Thinking Inside The Box: Privacy Against Stronger Adversaries
Eldon Chung

TL;DR
This thesis advances cryptographic primitives by establishing new leakage-resilient secret sharing requirements, developing collision-resistant extractors for privacy amplification, and analyzing data structure hardness for 3SUM, addressing security against stronger adversaries.
Contribution
It introduces the necessity of extractable randomness for leakage-resilient secret sharing, constructs collision-resistant extractors for privacy amplification, and provides new hardness bounds for 3SUM data structures against adaptive and non-adaptive adversaries.
Findings
Leakage-resilient secret sharing requires extractable sources.
Constructed collision-resistant seeded extractors with small seed overhead.
Established worst-case data structure hardness for 3SUM matching known barriers.
Abstract
In this thesis, we study extensions of statistical cryptographic primitives. In particular we study leakage-resilient secret sharing, non-malleable extractors, and immunized ideal one-way functions. The thesis is divided into three main chapters. In the first chapter, we show that 2-out-of-2 leakage resilient (and also non-malleable) secret sharing requires randomness sources that are also extractable. This rules out the possibility of using min-entropic sources. In the second, we introduce collision-resistant seeded extractors and show that any seeded extractor can be made collision resistant at a small overhead in seed length. We then use it to give a two-source non-malleable extractor with entropy rate 0.81 in one source and polylogarithmic in the other. The non-malleable extractor lead to the first statistical privacy amplification protocol against memory tampering adversaries. In…
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Taxonomy
TopicsPrivacy, Security, and Data Protection · Cybercrime and Law Enforcement Studies · Crime Patterns and Interventions
