8 Search Results for "Cohen, Ran"

Document
DOI: 10.4230/LIPIcs.DISC.2023.10
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
DOI: 10.4230/LIPIcs.ITC.2022.15
Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW

Authors: Gilad Asharov, Ran Cohen, and Oren Shochat

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

Abstract
Adaptive security is a highly desirable property in the design of secure protocols. It tolerates adversaries that corrupt parties as the protocol proceeds, as opposed to static security where the adversary corrupts the parties at the onset of the execution. The well-accepted folklore is that static and adaptive securities are equivalent for perfectly secure protocols. Indeed, this folklore is backed up with a transformation by Canetti et al. (EUROCRYPT'01), showing that any perfectly secure protocol that is statically secure and satisfies some basic requirements is also adaptively secure. Yet, the transformation results in an adaptively secure protocol with inefficient simulation (i.e., where the simulator might run in super-polynomial time even if the adversary runs just in polynomial time). Inefficient simulation is problematic when using the protocol as a sub-routine in the computational setting. Our main question is whether an alternative efficient transformation from static to adaptive security exists. We show an inherent difficulty in achieving this goal generically. In contrast to the folklore, we present a protocol that is perfectly secure with efficient static simulation (therefore also adaptively secure with inefficient simulation), but for which efficient adaptive simulation does not exist (assuming the existence of one-way permutations). In addition, we prove that the seminal protocol of Ben-Or, Goldwasser and Wigderson (STOC'88) is secure against adaptive, semi-honest corruptions with efficient simulation. Previously, adaptive security of the protocol, as is, was only known either for a restricted class of circuits, or for all circuits but with inefficient simulation.
Cite as

Gilad Asharov, Ran Cohen, and Oren Shochat. Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{asharov_et_al:LIPIcs.ITC.2022.15,
  author =	{Asharov, Gilad and Cohen, Ran and Shochat, Oren},
  title =	{{Static vs. Adaptive Security in Perfect MPC: A Separation and the Adaptive Security of BGW}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{15:1--15:16},
  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.2022.15},
  URN =		{urn:nbn:de:0030-drops-164933},
  doi =		{10.4230/LIPIcs.ITC.2022.15},
  annote =	{Keywords: secure multiparty computation, perfect security, adaptive security, BGW protocol}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.79
Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time

Authors: Hanlin Ren

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We consider the problem of building Distance Sensitivity Oracles (DSOs). Given a directed graph G = (V, E) with edge weights in {1, 2, … , M}, we need to preprocess it into a data structure, and answer the following queries: given vertices u,v,x ∈ V, output the length of the shortest path from u to v that does not go through x. Our main result is a simple DSO with Õ(n^2.7233 M²) preprocessing time and O(1) query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to Õ(n^2.6865 M²). Our algorithms are randomized with correct probability ≥ 1-1/n^c, for a constant c that can be made arbitrarily large. Previously, there is a DSO with Õ(n^2.8729 M) preprocessing time and polylog(n) query time [Chechik and Cohen, STOC'20]. At the core of our DSO is the following observation from [Bernstein and Karger, STOC'09]: if there is a DSO with preprocessing time P and query time Q, then we can construct a DSO with preprocessing time P+Õ(Mn²)⋅ Q and query time O(1). (Here Õ(⋅) hides polylog(n) factors.)
Cite as

Hanlin Ren. Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ren:LIPIcs.ESA.2020.79,
  author =	{Ren, Hanlin},
  title =	{{Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.79},
  URN =		{urn:nbn:de:0030-drops-129450},
  doi =		{10.4230/LIPIcs.ESA.2020.79},
  annote =	{Keywords: Graph theory, Failure-prone structures}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.12
On the Round Complexity of Randomized Byzantine Agreement

Authors: Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that: 1) BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1/2+ o(1)]. 2) BA protocols resilient against n/4 corruptions terminate at the end of the second round with probability at most 1-Theta(1). 3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against n/3 [resp., n/4] corruptions terminate at the end of the second round with probability at most o(1) [resp., 1/2 + o(1)]. The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI). The third bound essentially matches the recent protocol of Micali (ITCS'17) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability.
Cite as

Ran Cohen, Iftach Haitner, Nikolaos Makriyannis, Matan Orland, and Alex Samorodnitsky. On the Round Complexity of Randomized Byzantine Agreement. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cohen_et_al:LIPIcs.DISC.2019.12,
  author =	{Cohen, Ran and Haitner, Iftach and Makriyannis, Nikolaos and Orland, Matan and Samorodnitsky, Alex},
  title =	{{On the Round Complexity of Randomized Byzantine Agreement}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.12},
  URN =		{urn:nbn:de:0030-drops-113199},
  doi =		{10.4230/LIPIcs.DISC.2019.12},
  annote =	{Keywords: Byzantine agreement, lower bound, round complexity}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.13
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
DOI: 10.4230/LIPIcs.ICALP.2017.37
Round-Preserving Parallel Composition of Probabilistic-Termination Cryptographic Protocols

Authors: Ran Cohen, Sandro Coretti, Juan Garay, and Vassilis Zikas

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
An important benchmark for multi-party computation protocols (MPC) is their round complexity. For several important MPC tasks, (tight) lower bounds on the round complexity are known. However, for some of these tasks, such as broadcast, the lower bounds can be circumvented when the termination round of every party is not a priori known, and simultaneous termination is not guaranteed. Protocols with this property are called probabilistic-termination (PT) protocols. Running PT protocols in parallel affects the round complexity of the resulting protocol in somewhat unexpected ways. For instance, an execution of m protocols with constant expected round complexity might take O(log m) rounds to complete. In a seminal work, Ben-Or and El-Yaniv (Distributed Computing '03) developed a technique for parallel execution of arbitrarily many broadcast protocols, while preserving expected round complexity. More recently, Cohen et al. (CRYPTO '16) devised a framework for universal composition of PT protocols, and provided the first composable parallel-broadcast protocol with a simulation-based proof. These constructions crucially rely on the fact that broadcast is ``privacy free,'' and do not generalize to arbitrary protocols in a straightforward way. This raises the question of whether it is possible to execute arbitrary PT protocols in parallel, without increasing the round complexity. In this paper we tackle this question and provide both feasibility and infeasibility results. We construct a round-preserving protocol compiler, secure against a dishonest minority of actively corrupted parties, that compiles arbitrary protocols into a protocol realizing their parallel composition, while having a black-box access to the underlying protocols. Furthermore, we prove that the same cannot be achieved, using known techniques, given only black-box access to the functionalities realized by the protocols, unless merely security against semi-honest corruptions is required, for which case we provide a protocol.
Cite as

Ran Cohen, Sandro Coretti, Juan Garay, and Vassilis Zikas. Round-Preserving Parallel Composition of Probabilistic-Termination Cryptographic Protocols. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cohen_et_al:LIPIcs.ICALP.2017.37,
  author =	{Cohen, Ran and Coretti, Sandro and Garay, Juan and Zikas, Vassilis},
  title =	{{Round-Preserving Parallel Composition of Probabilistic-Termination Cryptographic Protocols}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.37},
  URN =		{urn:nbn:de:0030-drops-74124},
  doi =		{10.4230/LIPIcs.ICALP.2017.37},
  annote =	{Keywords: Cryptographic protocols, secure multi-party computation, broadcast.}
}
Document
DOI: 10.4230/LIPIcs.CCC.2016.8
Non-Malleable Extractors - New Tools and Improved Constructions

Authors: Gil Cohen

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

Abstract
A non-malleable extractor is a seeded extractor with a very strong guarantee - the output of a non-malleable extractor obtained using a typical seed is close to uniform even conditioned on the output obtained using any other seed. The first contribution of this paper consists of two new and improved constructions of non-malleable extractors: - We construct a non-malleable extractor with seed-length O(log(n) * log(log(n))) that works for entropy Omega(log(n)). This improves upon a recent exciting construction by Chattopadhyay, Goyal, and Li (STOC'16) that has seed length O(log^{2}(n)) and requires entropy Omega(log^{2}(n)). - Secondly, we construct a non-malleable extractor with optimal seed length O(log(n)) for entropy n/log^{O(1)}(n). Prior to this construction, non-malleable extractors with a logarithmic seed length, due to Li (FOCS'12), required entropy 0.49*n. Even non-malleable condensers with seed length O(log(n)), by Li (STOC'12), could only support linear entropy. We further devise several tools for enhancing a given non-malleable extractor in a black-box manner. One such tool is an algorithm that reduces the entropy requirement of a non-malleable extractor at the expense of a slightly longer seed. A second algorithm increases the output length of a non-malleable extractor from constant to linear in the entropy of the source. We also devise an algorithm that transforms a non-malleable extractor to the so-called t-non-malleable extractor for any desired t. Besides being useful building blocks for our constructions, we consider these modular tools to be of independent interest.
Cite as

Gil Cohen. Non-Malleable Extractors - New Tools and Improved Constructions. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 8:1-8:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{cohen:LIPIcs.CCC.2016.8,
  author =	{Cohen, Gil},
  title =	{{Non-Malleable Extractors - New Tools and Improved Constructions}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{8:1--8:29},
  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.2016.8},
  URN =		{urn:nbn:de:0030-drops-58348},
  doi =		{10.4230/LIPIcs.CCC.2016.8},
  annote =	{Keywords: extractors, non-malleable, explicit constructions}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.618
Two Sides of the Coin Problem

Authors: Gil Cohen, Anat Ganor, and Ran Raz

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
In the coin problem, one is given n independent flips of a coin that has bias b > 0 towards either Head or Tail. The goal is to decide which side the coin is biased towards, with high confidence. An optimal strategy for solving the coin problem is to apply the majority function on the n samples. This simple strategy works as long as b > c(1/sqrt n) for some constant c. However, computing majority is an impossible task for several natural computational models, such as bounded width read once branching programs and AC^0 circuits. Brody and Verbin proved that a length n, width w read once branching program cannot solve the coin problem for b < O(1/(log n)^w). This result was tightened by Steinberger to O(1/(log n)^(w-2)). The coin problem in the model of AC^0 circuits was first studied by Shaltiel and Viola, and later by Aaronson who proved that a depth d size s Boolean circuit cannot solve the coin problem for b < O(1/(log s)^(d+2)). This work has two contributions: 1. We strengthen Steinberger's result and show that any Santha-Vazirani source with bias b < O(1/(log n)^(w-2)) fools length n, width w read once branching programs. In other words, the strong independence assumption in the coin problem is completely redundant in the model of read once branching programs, assuming the bias remains small. That is, the exact same result holds for a much more general class of sources. 2. We tighten Aaronson's result and show that a depth d, size s Boolean circuit cannot solve the coin problem for b < O(1/(log s)^(d-1)). Moreover, our proof technique is different and we believe that it is simpler and more natural.
Cite as

Gil Cohen, Anat Ganor, and Ran Raz. Two Sides of the Coin Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 618-629, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{cohen_et_al:LIPIcs.APPROX-RANDOM.2014.618,
  author =	{Cohen, Gil and Ganor, Anat and Raz, Ran},
  title =	{{Two Sides of the Coin Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{618--629},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.618},
  URN =		{urn:nbn:de:0030-drops-47265},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.618},
  annote =	{Keywords: bounded depth circuits, read once branching programs, Santha-Vazirani sources, the coin problem}
}
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