Haitner, Iftach, and Salil Vadhan. “
The Many Entropies in One-way Functions.” In
Tutorials on the Foundations of Cryptography, 159-217. Springer, Yehuda Lindell, ed. 2017.
Publisher's VersionAbstract
Version History:
Earlier versions: May 2017: ECCC TR 17-084
Dec. 2017: ECCC TR 17-084 (revised)
Computational analogues of information-theoretic notions have given rise to some of the most interesting phenomena in the theory of computation. For example, computational indistinguishability, Goldwasser and Micali [9], which is the computational analogue of statistical distance, enabled the bypassing of Shannon’s impossibility results on perfectly secure encryption, and provided the basis for the computational theory of pseudorandomness. Pseudoentropy, Håstad, Impagliazzo, Levin, and Luby [17], a computational analogue of entropy, was the key to the fundamental result establishing the equivalence of pseudorandom generators and one-way functions, and has become a basic concept in complexity theory and cryptography.
This tutorial discusses two rather recent computational notions of entropy, both of which can be easily found in any one-way function, the most basic cryptographic primitive. The first notion is next-block pseudoentropy, Haitner, Reingold, and Vadhan [14], a refinement of pseudoentropy that enables simpler and more ecient construction of pseudorandom generators. The second is inaccessible entropy, Haitner, Reingold, Vadhan, andWee [11], which relates to unforgeability and is used to construct simpler and more efficient universal one-way hash functions and statistically hiding commitments.
SPRINGER 2017.pdf ECCC 5-2017.pdf ECCC 12-2017.pdf Vadhan, Salil. “
The Complexity of Differential Privacy.” In
Tutorials on the Foundations of Cryptography, 347-450. Springer, Yehuda Lindell, ed. 2017.
Publisher's VersionAbstract
Version History:
August 2016: Manuscript v1 (see files attached)
March 2017: Manuscript v2 (see files attached); Errata
April 2017: Published Version (in Tutorials on the Foundations of Cryptography; see Publisher's Version link and also SPRINGER 2017.PDF, below)
Differential privacy is a theoretical framework for ensuring the privacy of individual-level data when performing statistical analysis of privacy-sensitive datasets. This tutorial provides an introduction to and overview of differential privacy, with the goal of conveying its deep connections to a variety of other topics in computational complexity, cryptography, and theoretical computer science at large. This tutorial is written in celebration of Oded Goldreich’s 60th birthday, starting from notes taken during a minicourse given by the author and Kunal Talwar at the 26th McGill Invitational Workshop on Computational Complexity [1].
SPRINGER 2017.pdf ERRATA 2017.pdf MANUSCRIPT 2017.pdf MANUSCRIPT 2016.pdf Chen, Yi-Hsiu, Kai-Min Chung, Ching-Yi Lai, Salil P. Vadhan, and Xiaodi Wu. “
Computational notions of quantum min-entropy.” In
Poster presention at QIP 2017 and oral presentation at QCrypt 2017, 2017.
Publisher's VersionAbstract
Version History:
We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold. Our main results are as follows. (1) The classical Leakage Chain Rule for pseudoentropy can be extended to the case that the leakage information is quantum (while the source remains classical). Specifically, if the source has pseudoentropy at least \(k\), then it has pseudoentropy at least \(k−ℓ \) conditioned on an \(ℓ \)-qubit leakage. (2) As an application of the Leakage Chain Rule, we construct the first quantum leakage-resilient stream-cipher in the bounded-quantum-storage model, assuming the existence of a quantum-secure pseudorandom generator. (3) We show that the general form of the classical Dense Model Theorem (interpreted as the equivalence between two definitions of pseudo-relative-min-entropy) does not extend to quantum states. Along the way, we develop quantum analogues of some classical techniques (e.g. the Leakage Simulation Lemma, which is proven by a Non-uniform Min-Max Theorem or Boosting). On the other hand, we also identify some classical techniques (e.g. Gap Amplification) that do not work in the quantum setting. Moreover, we introduce a variety of notions that combine quantum information and quantum complexity, and this raises several directions for future work.
ArXiv2017.pdf