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Documents authored by Garg, Sanjam

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.28
Factoring and Pairings Are Not Necessary for IO: Circular-Secure LWE Suffices

Authors: Zvika Brakerski, Nico Döttling, Sanjam Garg, and Giulio Malavolta

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We construct indistinguishability obfuscation (iO) solely under circular-security properties of encryption schemes based on the Learning with Errors (LWE) problem. Circular-security assumptions were used before to construct (non-leveled) fully-homomorphic encryption (FHE), but our assumption is stronger and requires circular randomness-leakage-resilience. In contrast with prior works, this assumption can be conjectured to be post-quantum secure; yielding the first provably secure iO construction that is (plausibly) post-quantum secure. Our work follows the high-level outline of the recent work of Gay and Pass [STOC 2021], who showed a way to remove the heuristic step from the homomorphic-encryption based iO approach of Brakerski, Döttling, Garg, and Malavolta [EUROCRYPT 2020]. They thus obtain a construction proved secure under circular security assumption of natural homomorphic encryption schemes - specifically, they use homomorphic encryption schemes based on LWE and DCR, respectively. In this work we show how to remove the DCR assumption and remain with a scheme based on the circular security of LWE alone. Along the way we relax some of the requirements in the Gay-Pass blueprint and thus obtain a scheme that is secure under a different assumption. Specifically, we do not require security in the presence of a key-cycle, but rather only in the presence of a key-randomness cycle. An additional contribution of our work is to point out a problem in one of the building blocks used by many iO candidates, including all existing provable post-quantum candidates. Namely, in the transformation from exponentially-efficient iO (XiO) from Lin, Pass, Seth and Telang [PKC 2016]. We show why their transformation inherently falls short of achieving the desired goal, and then rectify this situation by showing that shallow XiO (i.e. one where the obfuscator is depth-bounded) does translate to iO using LWE.
Cite as

Zvika Brakerski, Nico Döttling, Sanjam Garg, and Giulio Malavolta. Factoring and Pairings Are Not Necessary for IO: Circular-Secure LWE Suffices. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{brakerski_et_al:LIPIcs.ICALP.2022.28,
  author =	{Brakerski, Zvika and D\"{o}ttling, Nico and Garg, Sanjam and Malavolta, Giulio},
  title =	{{Factoring and Pairings Are Not Necessary for IO: Circular-Secure LWE Suffices}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.28},
  URN =		{urn:nbn:de:0030-drops-163699},
  doi =		{10.4230/LIPIcs.ICALP.2022.28},
  annote =	{Keywords: Cryptography, Obfuscation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.40
Ad Hoc Multi-Input Functional Encryption

Authors: Shweta Agrawal, Michael Clear, Ophir Frieder, Sanjam Garg, Adam O'Neill, and Justin Thaler

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

Abstract
Consider sources that supply sensitive data to an aggregator. Standard encryption only hides the data from eavesdroppers, but using specialized encryption one can hope to hide the data (to the extent possible) from the aggregator itself. For flexibility and security, we envision schemes that allow sources to supply encrypted data, such that at any point a dynamically-chosen subset of sources can allow an agreed-upon joint function of their data to be computed by the aggregator. A primitive called multi-input functional encryption (MIFE), due to Goldwasser et al. (EUROCRYPT 2014), comes close, but has two main limitations: - it requires trust in a third party, who is able to decrypt all the data, and - it requires function arity to be fixed at setup time and to be equal to the number of parties. To drop these limitations, we introduce a new notion of ad hoc MIFE. In our setting, each source generates its own public key and issues individual, function-specific secret keys to an aggregator. For successful decryption, an aggregator must obtain a separate key from each source whose ciphertext is being computed upon. The aggregator could obtain multiple such secret-keys from a user corresponding to functions of varying arity. For this primitive, we obtain the following results: - We show that standard MIFE for general functions can be bootstrapped to ad hoc MIFE for free, i.e. without making any additional assumption. - We provide a direct construction of ad hoc MIFE for the inner product functionality based on the Learning with Errors (LWE) assumption. This yields the first construction of this natural primitive based on a standard assumption. At a technical level, our results are obtained by combining standard MIFE schemes and two-round secure multiparty computation (MPC) protocols in novel ways highlighting an interesting interplay between MIFE and two-round MPC.
Cite as

Shweta Agrawal, Michael Clear, Ophir Frieder, Sanjam Garg, Adam O'Neill, and Justin Thaler. Ad Hoc Multi-Input Functional Encryption. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 40:1-40:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agrawal_et_al:LIPIcs.ITCS.2020.40,
  author =	{Agrawal, Shweta and Clear, Michael and Frieder, Ophir and Garg, Sanjam and O'Neill, Adam and Thaler, Justin},
  title =	{{Ad Hoc Multi-Input Functional Encryption}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{40:1--40:41},
  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.2020.40},
  URN =		{urn:nbn:de:0030-drops-117258},
  doi =		{10.4230/LIPIcs.ITCS.2020.40},
  annote =	{Keywords: Multi-Input Functional Encryption}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.71
Separating Two-Round Secure Computation From Oblivious Transfer

Authors: Benny Applebaum, Zvika Brakerski, Sanjam Garg, Yuval Ishai, and Akshayaram Srinivasan

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

Abstract
We consider the question of minimizing the round complexity of protocols for secure multiparty computation (MPC) with security against an arbitrary number of semi-honest parties. Very recently, Garg and Srinivasan (Eurocrypt 2018) and Benhamouda and Lin (Eurocrypt 2018) constructed such 2-round MPC protocols from minimal assumptions. This was done by showing a round preserving reduction to the task of secure 2-party computation of the oblivious transfer functionality (OT). These constructions made a novel non-black-box use of the underlying OT protocol. The question remained whether this can be done by only making black-box use of 2-round OT. This is of theoretical and potentially also practical value as black-box use of primitives tends to lead to more efficient constructions. Our main result proves that such a black-box construction is impossible, namely that non-black-box use of OT is necessary. As a corollary, a similar separation holds when starting with any 2-party functionality other than OT. As a secondary contribution, we prove several additional results that further clarify the landscape of black-box MPC with minimal interaction. In particular, we complement the separation from 2-party functionalities by presenting a complete 4-party functionality, give evidence for the difficulty of ruling out a complete 3-party functionality and for the difficulty of ruling out black-box constructions of 3-round MPC from 2-round OT, and separate a relaxed "non-compact" variant of 2-party homomorphic secret sharing from 2-round OT.
Cite as

Benny Applebaum, Zvika Brakerski, Sanjam Garg, Yuval Ishai, and Akshayaram Srinivasan. Separating Two-Round Secure Computation From Oblivious Transfer. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 71:1-71:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{applebaum_et_al:LIPIcs.ITCS.2020.71,
  author =	{Applebaum, Benny and Brakerski, Zvika and Garg, Sanjam and Ishai, Yuval and Srinivasan, Akshayaram},
  title =	{{Separating Two-Round Secure Computation From Oblivious Transfer}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{71:1--71:18},
  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.2020.71},
  URN =		{urn:nbn:de:0030-drops-117560},
  doi =		{10.4230/LIPIcs.ITCS.2020.71},
  annote =	{Keywords: Oracle Separation, Oblivious Transfer, Secure Multiparty Computation}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.38
Cryptanalysis of Indistinguishability Obfuscations of Circuits over GGH13

Authors: Daniel Apon, Nico Döttling, Sanjam Garg, and Pratyay Mukherjee

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

Abstract
Annihilation attacks, introduced in the work of Miles, Sahai, and Zhandry (CRYPTO 2016), are a class of polynomial-time attacks against several candidate indistinguishability obfuscation (IO) schemes, built from Garg, Gentry, and Halevi (EUROCRYPT 2013) multilinear maps. In this work, we provide a general efficiently-testable property for two single-input branching programs, called partial inequivalence, which we show is sufficient for our variant of annihilation attacks on several obfuscation constructions based on GGH13 multilinear maps. We give examples of pairs of natural NC1 circuits, which - when processed via Barrington's Theorem - yield pairs of branching programs that are partially inequivalent. As a consequence we are also able to show examples of "bootstrapping circuits,'' (albeit somewhat artificially crafted) used to obtain obfuscations for all circuits (given an obfuscator for NC1 circuits), in certain settings also yield partially inequivalent branching programs. Prior to our work, no attacks on any obfuscation constructions for these settings were known.
Cite as

Daniel Apon, Nico Döttling, Sanjam Garg, and Pratyay Mukherjee. Cryptanalysis of Indistinguishability Obfuscations of Circuits over GGH13. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{apon_et_al:LIPIcs.ICALP.2017.38,
  author =	{Apon, Daniel and D\"{o}ttling, Nico and Garg, Sanjam and Mukherjee, Pratyay},
  title =	{{Cryptanalysis of Indistinguishability Obfuscations of Circuits over GGH13}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{38:1--38:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.38},
  URN =		{urn:nbn:de:0030-drops-73814},
  doi =		{10.4230/LIPIcs.ICALP.2017.38},
  annote =	{Keywords: Obfuscation, Multilinear Maps, Cryptanalysis.}
}
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