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Documents authored by Tessaro, Stefano

Document
DOI: 10.4230/LIPIcs.ITC.2022.9
On Seedless PRNGs and Premature Next

Authors: Sandro Coretti, Yevgeniy Dodis, Harish Karthikeyan, Noah Stephens-Davidowitz, and Stefano Tessaro

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

Abstract
Pseudorandom number generators with input (PRNGs) are cryptographic algorithms that generate pseudorandom bits from accumulated entropic inputs (e.g., keystrokes, interrupt timings, etc.). This paper studies in particular PRNGs that are secure against premature next attacks (Kelsey et al., FSE '98), a class of attacks leveraging the fact that a PRNG may produce an output (which could be seen by an adversary!) before enough entropy has been accumulated. Practical designs adopt either unsound entropy-estimation methods to prevent such attacks (as in Linux’s /dev/random) or sophisticated pool-based approaches as in Yarrow (MacOS/FreeBSD) and Fortuna (Windows). The only prior theoretical study of premature next attacks (Dodis et al., Algorithmica '17) considers either a seeded setting or assumes constant entropy rate, and thus falls short of providing and validating practical designs. Assuming the availability of random seed is particularly problematic, first because this requires us to somehow generate a random seed without using our PRNG, but also because we must ensure that the entropy inputs to the PRNG remain independent of the seed. Indeed, all practical designs are seedless. However, prior works on seedless PRNGs (Coretti et al., CRYPTO '19; Dodis et al., ITC '21, CRYPTO'21) do not consider premature next attacks. The main goal of this paper is to investigate the feasibility of theoretically sound seedless PRNGs that are secure against premature next attacks. To this end, we make the following contributions: 1) We prove that it is impossible to achieve seedless PRNGs that are secure against premature-next attacks, even in a rather weak model. Namely, the impossibility holds even when the entropic inputs to the PRNG are independent. In particular, our impossibility result holds in settings where seedless PRNGs are otherwise possible. 2) Given the above impossibility result, we investigate whether existing seedless pool-based approaches meant to overcome premature next attacks in practical designs provide meaningful guarantees in certain settings. Specifically, we show the following. 3) We introduce a natural condition on the entropic input and prove that it implies security of the round-robin entropy accumulation PRNG used by Windows 10, called Fortuna. Intuitively, our condition requires the input entropy "not to vary too wildly" within a given round-robin round. 4) We prove that the "root pool" approach (also used in Windows 10) is secure for general entropy inputs, provided that the system’s state is not compromised after system startup.
Cite as

Sandro Coretti, Yevgeniy Dodis, Harish Karthikeyan, Noah Stephens-Davidowitz, and Stefano Tessaro. On Seedless PRNGs and Premature Next. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{coretti_et_al:LIPIcs.ITC.2022.9,
  author =	{Coretti, Sandro and Dodis, Yevgeniy and Karthikeyan, Harish and Stephens-Davidowitz, Noah and Tessaro, Stefano},
  title =	{{On Seedless PRNGs and Premature Next}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{9:1--9:20},
  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.2022.9},
  URN =		{urn:nbn:de:0030-drops-164870},
  doi =		{10.4230/LIPIcs.ITC.2022.9},
  annote =	{Keywords: seedless PRNGs, pseudorandom number generators, PRNG, Fortuna, premature next}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ITC.2021
LIPIcs, Volume 199, ITC 2021, Complete Volume

Authors: Stefano Tessaro

Published in: LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021)

Abstract
LIPIcs, Volume 199, ITC 2021, Complete Volume
Cite as

2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 1-590, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{tessaro:LIPIcs.ITC.2021,
  title =	{{LIPIcs, Volume 199, ITC 2021, Complete Volume}},
  booktitle =	{2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
  pages =	{1--590},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-197-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{199},
  editor =	{Tessaro, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021},
  URN =		{urn:nbn:de:0030-drops-143187},
  doi =		{10.4230/LIPIcs.ITC.2021},
  annote =	{Keywords: LIPIcs, Volume 199, ITC 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ITC.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Stefano Tessaro

Published in: LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021)

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

2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{tessaro:LIPIcs.ITC.2021.0,
  author =	{Tessaro, Stefano},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-197-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{199},
  editor =	{Tessaro, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.0},
  URN =		{urn:nbn:de:0030-drops-143195},
  doi =		{10.4230/LIPIcs.ITC.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.21
Foundations of Homomorphic Secret Sharing

Authors: Elette Boyle, Niv Gilboa, Yuval Ishai, Huijia Lin, and Stefano Tessaro

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
Homomorphic secret sharing (HSS) is the secret sharing analogue of homomorphic encryption. An HSS scheme supports a local evaluation of functions on shares of one or more secret inputs, such that the resulting shares of the output are short. Some applications require the stronger notion of additive HSS, where the shares of the output add up to the output over some finite Abelian group. While some strong positive results for HSS are known under specific cryptographic assumptions, many natural questions remain open. We initiate a systematic study of HSS, making the following contributions. - A definitional framework. We present a general framework for defining HSS schemes that unifies and extends several previous notions from the literature, and cast known results within this framework. - Limitations. We establish limitations on information-theoretic multi-input HSS with short output shares via a relation with communication complexity. We also show that additive HSS for non-trivial functions, even the AND of two input bits, implies non-interactive key exchange, and is therefore unlikely to be implied by public-key encryption or even oblivious transfer. - Applications. We present two types of applications of HSS. First, we construct 2-round protocols for secure multiparty computation from a simple constant-size instance of HSS. As a corollary, we obtain 2-round protocols with attractive asymptotic efficiency features under the Decision Diffie Hellman (DDH) assumption. Second, we use HSS to obtain nearly optimal worst-case to average-case reductions in P. This in turn has applications to fine-grained average-case hardness and verifiable computation.
Cite as

Elette Boyle, Niv Gilboa, Yuval Ishai, Huijia Lin, and Stefano Tessaro. Foundations of Homomorphic Secret Sharing. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{boyle_et_al:LIPIcs.ITCS.2018.21,
  author =	{Boyle, Elette and Gilboa, Niv and Ishai, Yuval and Lin, Huijia and Tessaro, Stefano},
  title =	{{Foundations of Homomorphic Secret Sharing}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{21:1--21:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.21},
  URN =		{urn:nbn:de:0030-drops-83659},
  doi =		{10.4230/LIPIcs.ITCS.2018.21},
  annote =	{Keywords: Cryptography, homomorphic secret sharing, secure computation, communication complexity, worst-case to average case reductions.}
}
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