Date of Award
12-2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Shuhong Gao
Committee Member
Richard Brooks
Committee Member
Felice Manganiello
Committee Member
Hui Xue
Abstract
The changes in computing paradigms to shift computations to third parties have resulted in the necessity of these computations to be provable. Zero-knowledge arguments are probabilistic arguments that are used to to verify computations without secret data being leaked to the verifying party.
In this dissertation, we study zero-knowledge arguments with specific focus on reductions. Our main contributions are:
- Provide a thorough survey in a variety of zero-knowledge techniques and protocols.
- Prove various results of reductions that can be used to study interactive protocols in terms of subroutines. Additionally, we identify an issue in the analogous definition of zero-knowledge for reductions. We propose a potential solution to this issue.
- Design a novel matrix multiplication protocol based on reductions.
- Design protocols for arithmetic of fixed-point values of fixed-length.
Recommended Citation
Jones, Marvin, "Zero-Knowledge Reductions and Confidential Arithmetic" (2023). All Dissertations. 3472.
https://open.clemson.edu/all_dissertations/3472