7 Search Results for "Randolph, Tim"

Document
DOI: 10.4230/LIPIcs.ESA.2025.14
Testing Sumsets Is Hard

Authors: Xi Chen, Shivam Nadimpalli, Tim Randolph, Rocco A. Servedio, and Or Zamir

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A subset S of the Boolean hypercube 𝔽₂ⁿ is a sumset if S = {a + b : a, b ∈ A} for some A ⊆ 𝔽₂ⁿ. Sumsets are central objects of study in additive combinatorics, where they play a role in several of the field’s most important results. We prove a lower bound of Ω(2^{n/2}) for the number of queries needed to test whether a Boolean function f:𝔽₂ⁿ → {0,1} is the indicator function of a sumset, ruling out an efficient testing algorithm for sumsets. Our lower bound for testing sumsets follows from sharp bounds on the related problem of shift testing, which may be of independent interest. We also give a near-optimal {2^{n/2} ⋅ poly(n)}-query algorithm for a smoothed analysis formulation of the sumset refutation problem. Finally, we include a simple proof that the number of different sumsets in 𝔽₂ⁿ is 2^{(1±o(1))2^{n-1}}.
Cite as

Xi Chen, Shivam Nadimpalli, Tim Randolph, Rocco A. Servedio, and Or Zamir. Testing Sumsets Is Hard. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.ESA.2025.14,
  author =	{Chen, Xi and Nadimpalli, Shivam and Randolph, Tim and Servedio, Rocco A. and Zamir, Or},
  title =	{{Testing Sumsets Is Hard}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.14},
  URN =		{urn:nbn:de:0030-drops-244822},
  doi =		{10.4230/LIPIcs.ESA.2025.14},
  annote =	{Keywords: Sumsets, additive combinatorics, property testing, Boolean functions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.86
New Algorithms for Pigeonhole Equal Subset Sum

Authors: Ce Jin, Ryan Williams, and Stan Zhang

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We study the Pigeonhole Equal Subset Sum problem, which is a total-search variant of the Subset Sum problem introduced by Papadimitriou (1994): we are given a set of n positive integers {w₁,…,w_n} with the additional restriction that ∑_{i=1}^n w_i < 2ⁿ - 1, and want to find two different subsets A,B ⊆ [n] such that ∑_{i∈A} w_i = ∑_{i∈B} w_i. Very recently, Jin and Wu (ICALP 2024) gave a randomized algorithm solving Pigeonhole Equal Subset Sum in O^*(2^{0.4n}) time, beating the classical meet-in-the-middle algorithm with O^*(2^{n/2}) runtime. In this paper, we refine Jin and Wu’s techniques to improve the runtime even further to O^*(2^{n/3}).
Cite as

Ce Jin, Ryan Williams, and Stan Zhang. New Algorithms for Pigeonhole Equal Subset Sum. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 86:1-86:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{jin_et_al:LIPIcs.ESA.2025.86,
  author =	{Jin, Ce and Williams, Ryan and Zhang, Stan},
  title =	{{New Algorithms for Pigeonhole Equal Subset Sum}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{86:1--86:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.86},
  URN =		{urn:nbn:de:0030-drops-245541},
  doi =		{10.4230/LIPIcs.ESA.2025.86},
  annote =	{Keywords: pigeonhole principle, subset sums}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.72
Card-Based Protocols Imply PSM Protocols

Authors: Kazumasa Shinagawa and Koji Nuida

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Card-based cryptography is the art of cryptography using a deck of physical cards. While this area is known as a research area of recreational cryptography and is recently paid attention in educational purposes, there is no systematic study of the relationship between card-based cryptography and the other "conventional" cryptography. This paper establishes the first generic conversion from card-based protocols to private simultaneous messages (PSM) protocols, a special kind of secure multiparty computation. Our compiler supports "simple" card-based protocols, which is a natural subclass of finite-runtime protocols. The communication complexity of the resulting PSM protocol depends on how many cards are opened in total in all possible branches of the original card-based protocol. This result shows theoretical importance of such "opening complexity" of card-based protocols, which had not been focused in this area. As a consequence, lower bounds for PSM protocols imply those for simple card-based protocols. In particular, if there exists no PSM protocol with subexponential communication complexity for a function f, then there exists no simple card-based protocol with subexponential opening complexity for the same f.
Cite as

Kazumasa Shinagawa and Koji Nuida. Card-Based Protocols Imply PSM Protocols. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 72:1-72:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{shinagawa_et_al:LIPIcs.STACS.2025.72,
  author =	{Shinagawa, Kazumasa and Nuida, Koji},
  title =	{{Card-Based Protocols Imply PSM Protocols}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{72:1--72:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.72},
  URN =		{urn:nbn:de:0030-drops-228975},
  doi =		{10.4230/LIPIcs.STACS.2025.72},
  annote =	{Keywords: Card-based cryptography, private simultaneous messages}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.25
Reliable Communication in Hybrid Authentication and Trust Models

Authors: Rowdy Chotkan, Bart Cox, Vincent Rahli, and Jérémie Decouchant

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
Reliable communication is a fundamental distributed communication abstraction that allows any two nodes within a network to communicate with each other. It is necessary for more powerful communication primitives, such as broadcast and consensus. Using different authentication models, two classical protocols implement reliable communication in unknown and sufficiently connected networks. In the former, network links are authenticated, and processes rely on dissemination paths to authenticate messages. In the latter, processes generate digital signatures that are flooded throughout the network. This work considers the hybrid system model that combines authenticated links and authenticated processes. Additionally, we aim to leverage the possible presence of trusted nodes (e.g., network gateways) and trusted components (e.g., Intel SGX enclaves). We first extend the two classical reliable communication protocols to leverage trusted nodes. Then we propose DualRC, our most generic algorithm that considers the hybrid authentication model by manipulating dissemination paths and digital signatures, and leverages the possible presence of trusted nodes and trusted components. We describe and prove methods that establish whether our algorithms implement reliable communication on a given network.
Cite as

Rowdy Chotkan, Bart Cox, Vincent Rahli, and Jérémie Decouchant. Reliable Communication in Hybrid Authentication and Trust Models. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 25:1-25:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{chotkan_et_al:LIPIcs.OPODIS.2024.25,
  author =	{Chotkan, Rowdy and Cox, Bart and Rahli, Vincent and Decouchant, J\'{e}r\'{e}mie},
  title =	{{Reliable Communication in Hybrid Authentication and Trust Models}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{25:1--25:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.25},
  URN =		{urn:nbn:de:0030-drops-225611},
  doi =		{10.4230/LIPIcs.OPODIS.2024.25},
  annote =	{Keywords: Reliable communication, Byzantine, Authentication models, Trust}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.96
Parameterized Algorithms on Integer Sets with Small Doubling: Integer Programming, Subset Sum and k-SUM

Authors: Tim Randolph and Karol Węgrzycki

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We study the parameterized complexity of algorithmic problems whose input is an integer set A in terms of the doubling constant 𝒞 := |A+A| / |A|, a fundamental measure of additive structure. We present evidence that this new parameterization is algorithmically useful in the form of new results for two difficult, well-studied problems: Integer Programming and Subset Sum. First, we show that determining the feasibility of bounded Integer Programs is a tractable problem when parameterized in the doubling constant. Specifically, we prove that the feasibility of an integer program ℐ with n polynomially-bounded variables and m constraints can be determined in time n^{O_𝒞(1)} ⋅ poly(|ℐ|) when the column set of the constraint matrix has doubling constant 𝒞. Second, we show that the Subset Sum and Unbounded Subset Sum problems can be solved in time n^{O_C(1)} and n^{O_𝒞(log log log n)}, respectively, where the O_C notation hides functions that depend only on the doubling constant 𝒞. We also show the equivalence of achieving an FPT algorithm for Subset Sum with bounded doubling and achieving a milestone result for the parameterized complexity of Box ILP. Finally, we design near-linear time algorithms for k-SUM as well as tight lower bounds for 4-SUM and nearly tight lower bounds for k-SUM, under the k-SUM conjecture. Several of our results rely on a new proof that Freiman’s Theorem, a central result in additive combinatorics, can be made efficiently constructive. This result may be of independent interest.
Cite as

Tim Randolph and Karol Węgrzycki. Parameterized Algorithms on Integer Sets with Small Doubling: Integer Programming, Subset Sum and k-SUM. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 96:1-96:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{randolph_et_al:LIPIcs.ESA.2024.96,
  author =	{Randolph, Tim and W\k{e}grzycki, Karol},
  title =	{{Parameterized Algorithms on Integer Sets with Small Doubling: Integer Programming, Subset Sum and k-SUM}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{96:1--96:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.96},
  URN =		{urn:nbn:de:0030-drops-211672},
  doi =		{10.4230/LIPIcs.ESA.2024.96},
  annote =	{Keywords: Parameterized algorithms, parameterized complexity, additive combinatorics, Subset Sum, integer programming, doubling constant}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.39
Subset Sum in Time 2^{n/2} / poly(n)

Authors: Xi Chen, Yaonan Jin, Tim Randolph, and Rocco A. Servedio

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) n-input Subset Sum problem that runs in time 2^{(1/2 - c)n} for some constant c > 0. In this paper we give a Subset Sum algorithm with worst-case running time O(2^{n/2} ⋅ n^{-γ}) for a constant γ > 0.5023 in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical "meet-in-the-middle" algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time O(2^{n/2}) in these memory models [Horowitz and Sahni, 1974]. Our algorithm combines a number of different techniques, including the "representation method" introduced by Howgrave-Graham and Joux [Howgrave-Graham and Joux, 2010] and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof [Austrin et al., 2016], and Nederlof and Węgrzycki [Jesper Nederlof and Karol Wegrzycki, 2021], and "bit-packing" techniques used in the work of Baran, Demaine, and Pǎtraşcu [Baran et al., 2005] on subquadratic algorithms for 3SUM.
Cite as

Xi Chen, Yaonan Jin, Tim Randolph, and Rocco A. Servedio. Subset Sum in Time 2^{n/2} / poly(n). In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2023.39,
  author =	{Chen, Xi and Jin, Yaonan and Randolph, Tim and Servedio, Rocco A.},
  title =	{{Subset Sum in Time 2^\{n/2\} / poly(n)}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{39:1--39:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.39},
  URN =		{urn:nbn:de:0030-drops-188641},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.39},
  annote =	{Keywords: Exact algorithms, subset sum, log shaving}
}
Document
DOI: 10.4230/LIPIcs.ITC.2022.7
A Note on the Complexity of Private Simultaneous Messages with Many Parties

Authors: Marshall Ball and Tim Randolph

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

Abstract
For k = ω(log n), we prove a Ω(k²n / log(kn)) lower bound on private simultaneous messages (PSM) with k parties who receive n-bit inputs. This extends the Ω(n) lower bound due to Appelbaum, Holenstein, Mishra and Shayevitz [Journal of Cryptology, 2019] to the many-party (k = ω(log n)) setting. It is the first PSM lower bound that increases quadratically with the number of parties, and moreover the first unconditional, explicit bound that grows with both k and n. This note extends the work of Ball, Holmgren, Ishai, Liu, and Malkin [ITCS 2020], who prove communication complexity lower bounds on decomposable randomized encodings (DREs), which correspond to the special case of k-party PSMs with n = 1. To give a concise and readable introduction to the method, we focus our presentation on perfect PSM schemes.
Cite as

Marshall Ball and Tim Randolph. A Note on the Complexity of Private Simultaneous Messages with Many Parties. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 7:1-7:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ball_et_al:LIPIcs.ITC.2022.7,
  author =	{Ball, Marshall and Randolph, Tim},
  title =	{{A Note on the Complexity of Private Simultaneous Messages with Many Parties}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{7:1--7:12},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.7},
  URN =		{urn:nbn:de:0030-drops-164855},
  doi =		{10.4230/LIPIcs.ITC.2022.7},
  annote =	{Keywords: Secure computation, Private Simultaneous Messages}
}
  • Refine by Type
  • 7 Document/PDF
  • 3 Document/HTML

  • Refine by Publication Year
  • 4 2025
  • 1 2024
  • 1 2023
  • 1 2022

  • Refine by Author
  • 4 Randolph, Tim
  • 2 Chen, Xi
  • 2 Servedio, Rocco A.
  • 1 Ball, Marshall
  • 1 Chotkan, Rowdy
  • Show More...

  • Refine by Series/Journal
  • 7 LIPIcs

  • Refine by Classification
  • 3 Theory of computation → Design and analysis of algorithms
  • 2 Security and privacy → Information-theoretic techniques
  • 1 Computer systems organization → Fault-tolerant network topologies
  • 1 Theory of computation → Communication complexity
  • 1 Theory of computation → Cryptographic protocols
  • Show More...

  • Refine by Keyword
  • 2 additive combinatorics
  • 1 Authentication models
  • 1 Boolean functions
  • 1 Byzantine
  • 1 Card-based cryptography
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact