Date of Award
12-2025
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
School of Mathematical and Statistical Sciences
Committee Chair/Advisor
Rafael D'Oliveira
Committee Member
Ryann Cartor
Committee Member
Felice Manganiello
Abstract
Secure multiparty computation (MPC) enables multiple participants to jointly compute functions over their private inputs without revealing them. Classical threshold based protocols, such as the BGW protocol, perform computations on scalar values using (k,n)-threshold secret sharing. While these protocols provide strong security guarantees, they become computationally expensive when applied to large matrices or multiple secret values. In this work, we investigate the use of ramp schemes, secret sharing schemes that encode sets of secrets with a trade-off between privacy and efficiency, to generalize BGW computations. We show that the linear operations performed on shares (k,n)-threshold schemes in BGW can be applied to (d,k,n)-ramp schemes as well, allowing servers to perform secure computations on matrices more efficiently. By partitioning a matrix into submatrices, and encoding them as secret sets in a ramp scheme, we can use ramp schemes to provide a more efficient framework for performing matrix operations securely, reducing both communication and computation costs compared to protocols that perform at the scalar level. Our framework establishes a foundation for extending BGW-like protocols to ramp schemes, offering greater flexibility and efficiency for secure multiparty computation. This work paves the way for practical implementations of ramp scheme based MPC in distributed matrix computations and other applications requiring efficient privacy preserving operations on structured data.
Recommended Citation
Tucker, Christian, "Generalizing Threshold-Based Multiparty Computation to Ramp Schemes" (2025). All Theses. 4617.
https://open.clemson.edu/all_theses/4617