5 Search Results for "Slívová, Veronika"

Document
DOI: 10.4230/LIPIcs.ITC.2022.6
On the Distributed Discrete Logarithm Problem with Preprocessing

Authors: Pavel Hubáček, Ľubica Jančová, and Veronika Králová

Published in: LIPIcs, Volume 230, 3rd Conference on Information-Theoretic Cryptography (ITC 2022)

Abstract
Protocols solving the Distributed Discrete Logarithm (DDLog) problem are a core component of many recent constructions of group-based homomorphic secret sharing schemes. On a high-level, these protocols enable two parties to transform multiplicative shares of a secret into additive share locally without any communication. Due to their important applications, various generic optimized DDLog protocols were proposed in the literature, culminating in the asymptotically optimal generic protocol of Dinur, Keller, and Klein (J. Cryptol. 2020) solving DDLog in time T with error probability O(W/T²) when the magnitude of the secret is bounded by W. Given that DDLog is solved repeatedly with respect to a fixed group in its applications, a natural approach for improving the efficiency of DDLog protocols could be via leveraging some precomputed group-specific advice. To understand the limitations of this approach, we revisit the distributed discrete logarithm problem in the preprocessing model and study the possible time-space trade-offs for DDLog in the generic group model. As our main result, we show that, in a group of size N, any generic DDLog protocol for secrets of magnitude W with parties running in time T using precomputed group-specific advice of size S has success probability ε = O (T²/W + max{S,log W} ⋅ T²/N) . Thus, assuming N ≥ W log W, we get a lower bound ST² = Ω(ε N) on the time-space trade-off for DDLog protocols using large advice of size S = Ω(N/W). Interestingly, for DDLog protocols using small advice of size S = O(N/W), we get a lower bound T² = Ω(ε W) on the running time, which, in the constant-error regime, asymptotically matches the running time of the DDLog protocol without any advice of Dinur et al. (J. Cryptol. 2020). In other words, we show that generic DDLog protocols achieving constant success probability do not benefit from any advice of size S = O(N/W) in the online phase of the DDLog problem.
Cite as

Pavel Hubáček, Ľubica Jančová, and Veronika Králová. On the Distributed Discrete Logarithm Problem with Preprocessing. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hubacek_et_al:LIPIcs.ITC.2022.6,
  author =	{Hub\'{a}\v{c}ek, Pavel and Jan\v{c}ov\'{a}, \v{L}ubica and Kr\'{a}lov\'{a}, Veronika},
  title =	{{On the Distributed Discrete Logarithm Problem with Preprocessing}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-238-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{230},
  editor =	{Dachman-Soled, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.6},
  URN =		{urn:nbn:de:0030-drops-164847},
  doi =		{10.4230/LIPIcs.ITC.2022.6},
  annote =	{Keywords: Distributed discrete logarithm problem, preprocessing, generic group model}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.39
Data Structures Lower Bounds and Popular Conjectures

Authors: Pavel Dvořák, Michal Koucký, Karel Král, and Veronika Slívová

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In this paper, we investigate the relative power of several conjectures that attracted recently lot of interest. We establish a connection between the Network Coding Conjecture (NCC) of Li and Li [Li and Li, 2004] and several data structure problems such as non-adaptive function inversion of Hellman [M. Hellman, 1980] and the well-studied problem of polynomial evaluation and interpolation. In turn these data structure problems imply super-linear circuit lower bounds for explicit functions such as integer sorting and multi-point polynomial evaluation.
Cite as

Pavel Dvořák, Michal Koucký, Karel Král, and Veronika Slívová. Data Structures Lower Bounds and Popular Conjectures. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dvorak_et_al:LIPIcs.ESA.2021.39,
  author =	{Dvo\v{r}\'{a}k, Pavel and Kouck\'{y}, Michal and Kr\'{a}l, Karel and Sl{\'\i}vov\'{a}, Veronika},
  title =	{{Data Structures Lower Bounds and Popular Conjectures}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.39},
  URN =		{urn:nbn:de:0030-drops-146207},
  doi =		{10.4230/LIPIcs.ESA.2021.39},
  annote =	{Keywords: Data structures, Circuits, Lower bounds, Network Coding Conjecture}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.88
Sorting Short Integers

Authors: Michal Koucký and Karel Král

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We build boolean circuits of size 𝒪(nm²) and depth 𝒪(log(n) + m log(m)) for sorting n integers each of m-bits. We build also circuits that sort n integers each of m-bits according to their first k bits that are of size 𝒪(nmk (1 + log^*(n) - log^*(m))) and depth 𝒪(log³(n)). This improves on the results of Asharov et al. [Asharov et al., 2021] and resolves some of their open questions.
Cite as

Michal Koucký and Karel Král. Sorting Short Integers. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 88:1-88:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{koucky_et_al:LIPIcs.ICALP.2021.88,
  author =	{Kouck\'{y}, Michal and Kr\'{a}l, Karel},
  title =	{{Sorting Short Integers}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{88:1--88:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.88},
  URN =		{urn:nbn:de:0030-drops-141577},
  doi =		{10.4230/LIPIcs.ICALP.2021.88},
  annote =	{Keywords: sorting, small integers, boolean circuits}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.5
Colouring (P_r+P_s)-Free Graphs

Authors: Tereza Klimosová, Josef Malík, Tomás Masarík, Jana Novotná, Daniël Paulusma, and Veronika Slívová

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u) subseteq {1,...,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. We prove that List 3-Colouring is polynomial-time solvable for (P_2+P_5)-free graphs and for (P_3+P_4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices. We also prove that 5-Colouring is NP-complete for (P_3+P_5)-free graphs.
Cite as

Tereza Klimosová, Josef Malík, Tomás Masarík, Jana Novotná, Daniël Paulusma, and Veronika Slívová. Colouring (P_r+P_s)-Free Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{klimosova_et_al:LIPIcs.ISAAC.2018.5,
  author =	{Klimosov\'{a}, Tereza and Mal{\'\i}k, Josef and Masar{\'\i}k, Tom\'{a}s and Novotn\'{a}, Jana and Paulusma, Dani\"{e}l and Sl{\'\i}vov\'{a}, Veronika},
  title =	{{Colouring (P\underliner+P\underlines)-Free Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.5},
  URN =		{urn:nbn:de:0030-drops-99533},
  doi =		{10.4230/LIPIcs.ISAAC.2018.5},
  annote =	{Keywords: vertex colouring, H-free graph, linear forest}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.60
ARRIVAL: Next Stop in CLS

Authors: Bernd Gärtner, Thomas Dueholm Hansen, Pavel Hubácek, Karel Král, Hagar Mosaad, and Veronika Slívová

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We study the computational complexity of Arrival, a zero-player game on n-vertex switch graphs introduced by Dohrau, Gärtner, Kohler, Matousek, and Welzl. They showed that the problem of deciding termination of this game is contained in NP n coNP. Karthik C. S. recently introduced a search variant of Arrival and showed that it is in the complexity class PLS. In this work, we significantly improve the known upper bounds for both the decision and the search variants of Arrival. First, we resolve a question suggested by Dohrau et al. and show that the decision variant of Arrival is in UP n coUP. Second, we prove that the search variant of Arrival is contained in CLS. Third, we give a randomized O(1.4143^n)-time algorithm to solve both variants. Our main technical contributions are (a) an efficiently verifiable characterization of the unique witness for termination of the Arrival game, and (b) an efficient way of sampling from the state space of the game. We show that the problem of finding the unique witness is contained in CLS, whereas it was previously conjectured to be FPSPACE-complete. The efficient sampling procedure yields the first algorithm for the problem that has expected runtime O(c^n) with c<2.
Cite as

Bernd Gärtner, Thomas Dueholm Hansen, Pavel Hubácek, Karel Král, Hagar Mosaad, and Veronika Slívová. ARRIVAL: Next Stop in CLS. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 60:1-60:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gartner_et_al:LIPIcs.ICALP.2018.60,
  author =	{G\"{a}rtner, Bernd and Hansen, Thomas Dueholm and Hub\'{a}cek, Pavel and Kr\'{a}l, Karel and Mosaad, Hagar and Sl{\'\i}vov\'{a}, Veronika},
  title =	{{ARRIVAL: Next Stop in CLS}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{60:1--60:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.60},
  URN =		{urn:nbn:de:0030-drops-90641},
  doi =		{10.4230/LIPIcs.ICALP.2018.60},
  annote =	{Keywords: CLS, switch graphs, zero-player game, UP n coUP}
}
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