Theoretical and practical advances in preprocessing based secure computation

Secure computation — often called multiparty computation (MPC) — is a cornerstone of modern cryptography, enabling multiple parties to jointly compute functions over their private inputs without revealing those inputs. Over the past two decades, the preprocessing model of MPC has emerged as a powerful paradigm for improving practical efficiency. In this approach, the protocol is split into two distinct phases: 1.) Offline (input-independent) phase: Parties perform the bulk of the cryptographic work ahead of time to generate “correlated randomness.” 2.) Online (input-dependent) phase: Parties consume that precomputed “correlated randomness” to execute the actual secure computation task in an efficient way. By shifting intensive computations to the offline phase, the online phase can run with minimal latency, significantly reducing the response time of the protocol. This dissertation tackles the two core challenges of preprocessing-based MPC: 1.) Choosing the right correlated randomness: We study two important applications — secure sorting and secure logistic regression — and identify specialized forms of correlated randomness that yield communication-efficient online protocols for each task. 2.) Generating and storing correlated randomness efficiently: We introduce new techniques for producing two key types of correlations — unit-vector correlations and doubly-authenticated bits — by harnessing pseudorandom generators with enhanced properties. We further demonstrate how these correlations accelerate secure computation and zero-knowledge proofs respectively. Together, these contributions advance the state of the art in MPC by both broadening the range of efficiently. solvable tasks and streamlining the resources required to prepare for them.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Agarwal, Amit

Contributors dc:contributor

• Khurana, Dakshita
• Miller, Andrew
• Gunter, Carl
• Beaver, Donald

• Secure Computation
• Zero-knowledge Proofs
• Cryptography

Statement dc:rights

• Copyright 2025 Amit Agarwal

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/130186

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F130186