layouts. Second, it introduces the Compressed Sparse Sorted Column (CSSC) format for sparse matrix-vector multiplication (SpMV), enabling efficient ciphertext-ciphertext computation by aligning sparse matrix structures with ciphertext packing strategies. Third, it develops a privacy-preserving retrieval framework for retrieval-augmented generation (RAG) in large language models, enabling encrypted similarity computation and document selection while preventing information leakage.

Extensive evaluations demonstrate that the proposed methods substantially improve efficiency, scalability, and privacy compared with existing approaches, making homomorphic computation more practical for real-world use.

Overall, this work advances the state of the art in homomorphic encryption by narrowing the gap between cryptographic theory and practical system deployment. The proposed methods provide a foundation for secure and efficient data processing in privacy-sensitive domains.

Completion Date

2026

Semester

Spring

Committee Chair

Liqiang Wang

Degree

Doctor of Philosophy (Ph.D.)

College

College of Engineering and Computer Science

Department

Computer Science

Format

PDF

Document Type

Dissertation

Identifier

DP0053274

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