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Documents authored by Malavolta, Giulio

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.2022.2
Algebraic Restriction Codes and Their Applications

Authors: Divesh Aggarwal, Nico Döttling, Jesko Dujmovic, Mohammad Hajiabadi, Giulio Malavolta, and Maciej Obremski

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Consider the following problem: You have a device that is supposed to compute a linear combination of its inputs, which are taken from some finite field. However, the device may be faulty and compute arbitrary functions of its inputs. Is it possible to encode the inputs in such a way that only linear functions can be evaluated over the encodings? I.e., learning an arbitrary function of the encodings will not reveal more information about the inputs than a linear combination. In this work, we introduce the notion of algebraic restriction codes (AR codes), which constrain adversaries who might compute any function to computing a linear function. Our main result is an information-theoretic construction AR codes that restrict any class of function with a bounded number of output bits to linear functions. Our construction relies on a seed which is not provided to the adversary. While interesting and natural on its own, we show an application of this notion in cryptography. In particular, we show that AR codes lead to the first construction of rate-1 oblivious transfer with statistical sender security from the Decisional Diffie-Hellman assumption, and the first-ever construction that makes black-box use of cryptography. Previously, such protocols were known only from the LWE assumption, using non-black-box cryptographic techniques. We expect our new notion of AR codes to find further applications, e.g., in the context of non-malleability, in the future.
Cite as

Divesh Aggarwal, Nico Döttling, Jesko Dujmovic, Mohammad Hajiabadi, Giulio Malavolta, and Maciej Obremski. Algebraic Restriction Codes and Their Applications. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{aggarwal_et_al:LIPIcs.ITCS.2022.2,
  author =	{Aggarwal, Divesh and D\"{o}ttling, Nico and Dujmovic, Jesko and Hajiabadi, Mohammad and Malavolta, Giulio and Obremski, Maciej},
  title =	{{Algebraic Restriction Codes and Their Applications}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{2:1--2:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.2},
  URN =		{urn:nbn:de:0030-drops-155987},
  doi =		{10.4230/LIPIcs.ITCS.2022.2},
  annote =	{Keywords: Algebraic Restriction Codes, Oblivious Transfer, Rate 1, Statistically Sender Private, OT, Diffie-Hellman, DDH}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.4
Pre-Constrained Encryption

Authors: Prabhanjan Ananth, Abhishek Jain, Zhengzhong Jin, and Giulio Malavolta

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
In all existing encryption systems, the owner of the master secret key has the ability to decrypt all ciphertexts. In this work, we propose a new notion of pre-constrained encryption (PCE) where the owner of the master secret key does not have "full" decryption power. Instead, its decryption power is constrained in a pre-specified manner during the system setup. We present formal definitions and constructions of PCE, and discuss societal applications and implications to some well-studied cryptographic primitives.
Cite as

Prabhanjan Ananth, Abhishek Jain, Zhengzhong Jin, and Giulio Malavolta. Pre-Constrained Encryption. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ananth_et_al:LIPIcs.ITCS.2022.4,
  author =	{Ananth, Prabhanjan and Jain, Abhishek and Jin, Zhengzhong and Malavolta, Giulio},
  title =	{{Pre-Constrained Encryption}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.4},
  URN =		{urn:nbn:de:0030-drops-156001},
  doi =		{10.4230/LIPIcs.ITCS.2022.4},
  annote =	{Keywords: Advanced encryption systems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.15
Indistinguishability Obfuscation of Null Quantum Circuits and Applications

Authors: James Bartusek and Giulio Malavolta

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of "dual-mode" classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP.
Cite as

James Bartusek and Giulio Malavolta. Indistinguishability Obfuscation of Null Quantum Circuits and Applications. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bartusek_et_al:LIPIcs.ITCS.2022.15,
  author =	{Bartusek, James and Malavolta, Giulio},
  title =	{{Indistinguishability Obfuscation of Null Quantum Circuits and Applications}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.15},
  URN =		{urn:nbn:de:0030-drops-156115},
  doi =		{10.4230/LIPIcs.ITCS.2022.15},
  annote =	{Keywords: Obfuscation, Witness Encryption, Classical Verification of Quantum Computation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.57
Interaction-Preserving Compilers for Secure Computation

Authors: Nico Döttling, Vipul Goyal, Giulio Malavolta, and Justin Raizes

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
In this work we consider the following question: What is the cost of security for multi-party protocols? Specifically, given an insecure protocol where parties exchange (in the worst case) Γ bits in N rounds, is it possible to design a secure protocol with communication complexity close to Γ and N rounds? We systematically study this problem in a variety of settings and we propose solutions based on the intractability of different cryptographic problems. For the case of two parties we design an interaction-preserving compiler where the number of bits exchanged in the secure protocol approaches Γ and the number of rounds is exactly N, assuming the hardness of standard problems over lattices. For the more general multi-party case, we obtain the same result assuming either (i) an additional round of interaction or (ii) the existence of extractable witness encryption and succinct non-interactive arguments of knowledge. As a contribution of independent interest, we construct the first multi-key fully homomorphic encryption scheme with message-to-ciphertext ratio (i.e., rate) of 1 - o(1), assuming the hardness of the learning with errors (LWE) problem. We view our work as a support for the claim that, as far as interaction and communication are concerned, one does not need to pay a significant price for security in multi-party protocols.
Cite as

Nico Döttling, Vipul Goyal, Giulio Malavolta, and Justin Raizes. Interaction-Preserving Compilers for Secure Computation. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dottling_et_al:LIPIcs.ITCS.2022.57,
  author =	{D\"{o}ttling, Nico and Goyal, Vipul and Malavolta, Giulio and Raizes, Justin},
  title =	{{Interaction-Preserving Compilers for Secure Computation}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{57:1--57:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.57},
  URN =		{urn:nbn:de:0030-drops-156534},
  doi =		{10.4230/LIPIcs.ITCS.2022.57},
  annote =	{Keywords: Multiparty Computation, Communication Complexity, Fully Homomorphic Encryption}
}
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