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Thinking Inside The Box: Privacy Against Stronger Adversaries

Eldon Chung

TL;DR

This thesis analyzes robustness of cryptographic primitives under in-the-box adversaries, focusing on leakage, tampering, and backdoors. It develops a foundational link between leakage-resilient secret sharing and the need for extractable randomness, showing that efficient LRSS implies efficient extractors and, conversely, that non-extractable randomness cannot suffice for 2-out-of-2 schemes. It introduces collision-resistant seeded extractors and leverages them to construct two-source non-malleable extractors with favorable entropy requirements, enabling privacy amplification against memory-tampering adversaries. The work also strengthens immunization perspectives by proving stronger data-structure lower bounds for 3SUM-Indexing, including adaptive and near-linear-universe regimes, tying oracle immunization to hard data-structure problems. Collectively, the results bridge theory and real-world attack models, advancing leakage-resilient secret sharing, non-malleable extraction, and immunized cryptographic constructions with potential practical security implications in noisy, adversarial environments.

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 the final chapter, we study the hardness of the data structure variant of the 3SUM problem which is motivated by a recent construction to immunise random oracles against pre-processing adversaries. We give worst-case data structure hardness for the 3SUM problem matching known barriers in data structures for adaptive adversaries. We also give a slightly stronger lower bound in the case of non-adaptivity. Lastly, we give a novel result in the bit-probe setting.

Thinking Inside The Box: Privacy Against Stronger Adversaries

TL;DR

This thesis analyzes robustness of cryptographic primitives under in-the-box adversaries, focusing on leakage, tampering, and backdoors. It develops a foundational link between leakage-resilient secret sharing and the need for extractable randomness, showing that efficient LRSS implies efficient extractors and, conversely, that non-extractable randomness cannot suffice for 2-out-of-2 schemes. It introduces collision-resistant seeded extractors and leverages them to construct two-source non-malleable extractors with favorable entropy requirements, enabling privacy amplification against memory-tampering adversaries. The work also strengthens immunization perspectives by proving stronger data-structure lower bounds for 3SUM-Indexing, including adaptive and near-linear-universe regimes, tying oracle immunization to hard data-structure problems. Collectively, the results bridge theory and real-world attack models, advancing leakage-resilient secret sharing, non-malleable extraction, and immunized cryptographic constructions with potential practical security implications in noisy, adversarial environments.

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 the final chapter, we study the hardness of the data structure variant of the 3SUM problem which is motivated by a recent construction to immunise random oracles against pre-processing adversaries. We give worst-case data structure hardness for the 3SUM problem matching known barriers in data structures for adaptive adversaries. We also give a slightly stronger lower bound in the case of non-adaptivity. Lastly, we give a novel result in the bit-probe setting.

Paper Structure

This paper contains 125 sections, 76 theorems, 169 equations, 3 figures, 1 table.

Table of Contents

  1. Summary
  2. Papers
  3. Introduction
  4. Side-Channel Attacks
  5. Leakage Resilience Cryptography.
  6. Non-malleable Cryptography.
  7. Backdoors, and Immunisation.
  8. Cryptographic Primitives
  9. Randomness in Cryptography, and Extractors
  10. (Seeded Extractors)
  11. (Two-source Extractors)
  12. (Non-malleable Extractors)
  13. Secret Sharing, and its extensions
  14. (Leakage Resilient Secret Sharing)
  15. Privacy Amplification
  16. ...and 110 more sections

Key Result

Theorem 2

Let $(\texttt{Sh},\texttt{Rec},\mathcal{Y})$ be an $(\varepsilon_1,\varepsilon_2)$-leakage-resilient secret sharing scheme for $b$-bit messages (with $1$ bit of leakage). Then, either: Furthermore, if $\texttt{Sh}$ is an efficient algorithm, the extractor can be given as a family of $\text{poly}(b)$-sized circuits.

Figures (3)

  • Figure 1: Verbatim from AORSS20. Privacy amplification protocol against memory-tampering active adversaries. In the above, for an $n$-bit string $x$ we define $[x]_i=(x_1,x_2,\dots,x_i)$, $[x]_{i:j}=(x_{i+1},\dots,x_j)$, and $[x]_{j:}=(x_{j+1},\dots,x_n)$.
  • Figure 2: Extension of the original PA protocol. $R$ is split into $4$ parts instead of $3$. Here $\mathtt{MAC}$ is a standard information theoretic message authentication code (MAC). And $\mathbf{SExt}$ is any seeded extractor. When party Aborts it stops responding and the final output is $\bot$.
  • Figure :

Theorems & Definitions (162)

  • Remark 1: Informal, GGHPV20
  • Theorem 2: Formally stated in \ref{['thm:final']}
  • Corollary 3: Informal
  • Corollary 4: Informal
  • Definition 5: Collision Resistance Hash Function (CRHF)
  • Theorem 6
  • Definition 7: Collision Resistant Extractors
  • Theorem 8
  • Theorem 9: Informal
  • Theorem 10
  • ...and 152 more