New hardness results for total search problems and non-interactive lattice-based protocols
Name
1227780114-MIT.pdf
Size
1.85 MB
Format
Adobe PDF
Checksum (MD5)
ab71e53f96c1509e9fcec8c738a32512
Author(s)
Sotiraki, Aikaterini.
Advisor(s)
Vinod Vaikuntanathan.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
We investigate new hardness results for total search problems, namely search problems that always have a solution, and non-interactive lattice protocols. 1. A question of particular importance, raised together with the definition of the class of total search problems, is to identify complete problems that do not have explicitly a Turing machine or a circuit as a part of their input. We provide natural complete problems for various TFNP subclasses. We first consider the classes PPP and PWPP, where our complete problems are inspired by lattice theory and lead towards answering important questions in cryptography. Additionally, we identify complete problems for classes that generalize the class PPA, called PPA[subscript q]. In this case, our results have connections to number theory, and in particular to the Chevalley-Warning theorem. 2. The Learning With Errors (LWE) problem, introduced by Regev has had a profound impact on cryptography. We consider non-interactive protocols that are secure under the LWE assumption, such as non-interactive zero-knowledge and non-interactive key-exchange. We show new strategies and new barriers towards constructing such protocols.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, September, 2020
Cataloged from student-submitted PDF of thesis.
Includes bibliographical references (pages 217-230).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
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