Abstract
Streaming algorithms are algorithms for processing large data streams, using only a limited amount of memory. Classical streaming algorithms typically work under the assumption that the input stream is chosen independently from the internal state of the algorithm. Algorithms that utilize this assumption are called oblivious algorithms. Recently, there is a growing interest in studying streaming algorithms that maintain utility also when the input stream is chosen by an adaptive adversary, possibly as a function of previous estimates given by the streaming algorithm. Such streaming algorithms are said to be adversarially-robust.
By combining techniques from learning theory with cryptographic tools from the bounded storage model, we separate the oblivious streaming model from the adversarially-robust streaming model. Specifically, we present a streaming problem for which every adversarially-robust streaming algorithm must use polynomial space, while there exists a classical (oblivious) streaming algorithm that uses only polylogarithmic space. This is the first general separation between the capabilities of these two models, resolving one of the central open questions in adversarial robust streaming.
H. Kaplan—Partially supported by the Israel Science Foundation (grant 1595/19), the German-Israeli Foundation (grant 1367/2017), and by the Blavatnik Family Foundation.
Y. Mansour—This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 882396), by the Israel Science Foundation (grant number 993/17) and the Yandex Initiative for Machine Learning at Tel Aviv University.
K. Nissim—Supported by NSF grant No. 1565387 TWC: Large: Collaborative: Computing Over Distributed Sensitive Data and by a gift to Georgetown University, the Data Co-Ops project.
U. Stemmer—Partially Supported by the Israel Science Foundation (grant 1871/19) and by the Cyber Security Research Center at Ben-Gurion University of the Negev.
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Notes
- 1.
A streaming algorithm is linear if for some (possibly randomized) matrix A, its output depends only on A and Af, where f is the frequency vector of the stream.
- 2.
While there exist information theoretic impossibility results for the ADA problem, they are too weak to give a meaningful result in our context.
- 3.
Specifically, recall that the error in the ADA problem is additive while the error in the streaming setting is multiplicative. We add a (relatively small) number of \(\bot \)’s to S in order to bridge this technical gap.
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Kaplan, H., Mansour, Y., Nissim, K., Stemmer, U. (2021). Separating Adaptive Streaming from Oblivious Streaming Using the Bounded Storage Model. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12827. Springer, Cham. https://doi.org/10.1007/978-3-030-84252-9_4
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