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Vinod Vaikuntanathan. Degwekar, Akshay(Akshay Dhananjai) Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2020-03-09T18:51:36Z 2020-03-09T18:51:36Z 2019 2019 https://hdl.handle.net/1721.1/124060 1142101291 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). 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. by Akshay Dhananjai Degwekar. Ph.D. Ph.D. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science 166 pages eng Massachusetts Institute of Technology MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. On foundations of public-key encryption and secret sharing Thesis application/pdf 2020-03-09T18:51:35Z Publication Doctoral EECS unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="92497269-647f-4590-ba52-4dc0e4a5d228"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>On foundations of public-key encryption and secret sharing</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2019</PublicationDate> <Authors> <Author> <DisplayName>Degwekar, Akshay(Akshay Dhananjai)</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>