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Documents authored by Tzalik, Elad

Document
DOI: 10.4230/LIPIcs.DISC.2024.36
Connectivity Labeling in Faulty Colored Graphs

Authors: Asaf Petruschka, Shay Spair, and Elad Tzalik

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
Fault-tolerant connectivity labelings are schemes that, given an n-vertex graph G = (V,E) and a parameter f, produce succinct yet informative labels for the elements of the graph. Given only the labels of two vertices u,v and of the elements in a faulty-set F with |F| ≤ f, one can determine if u,v are connected in G-F, the surviving graph after removing F. For the edge or vertex faults models, i.e., F ⊆ E or F ⊆ V, a sequence of recent work established schemes with poly(f,log n)-bit labels for general graphs. This paper considers the color faults model, recently introduced in the context of spanners [Petruschka, Sapir and Tzalik, ITCS '24], which accounts for known correlations between failures. Here, the edges (or vertices) of the input G are arbitrarily colored, and the faulty elements in F are colors; a failing color causes all edges (vertices) of that color to crash. While treating color faults by naïvly applying solutions for many failing edges or vertices is inefficient, the known correlations could potentially be exploited to provide better solutions. Our main contribution is settling the label length complexity for connectivity under one color fault (f = 1). The existing implicit solution, by black-box application of the state-of-the-art scheme for edge faults of [Dory and Parter, PODC '21], might yield labels of Ω(n) bits. We provide a deterministic scheme with labels of Õ(√n) bits in the worst case, and a matching lower bound. Moreover, our scheme is universally optimal: even schemes tailored to handle only colorings of one specific graph topology (i.e., may store the topology "for free") cannot produce asymptotically smaller labels. We characterize the optimal length by a new graph parameter bp(G) called the ball packing number. We further extend our labeling approach to yield a routing scheme avoiding a single forbidden color, with routing tables of size Õ(bp(G)) bits. We also consider the centralized setting, and show an Õ(n)-space oracle, answering connectivity queries under one color fault in Õ(1) time. Curiously, by our results, no oracle with such space can be evenly distributed as labels. Turning to f ≥ 2 color faults, we give a randomized labeling scheme with Õ(n^{1-1/2^f})-bit labels, along with a lower bound of Ω(n^{1-1/(f+1)}) bits. For f = 2, we make partial improvement by providing labels of Õ(diam(G)√n) bits, and show that this scheme is (nearly) optimal when diam(G) = Õ(1). Additionally, we present a general reduction from the above all-pairs formulation of fault-tolerant connectivity labeling (in any fault model) to the single-source variant, which could also be applicable for centralized oracles, streaming, or dynamic algorithms.
Cite as

Asaf Petruschka, Shay Spair, and Elad Tzalik. Connectivity Labeling in Faulty Colored Graphs. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{petruschka_et_al:LIPIcs.DISC.2024.36,
  author =	{Petruschka, Asaf and Spair, Shay and Tzalik, Elad},
  title =	{{Connectivity Labeling in Faulty Colored Graphs}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.36},
  URN =		{urn:nbn:de:0030-drops-212622},
  doi =		{10.4230/LIPIcs.DISC.2024.36},
  annote =	{Keywords: Labeling schemes, Fault-tolerance}
}
Document
DOI: 10.4230/LIPIcs.ITC.2024.3
Are Your Keys Protected? Time Will Tell

Authors: Yoav Ben Dov, Liron David, Moni Naor, and Elad Tzalik

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract
Side channel attacks, and in particular timing attacks, are a fundamental obstacle to obtaining secure implementation of algorithms and cryptographic protocols, and have been widely researched for decades. While cryptographic definitions for the security of cryptographic systems have been well established for decades, none of these accepted definitions take into account the running time information leaked from executing the system. In this work, we give the foundation of new cryptographic definitions for cryptographic systems that take into account information about their leaked running time, focusing mainly on keyed functions such as signature and encryption schemes. Specifically, [(1)] 1) We define several cryptographic properties to express the claim that the timing information does not help an adversary to extract sensitive information, e.g. the key or the queries made. We highlight the definition of key-obliviousness, which means that an adversary cannot tell whether it received the timing of the queries with the actual key or the timing of the same queries with a random key. 2) We present a construction of key-oblivious pseudorandom permutations on a small or medium-sized domain. This construction is not "fixed-time," and at the same time is secure against any number of queries even in case the adversary knows the running time exactly. Our construction, which we call Janus Sometimes Recurse, is a variant of the "Sometimes Recurse" shuffle by Morris and Rogaway. 3) We suggest a new security notion for keyed functions, called noticeable security, and prove that cryptographic schemes that have noticeable security remain secure even when the exact timings are leaked, provided the implementation is key-oblivious. We show that our notion applies to cryptographic signatures, private key encryption and PRPs.
Cite as

Yoav Ben Dov, Liron David, Moni Naor, and Elad Tzalik. Are Your Keys Protected? Time Will Tell. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 3:1-3:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bendov_et_al:LIPIcs.ITC.2024.3,
  author =	{Ben Dov, Yoav and David, Liron and Naor, Moni and Tzalik, Elad},
  title =	{{Are Your Keys Protected? Time Will Tell}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{3:1--3:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.3},
  URN =		{urn:nbn:de:0030-drops-205119},
  doi =		{10.4230/LIPIcs.ITC.2024.3},
  annote =	{Keywords: Side channel attacks, Timing attacks, Keyed functions, Key oblivious, Noticeable security}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.88
Color Fault-Tolerant Spanners

Authors: Asaf Petruschka, Shay Sapir, and Elad Tzalik

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We initiate the study of spanners in arbitrarily vertex- or edge-colored graphs (with no "legality" restrictions), that are resilient to failures of entire color classes. When a color fails, all vertices/edges of that color crash. An f-color fault-tolerant (f-CFT) t-spanner of an n-vertex colored graph G is a subgraph H that preserves distances up to factor t, even in the presence of at most f color faults. This notion generalizes the well-studied f-vertex/edge fault-tolerant (f-V/EFT) spanners. The size (number of edges) of an f-V/EFT spanner crucially depends on the number f of vertex/edge faults to be tolerated. In the colored variants, even a single color fault can correspond to an unbounded number of vertex/edge faults. The key conceptual contribution of this work is in showing that the size required by an f-CFT spanner is in fact comparable to its uncolored counterpart, with no dependency on the size of color classes. We provide optimal bounds on the size required by f-CFT (2k-1)-spanners, as follows: - When vertices have colors, we show an upper bound of O(f^{1-1/k} n^{1+1/k}) edges. This precisely matches the (tight) bounds for (2k-1)-spanners resilient to f individual vertex faults [Bodwin et al., SODA 2018; Bodwin and Patel, PODC 2019]. - For colored edges, we show that O(f n^{1+1/k}) edges are always sufficient. Further, we prove this is tight, i.e., we provide an Ω(f n^{1+1/k}) (worst-case) lower bound. The state-of-the-art bounds known for the corresponding uncolored setting of edge faults are (roughly) Θ(f^{1/2} n^{1+1/k}) [Bodwin et al., SODA 2018; Bodwin, Dinitz and Robelle, SODA 2022]. - We also consider a mixed model where both vertices and edges are colored. In this case, we show tight Θ(f^{2-1/k} n^{1+1/k}) bounds. Thus, CFT spanners exhibit an interesting phenomenon: while (individual) edge faults are "easier" than vertex faults, edge-color faults are "harder" than vertex-color faults. Our upper bounds are based on a generalization of the blocking set technique of [Bodwin and Patel, PODC 2019] for analyzing the (exponential-time) greedy algorithm for FT spanners. We complement them by providing efficient constructions of CFT spanners with similar size guarantees, based on the algorithm of [Dinitz and Robelle, PODC 2020].
Cite as

Asaf Petruschka, Shay Sapir, and Elad Tzalik. Color Fault-Tolerant Spanners. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 88:1-88:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{petruschka_et_al:LIPIcs.ITCS.2024.88,
  author =	{Petruschka, Asaf and Sapir, Shay and Tzalik, Elad},
  title =	{{Color Fault-Tolerant Spanners}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{88:1--88:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.88},
  URN =		{urn:nbn:de:0030-drops-196160},
  doi =		{10.4230/LIPIcs.ITCS.2024.88},
  annote =	{Keywords: Fault tolerance, Graph spanners}
}
Document
DOI: 10.4230/LIPIcs.FORC.2023.11
Resistance to Timing Attacks for Sampling and Privacy Preserving Schemes

Authors: Yoav Ben Dov, Liron David, Moni Naor, and Elad Tzalik

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Abstract
Side channel attacks, and in particular timing attacks, are a fundamental obstacle for secure implementation of algorithms and cryptographic protocols. These attacks and countermeasures have been widely researched for decades. We offer a new perspective on resistance to timing attacks. We focus on sampling algorithms and their application to differential privacy. We define sampling algorithms that do not reveal information about the sampled output through their running time. More specifically: (1) We characterize the distributions that can be sampled from in a "time oblivious" way, meaning that the running time does not leak any information about the output. We provide an optimal algorithm in terms of randomness used to sample for these distributions. We give an example of an efficient randomized algorithm 𝒜 such that there is no subexponential algorithm with the same output as 𝒜 that does not reveal information on the output or the input, therefore we show leaking information on either the input or the output is unavoidable. (2) We consider the impact of timing attacks on (pure) differential privacy mechanisms. It turns out that if the range of the mechanism is unbounded, such as counting, then any time oblivious pure DP mechanism must give a useless output with constant probability (the constant is mechanism dependent) and must have infinite expected running time. We show that up to this limitations it is possible to transform any pure DP mechanism into a time oblivious one.
Cite as

Yoav Ben Dov, Liron David, Moni Naor, and Elad Tzalik. Resistance to Timing Attacks for Sampling and Privacy Preserving Schemes. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bendov_et_al:LIPIcs.FORC.2023.11,
  author =	{Ben Dov, Yoav and David, Liron and Naor, Moni and Tzalik, Elad},
  title =	{{Resistance to Timing Attacks for Sampling and Privacy Preserving Schemes}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{11:1--11:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.11},
  URN =		{urn:nbn:de:0030-drops-179329},
  doi =		{10.4230/LIPIcs.FORC.2023.11},
  annote =	{Keywords: Differential Privacy}
}
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