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Documents authored by Shamir, Adi

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Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2021.4
Error Resilient Space Partitioning (Invited Talk)

Authors: Orr Dunkelman, Zeev Geyzel, Chaya Keller, Nathan Keller, Eyal Ronen, Adi Shamir, and Ran J. Tessler

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

Abstract
In this paper we consider a new type of space partitioning which bridges the gap between continuous and discrete spaces in an error resilient way. It is motivated by the problem of rounding noisy measurements from some continuous space such as ℝ^d to a discrete subset of representative values, in which each tile in the partition is defined as the preimage of one of the output points. Standard rounding schemes seem to be inherently discontinuous across tile boundaries, but in this paper we show how to make it perfectly consistent (with error resilience ε) by guaranteeing that any pair of consecutive measurements X₁ and X₂ whose L₂ distance is bounded by ε will be rounded to the same nearby representative point in the discrete output space. We achieve this resilience by allowing a few bits of information about the first measurement X₁ to be unidirectionally communicated to and used by the rounding process of the second measurement X₂. Minimizing this revealed information can be particularly important in privacy-sensitive applications such as COVID-19 contact tracing, in which we want to find out all the cases in which two persons were at roughly the same place at roughly the same time, by comparing cryptographically hashed versions of their itineraries in an error resilient way. The main problem we study in this paper is characterizing the achievable tradeoffs between the amount of information provided and the error resilience for various dimensions. We analyze the problem by considering the possible colored tilings of the space with k available colors, and use the color of the tile in which X₁ resides as the side information. We obtain our upper and lower bounds with a variety of techniques including isoperimetric inequalities, the Brunn-Minkowski theorem, sphere packing bounds, Sperner’s lemma, and Čech cohomology. In particular, we show that when X_i ∈ ℝ^d, communicating log₂(d+1) bits of information is both sufficient and necessary (in the worst case) to achieve positive resilience, and when d=3 we obtain a tight upper and lower asymptotic bound of (0.561 …)k^{1/3} on the achievable error resilience when we provide log₂(k) bits of information about X₁’s color.
Cite as

Orr Dunkelman, Zeev Geyzel, Chaya Keller, Nathan Keller, Eyal Ronen, Adi Shamir, and Ran J. Tessler. Error Resilient Space Partitioning (Invited Talk). In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dunkelman_et_al:LIPIcs.ICALP.2021.4,
  author =	{Dunkelman, Orr and Geyzel, Zeev and Keller, Chaya and Keller, Nathan and Ronen, Eyal and Shamir, Adi and Tessler, Ran J.},
  title =	{{Error Resilient Space Partitioning}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{4:1--4:22},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.4},
  URN =		{urn:nbn:de:0030-drops-140731},
  doi =		{10.4230/LIPIcs.ICALP.2021.4},
  annote =	{Keywords: space partition, high-dimensional rounding, error resilience, sphere packing, Sperner’s lemma, Brunn-Minkowski theorem, \v{C}ech cohomology}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.13
Tight Bounds on Online Checkpointing Algorithms

Authors: Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir

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

Abstract
The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain k memorized checkpoints during a long computation, where the only allowed operation is to move one of the checkpoints from its old time to the current time, and his goal is to keep the checkpoints as evenly spread out as possible at all times. At ICALP'13 Bringmann et al. studied this problem as a special case of an online/offline optimization problem in which the deviation from uniformity is measured by the natural discrepancy metric of the worst case ratio between real and ideal segment lengths. They showed this discrepancy is smaller than 1.59-o(1) for all k, and smaller than ln4-o(1)~~1.39 for the sparse subset of k's which are powers of 2. In addition, they obtained upper bounds on the achievable discrepancy for some small values of k. In this paper we solve the main problems left open in the ICALP'13 paper by proving that ln4 is a tight upper and lower bound on the asymptotic discrepancy for all large k, and by providing tight upper and lower bounds (in the form of provably optimal checkpointing algorithms, some of which are in fact better than those of Bringmann et al.) for all the small values of k <= 10.
Cite as

Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir. Tight Bounds on Online Checkpointing Algorithms. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baron_et_al:LIPIcs.ICALP.2018.13,
  author =	{Bar-On, Achiya and Dinur, Itai and Dunkelman, Orr and Hod, Rani and Keller, Nathan and Ronen, Eyal and Shamir, Adi},
  title =	{{Tight Bounds on Online Checkpointing Algorithms}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{13:1--13:13},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.13},
  URN =		{urn:nbn:de:0030-drops-90179},
  doi =		{10.4230/LIPIcs.ICALP.2018.13},
  annote =	{Keywords: checkpoint, checkpointing algorithm, online algorithm, uniform distribution, discrepancy}
}
Document
DOI: 10.4230/DagSemProc.09031.6
Cube Testers and Key Recovery Attacks On Reduced-Round MD6 and Trivium

Authors: Jean-Philippe Aumasson, Itai Dinur, Willi Meier, and Adi Shamir

Published in: Dagstuhl Seminar Proceedings, Volume 9031, Symmetric Cryptography (2009)

Abstract
CRYPTO 2008 saw the introduction of the hash function MD6 and of cube attacks, a type of algebraic attack applicable to cryptographic functions having a low-degree algebraic normal form over GF(2). This paper applies cube attacks to reduced round MD6, finding the full 128-bit key of a 14-round MD6 with complexity 2\^22 (which takes less than a minute on a single PC). This is the best key recovery attack announced so far for MD6. We then introduce a new class of attacks called cube testers, based on efficient property-testing algorithms, and apply them to MD6 and to the stream cipher Trivium. Unlike the standard cube attacks, cube testers detect nonrandom behavior rather than performing key extraction, but they can also attack cryptographic schemes described by nonrandom polynomials of relatively high degree. Applied to MD6, cube testers detect nonrandomness over 18 rounds in 2\^17 complexity; applied to a slightly modified version of the MD6 compression function, they can distinguish 66 rounds from random in 2\^24 complexity. Cube testers give distinguishers on Trivium reduced to 790 rounds from random with 2^30 complexity and detect nonrandomness over 885 rounds in 2\^27, improving on the original 767-round cube attack.
Cite as

Jean-Philippe Aumasson, Itai Dinur, Willi Meier, and Adi Shamir. Cube Testers and Key Recovery Attacks On Reduced-Round MD6 and Trivium. In Symmetric Cryptography. Dagstuhl Seminar Proceedings, Volume 9031, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{aumasson_et_al:DagSemProc.09031.6,
  author =	{Aumasson, Jean-Philippe and Dinur, Itai and Meier, Willi and Shamir, Adi},
  title =	{{Cube Testers and Key Recovery Attacks On Reduced-Round MD6 and Trivium}},
  booktitle =	{Symmetric Cryptography},
  pages =	{1--22},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9031},
  editor =	{Helena Handschuh and Stefan Lucks and Bart Preneel and Phillip Rogaway},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09031.6},
  URN =		{urn:nbn:de:0030-drops-19443},
  doi =		{10.4230/DagSemProc.09031.6},
  annote =	{Keywords: Cube attacks, property testing, MD6, Trivium}
}
Document
DOI: 10.4230/DagSemRep.355
Cryptography (Dagstuhl Seminar 02391)

Authors: Ueli Maurer, Adi Shamir, Jacques Stern, and Moti Yung

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Ueli Maurer, Adi Shamir, Jacques Stern, and Moti Yung. Cryptography (Dagstuhl Seminar 02391). Dagstuhl Seminar Report 355, pp. 1-21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2003)

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@TechReport{maurer_et_al:DagSemRep.355,
  author =	{Maurer, Ueli and Shamir, Adi and Stern, Jacques and Yung, Moti},
  title =	{{Cryptography (Dagstuhl Seminar 02391)}},
  pages =	{1--21},
  ISSN =	{1619-0203},
  year =	{2003},
  type = 	{Dagstuhl Seminar Report},
  number =	{355},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.355},
  URN =		{urn:nbn:de:0030-drops-152357},
  doi =		{10.4230/DagSemRep.355},
}
Document
DOI: 10.4230/DagSemRep.190
Cryptography (Dagstuhl Seminar 9739)

Authors: Andrew Odlyzko, Claus Peter Schnorr, Adi Shamir, and Jacques Stern

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Andrew Odlyzko, Claus Peter Schnorr, Adi Shamir, and Jacques Stern. Cryptography (Dagstuhl Seminar 9739). Dagstuhl Seminar Report 190, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1997)

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@TechReport{odlyzko_et_al:DagSemRep.190,
  author =	{Odlyzko, Andrew and Schnorr, Claus Peter and Shamir, Adi and Stern, Jacques},
  title =	{{Cryptography (Dagstuhl Seminar 9739)}},
  pages =	{1--15},
  ISSN =	{1619-0203},
  year =	{1997},
  type = 	{Dagstuhl Seminar Report},
  number =	{190},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.190},
  URN =		{urn:nbn:de:0030-drops-150778},
  doi =		{10.4230/DagSemRep.190},
}
Document
DOI: 10.4230/DagSemRep.74
Cryptography (Dagstuhl Seminar 9339)

Authors: Andrew M. Odlyzko, Claus P. Schnorr, and Adi Shamir

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Andrew M. Odlyzko, Claus P. Schnorr, and Adi Shamir. Cryptography (Dagstuhl Seminar 9339). Dagstuhl Seminar Report 74, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1993)

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@TechReport{odlyzko_et_al:DagSemRep.74,
  author =	{Odlyzko, Andrew M. and Schnorr, Claus P. and Shamir, Adi},
  title =	{{Cryptography (Dagstuhl Seminar 9339)}},
  pages =	{1--28},
  ISSN =	{1619-0203},
  year =	{1993},
  type = 	{Dagstuhl Seminar Report},
  number =	{74},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.74},
  URN =		{urn:nbn:de:0030-drops-149622},
  doi =		{10.4230/DagSemRep.74},
}
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