On foundations of public-key encryption and secret sharing
Name
1142101291-MIT.pdf
Size
12.65 MB
Format
Adobe PDF
Checksum (MD5)
0aafe92a332bcc390a2937f92b8b3436
Author(s)
Degwekar, Akshay(Akshay Dhananjai)
Advisor(s)
Vinod Vaikuntanathan.
Date Issued
2019
Publisher
Massachusetts Institute of Technology
Abstract
Since the inception of Cryptography, Information theory and Coding theory have influenced cryptography in myriad ways including numerous information-theoretic notions of security in secret sharing, multiparty computation and statistical zero knowledge; and by providing a large toolbox used extensively in cryptography. This thesis addresses two questions in this realm: Leakage Resilience of Secret Sharing Schemes. We show that classical secret sharing schemes like Shamir secret sharing and additive secret sharing over prime order fields are leakage resilient. Leakage resilience of secret sharing schemes is closely related to locally repairable codes and our results can be viewed as impossibility results for local recovery over prime order fields. As an application of the result, we show the leakage resilience of a variant of the Goldreich-Micali-Wigderson protocol. From Laconic Statistical Zero Knowledge Proofs to Public Key Encryption. Languages with statistical zero knowledge proofs that are also average-case hard have been used to construct various cryptographic primitives. We show that hard languages with laconic SZK proofs, that is proof systems where the communication from the prover to the verifier is small, imply public key encryption.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 153-164).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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