Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Shuhong Gao

Committee Member

Richard Brooks

Committee Member

Felice Manganiello

Committee Member

Hui Xue


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:

  1. Provide a thorough survey in a variety of zero-knowledge techniques and protocols.
  2. 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.
  3. Design a novel matrix multiplication protocol based on reductions.
  4. Design protocols for arithmetic of fixed-point values of fixed-length.



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