【直播】【QuACT系列报告】Data Structures Meet Cryptography: 3SUM with...

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本系列报告由中国科学院计算技术研究所主办，于2021年5月25日10:00开始，授权蔻享学术进行网络直播。

Data Structures Meet Cryptography: 3SUM with Preprocessing

报告人

Siyao Guo, NYU Shanghai

时间

2021年5月25日 10:00-11:00

This paper shows several connections between data structure problems and cryptography against preprocessing attacks. Our results span data structure upper bounds, cryptographic applications, and data structure lower bounds, as summarized next. First, we apply Fiat-Naor inversion, a technique with cryptographic origins, to obtain a data structure upper bound. In particular, our technique yields a suite of algorithms with space ‍‍ and (online) time ‍‍ for a preprocessing version of the ‍‍-input 3SUM problem where ‍‍. This disproves a strong conjecture (Goldstein et al., WADS 2017) that there is no data structure that solves this problem for ‍‍ and ‍‍ for any constant ‍‍. Secondly, we show equivalence between lower bounds for a broad class of (static) data structure problems and one-way functions in the random oracle model that resist a very strong form of preprocessing attack. Concretely, given a random function ‍‍ (accessed as an oracle) we show how to compile it into a function ‍‍ which resists ‍‍-bit preprocessing attacks that run in query time ‍‍ where ‍‍ (assuming a corresponding data structure lower bound on 3SUM). In contrast, a classical result of Hellman tells us that F itself can be more easily inverted, say with ‍‍-bit preprocessing in ‍‍ time. We also show that much stronger lower bounds follow from the hardness of kSUM. Our results can be equivalently interpreted as security against adversaries that are very non-uniform, or have large auxiliary input, or as security in the face of a powerfully backdoored random oracle. Thirdly, we give non-adaptive lower bounds for 3SUM which match the best known lower bounds for static data structure problems. Moreover, we show that our lower bound generalizes to a range of geometric problems, such as three points on a line, polygon containment, and others. This is a joint work with Alexander Golovnev, Thibaut Horel, Sunoo Park and Vinod Vaikuntanathan.

报告人简介

图 | 郭斯瑶Siyao Guo is an Assistant Professor of Computer Science, NYU Shanghai; Global Network Assistant Professor, NYU. Previously, she was a postdoctoral fellow at the Cybersecurity and Privacy Institute at Northeastern University, Simons Institute for the theory of computation at UC Berkeley, and the Courant Institute of Mathematical Sciences at New York University. Her research interests are cryptography, computational complexity and pseudorandomness.

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