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Documents authored by Dachman-Soled, Dana

Document
DOI: 10.4230/LIPIcs.ITC.2024.8
Breaking RSA Generically Is Equivalent to Factoring, with Preprocessing

Authors: Dana Dachman-Soled, Julian Loss, and Adam O'Neill

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

Abstract
We investigate the relationship between the classical RSA and factoring problems when preprocessing is considered. In such a model, adversaries can use an unbounded amount of precomputation to produce an "advice" string to then use during the online phase, when a problem instance becomes known. Previous work (e.g., [Bernstein, Lange ASIACRYPT '13]) has shown that preprocessing attacks significantly improve the runtime of the best-known factoring algorithms. Due to these improvements, we ask whether the relationship between factoring and RSA fundamentally changes when preprocessing is allowed. Specifically, we investigate whether there is a superpolynomial gap between the runtime of the best attack on RSA with preprocessing and on factoring with preprocessing. Our main result rules this out with respect to algorithms that perform generic computation on the RSA instance x^e od N yet arbitrary computation on the modulus N, namely a careful adaptation of the well-known generic ring model of Aggarwal and Maurer (Eurocrypt 2009) to the preprocessing setting. In particular, in this setting we show the existence of a factoring algorithm with polynomially related parameters, for any setting of RSA parameters. Our main technical contribution is a set of new information-theoretic techniques that allow us to handle or eliminate cases in which the Aggarwal and Maurer result does not yield a factoring algorithm in the standard model with parameters that are polynomially related to those of the RSA algorithm. These techniques include two novel compression arguments, and a variant of the Fiat-Naor/Hellman tables construction that is tailored to the factoring setting.
Cite as

Dana Dachman-Soled, Julian Loss, and Adam O'Neill. Breaking RSA Generically Is Equivalent to Factoring, with Preprocessing. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dachmansoled_et_al:LIPIcs.ITC.2024.8,
  author =	{Dachman-Soled, Dana and Loss, Julian and O'Neill, Adam},
  title =	{{Breaking RSA Generically Is Equivalent to Factoring, with Preprocessing}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{8:1--8:24},
  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.2024.8},
  URN =		{urn:nbn:de:0030-drops-205163},
  doi =		{10.4230/LIPIcs.ITC.2024.8},
  annote =	{Keywords: RSA, factoring, generic ring model, preprocessing}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ITC.2022
LIPIcs, Volume 230, ITC 2022, Complete Volume

Authors: Dana Dachman-Soled

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

Abstract
LIPIcs, Volume 230, ITC 2022, Complete Volume
Cite as

3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 1-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{dachmansoled:LIPIcs.ITC.2022,
  title =	{{LIPIcs, Volume 230, ITC 2022, Complete Volume}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{1--328},
  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},
  URN =		{urn:nbn:de:0030-drops-164775},
  doi =		{10.4230/LIPIcs.ITC.2022},
  annote =	{Keywords: LIPIcs, Volume 230, ITC 2022, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ITC.2022.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Dana Dachman-Soled

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dachmansoled:LIPIcs.ITC.2022.0,
  author =	{Dachman-Soled, Dana},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{0:i--0:xii},
  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.2022.0},
  URN =		{urn:nbn:de:0030-drops-164780},
  doi =		{10.4230/LIPIcs.ITC.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.80
Limits to Non-Malleability

Authors: Marshall Ball, Dana Dachman-Soled, Mukul Kulkarni, and Tal Malkin

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
There have been many successes in constructing explicit non-malleable codes for various classes of tampering functions in recent years, and strong existential results are also known. In this work we ask the following question: When can we rule out the existence of a non-malleable code for a tampering class ℱ? First, we start with some classes where positive results are well-known, and show that when these classes are extended in a natural way, non-malleable codes are no longer possible. Specifically, we show that no non-malleable codes exist for any of the following tampering classes: - Functions that change d/2 symbols, where d is the distance of the code; - Functions where each input symbol affects only a single output symbol; - Functions where each of the n output bits is a function of n-log n input bits. Furthermore, we rule out constructions of non-malleable codes for certain classes ℱ via reductions to the assumption that a distributional problem is hard for ℱ, that make black-box use of the tampering functions in the proof. In particular, this yields concrete obstacles for the construction of efficient codes for NC, even assuming average-case variants of P ⊈ NC.
Cite as

Marshall Ball, Dana Dachman-Soled, Mukul Kulkarni, and Tal Malkin. Limits to Non-Malleability. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 80:1-80:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ball_et_al:LIPIcs.ITCS.2020.80,
  author =	{Ball, Marshall and Dachman-Soled, Dana and Kulkarni, Mukul and Malkin, Tal},
  title =	{{Limits to Non-Malleability}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{80:1--80:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.80},
  URN =		{urn:nbn:de:0030-drops-117657},
  doi =		{10.4230/LIPIcs.ITCS.2020.80},
  annote =	{Keywords: non-malleable codes, black-box impossibility, tamper-resilient cryptogtaphy, average-case hardness}
}
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