5 Search Results for "Chen, Ran"


Document
Communication Lower Bounds for Cryptographic Broadcast Protocols

Authors: Erica Blum, Elette Boyle, Ran Cohen, and Chen-Da Liu-Zhang

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)


Abstract
Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even in the face of malicious parties who collude to attack the protocol. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on the protocol of Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved even using randomization and cryptography. On the other hand, the only nontrivial ω(n) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform "after the fact" removal of messages. We provide communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple protocol showing near tightness of our first bound. - Static adversary. We demonstrate a tradeoff between resiliency and communication for randomized protocols secure against n-o(n) static corruptions. For example, Ω(n⋅ polylog(n)) messages are needed when the number of honest parties is n/polylog(n); Ω(n√n) messages are needed for O(√n) honest parties; and Ω(n²) messages are needed for O(1) honest parties. Complementarily, we demonstrate broadcast with O(n⋅polylog(n)) total communication and balanced polylog(n) per-party cost, facing any constant fraction of static corruptions. - Weakly adaptive adversary. Our second bound considers n/2 + k corruptions and a weakly adaptive adversary that cannot remove messages "after the fact." We show that any broadcast protocol within this setting can be attacked to force an arbitrary party to send messages to k other parties. Our bound implies limitations on the feasibility of balanced low-communication protocols: For example, ruling out broadcast facing 51% corruptions, in which all non-sender parties have sublinear communication locality.

Cite as

Erica Blum, Elette Boyle, Ran Cohen, and Chen-Da Liu-Zhang. Communication Lower Bounds for Cryptographic Broadcast Protocols. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{blum_et_al:LIPIcs.DISC.2023.10,
  author =	{Blum, Erica and Boyle, Elette and Cohen, Ran and Liu-Zhang, Chen-Da},
  title =	{{Communication Lower Bounds for Cryptographic Broadcast Protocols}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.10},
  URN =		{urn:nbn:de:0030-drops-191361},
  doi =		{10.4230/LIPIcs.DISC.2023.10},
  annote =	{Keywords: broadcast, communication complexity, lower bounds, dishonest majority}
}
Document
A Super-Quadratic Lower Bound for Depth Four Arithmetic Circuits

Authors: Nikhil Gupta, Chandan Saha, and Bhargav Thankey

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)


Abstract
We show an Ω̃(n^2.5) lower bound for general depth four arithmetic circuits computing an explicit n-variate degree-Θ(n) multilinear polynomial over any field of characteristic zero. To our knowledge, and as stated in the survey [Amir Shpilka and Amir Yehudayoff, 2010], no super-quadratic lower bound was known for depth four circuits over fields of characteristic ≠ 2 before this work. The previous best lower bound is Ω̃(n^1.5) [Abhijat Sharma, 2017], which is a slight quantitative improvement over the roughly Ω(n^1.33) bound obtained by invoking the super-linear lower bound for constant depth circuits in [Ran Raz, 2010; Victor Shoup and Roman Smolensky, 1997]. Our lower bound proof follows the approach of the almost cubic lower bound for depth three circuits in [Neeraj Kayal et al., 2016] by replacing the shifted partials measure with a suitable variant of the projected shifted partials measure, but it differs from [Neeraj Kayal et al., 2016]’s proof at a crucial step - namely, the way "heavy" product gates are handled. Loosely speaking, a heavy product gate has a relatively high fan-in. Product gates of a depth three circuit compute products of affine forms, and so, it is easy to prune Θ(n) many heavy product gates by projecting the circuit to a low-dimensional affine subspace [Neeraj Kayal et al., 2016; Amir Shpilka and Avi Wigderson, 2001]. However, in a depth four circuit, the second (from the top) layer of product gates compute products of polynomials having arbitrary degree, and hence it was not clear how to prune such heavy product gates from the circuit. We show that heavy product gates can also be eliminated from a depth four circuit by projecting the circuit to a low-dimensional affine subspace, unless the heavy gates together account for Ω̃(n^2.5) size. This part of our argument is inspired by a well-known greedy approximation algorithm for the weighted set-cover problem.

Cite as

Nikhil Gupta, Chandan Saha, and Bhargav Thankey. A Super-Quadratic Lower Bound for Depth Four Arithmetic Circuits. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 23:1-23:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{gupta_et_al:LIPIcs.CCC.2020.23,
  author =	{Gupta, Nikhil and Saha, Chandan and Thankey, Bhargav},
  title =	{{A Super-Quadratic Lower Bound for Depth Four Arithmetic Circuits}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{23:1--23:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.23},
  URN =		{urn:nbn:de:0030-drops-125757},
  doi =		{10.4230/LIPIcs.CCC.2020.23},
  annote =	{Keywords: depth four arithmetic circuits, Projected Shifted Partials, super-quadratic lower bound}
}
Document
Formal Proofs of Tarjan’s Strongly Connected Components Algorithm in Why3, Coq and Isabelle

Authors: Ran Chen, Cyril Cohen, Jean-Jacques Lévy, Stephan Merz, and Laurent Théry

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)


Abstract
Comparing provers on a formalization of the same problem is always a valuable exercise. In this paper, we present the formal proof of correctness of a non-trivial algorithm from graph theory that was carried out in three proof assistants: Why3, Coq, and Isabelle.

Cite as

Ran Chen, Cyril Cohen, Jean-Jacques Lévy, Stephan Merz, and Laurent Théry. Formal Proofs of Tarjan’s Strongly Connected Components Algorithm in Why3, Coq and Isabelle. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{chen_et_al:LIPIcs.ITP.2019.13,
  author =	{Chen, Ran and Cohen, Cyril and L\'{e}vy, Jean-Jacques and Merz, Stephan and Th\'{e}ry, Laurent},
  title =	{{Formal Proofs of Tarjan’s Strongly Connected Components Algorithm in Why3, Coq and Isabelle}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.13},
  URN =		{urn:nbn:de:0030-drops-110683},
  doi =		{10.4230/LIPIcs.ITP.2019.13},
  annote =	{Keywords: Mathematical logic, Formal proof, Graph algorithm, Program verification}
}
Document
An Improved Algorithm for Incremental DFS Tree in Undirected Graphs

Authors: Lijie Chen, Ran Duan, Ruosong Wang, Hanrui Zhang, and Tianyi Zhang

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)


Abstract
Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph G=(V,E) with n vertices and m edges, the textbook algorithm takes O(n+m) time to construct a DFS tree. In this paper, we study the problem of maintaining a DFS tree when the graph is undergoing incremental updates. Formally, we show: Given an arbitrary online sequence of edge or vertex insertions, there is an algorithm that reports a DFS tree in O(n) worst case time per operation, and requires O (min {m log n, n^2}) preprocessing time. Our result improves the previous O(n log^3 n) worst case update time algorithm by Baswana et al. [Baswana et al., 2016] and the O(n log n) time by Nakamura and Sadakane [Nakamura and Sadakane, 2017], and matches the trivial Omega(n) lower bound when it is required to explicitly output a DFS tree. Our result builds on the framework introduced in the breakthrough work by Baswana et al. [Baswana et al., 2016], together with a novel use of a tree-partition lemma by Duan and Zhang [Duan and Zhang, 2016], and the celebrated fractional cascading technique by Chazelle and Guibas [Chazelle and Guibas, 1986a; Chazelle and Guibas, 1986b].

Cite as

Lijie Chen, Ran Duan, Ruosong Wang, Hanrui Zhang, and Tianyi Zhang. An Improved Algorithm for Incremental DFS Tree in Undirected Graphs. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{chen_et_al:LIPIcs.SWAT.2018.16,
  author =	{Chen, Lijie and Duan, Ran and Wang, Ruosong and Zhang, Hanrui and Zhang, Tianyi},
  title =	{{An Improved Algorithm for Incremental DFS Tree in Undirected Graphs}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{16:1--16:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.16},
  URN =		{urn:nbn:de:0030-drops-88427},
  doi =		{10.4230/LIPIcs.SWAT.2018.16},
  annote =	{Keywords: DFS tree, fractional cascading, fully dynamic algorithm}
}
Document
Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits

Authors: Ruiwen Chen, Rahul Santhanam, and Srikanth Srinivasan

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)


Abstract
We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer d > 1, there is epsilon_d > 0 such that Parity has correlation at most 1/n^{Omega(1)} with depth-d threshold circuits which have at most n^{1+epsilon_d} wires, and the Generalized Andreev Function has correlation at most 1/2^{n^{Omega(1)}} with depth-d threshold circuits which have at most n^{1+epsilon_d} wires. Previously, only worst-case lower bounds in this setting were known [Impagliazzo/Paturi/Saks, SIAM J. Comp., 1997]. We use our ideas to make progress on several related questions. We give satisfiability algorithms beating brute force search for depth-$d$ threshold circuits with a superlinear number of wires. These are the first such algorithms for depth greater than 2. We also show that Parity cannot be computed by polynomial-size AC^0 circuits with n^{o(1)} general threshold gates. Previously no lower bound for Parity in this setting could handle more than log(n) gates. This result also implies subexponential-time learning algorithms for AC^0 with n^{o(1)} threshold gates under the uniform distribution. In addition, we give almost optimal bounds for the number of gates in a depth-d threshold circuit computing Parity on average, and show average-case lower bounds for threshold formulas ofany depth. Our techniques include adaptive random restrictions, anti-concentration and the structural theory of linear threshold functions, and bounded-read Chernoff bounds.

Cite as

Ruiwen Chen, Rahul Santhanam, and Srikanth Srinivasan. Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 1:1-1:35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{chen_et_al:LIPIcs.CCC.2016.1,
  author =	{Chen, Ruiwen and Santhanam, Rahul and Srinivasan, Srikanth},
  title =	{{Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{1:1--1:35},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.1},
  URN =		{urn:nbn:de:0030-drops-58447},
  doi =		{10.4230/LIPIcs.CCC.2016.1},
  annote =	{Keywords: threshold circuit, satisfiability algorithm, circuit lower bound}
}
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