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Documents authored by Bitansky, Nir

Document
DOI: 10.4230/LIPIcs.ITCS.2023.17
Bootstrapping Homomorphic Encryption via Functional Encryption

Authors: Nir Bitansky and Tomer Solomon

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Homomorphic encryption is a central object in modern cryptography, with far-reaching applications. Constructions supporting homomorphic evaluation of arbitrary Boolean circuits have been known for over a decade, based on standard lattice assumptions. However, these constructions are leveled, meaning that they only support circuits up to some a-priori bounded depth. These leveled constructions can be bootstrapped into fully homomorphic ones, but this requires additional circular security assumptions, which are construction-dependent, and where reductions to standard lattice assumptions are no longer known. Alternative constructions are known based on indistinguishability obfuscation, which has been recently constructed under standard assumptions. However, this alternative requires subexponential hardness of the underlying primitives. We prove a new bootstrapping theorem based on functional encryption, which is known based on standard polynomial hardness assumptions. As a result we obtain the first fully homomorphic encryption scheme that avoids both circular security assumptions and super-polynomial hardness assumptions. The construction is secure against uniform adversaries, and can be made non-uniformly secure assuming a generalization of the time-hierarchy theorem, which follows for example from non-uniform ETH. At the heart of the construction is a new proof technique based on cryptographic puzzles and decomposable obfuscation. Unlike most cryptographic reductions, our security reduction does not fully treat the adversary as a black box, but rather makes explicit use of its running time (or circuit size).
Cite as

Nir Bitansky and Tomer Solomon. Bootstrapping Homomorphic Encryption via Functional Encryption. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 17:1-17:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bitansky_et_al:LIPIcs.ITCS.2023.17,
  author =	{Bitansky, Nir and Solomon, Tomer},
  title =	{{Bootstrapping Homomorphic Encryption via Functional Encryption}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{17:1--17:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.17},
  URN =		{urn:nbn:de:0030-drops-175200},
  doi =		{10.4230/LIPIcs.ITCS.2023.17},
  annote =	{Keywords: Fully Homomorphic Encryption, Polynomial Assumptions, Cryptographic Puzzles}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.6
On the Cryptographic Hardness of Local Search

Authors: Nir Bitansky and Idan Gerichter

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

Abstract
We show new hardness results for the class of Polynomial Local Search problems (PLS): - Hardness of PLS based on a falsifiable assumption on bilinear groups introduced by Kalai, Paneth, and Yang (STOC 2019), and the Exponential Time Hypothesis for randomized algorithms. Previous standard model constructions relied on non-falsifiable and non-standard assumptions. - Hardness of PLS relative to random oracles. The construction is essentially different than previous constructions, and in particular is unconditionally secure. The construction also demonstrates the hardness of parallelizing local search. The core observation behind the results is that the unique proofs property of incrementally-verifiable computations previously used to demonstrate hardness in PLS can be traded with a simple incremental completeness property.
Cite as

Nir Bitansky and Idan Gerichter. On the Cryptographic Hardness of Local Search. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 6:1-6:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bitansky_et_al:LIPIcs.ITCS.2020.6,
  author =	{Bitansky, Nir and Gerichter, Idan},
  title =	{{On the Cryptographic Hardness of Local Search}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{6:1--6:29},
  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.2020.6},
  URN =		{urn:nbn:de:0030-drops-116918},
  doi =		{10.4230/LIPIcs.ITCS.2020.6},
  annote =	{Keywords: Cryptography, PLS, Lower Bounds, Incremental Computation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.30
On Oblivious Amplification of Coin-Tossing Protocols

Authors: Nir Bitansky and Nathan Geier

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

Abstract
We consider the problem of amplifying two-party coin-tossing protocols: given a protocol where it is possible to bias the common output by at most ρ, we aim to obtain a new protocol where the output can be biased by at most ρ* < ρ. We rule out the existence of a natural type of amplifiers called oblivious amplifiers for every ρ* < ρ. Such amplifiers ignore the way that the underlying ρ-bias protocol works and can only invoke an oracle that provides ρ-bias bits. We provide two proofs of this impossibility. The first is by a reduction to the impossibility of deterministic randomness extraction from Santha-Vazirani sources. The second is a direct proof that is more general and also rules outs certain types of asymmetric amplification. In addition, it gives yet another proof for the Santha-Vazirani impossibility.
Cite as

Nir Bitansky and Nathan Geier. On Oblivious Amplification of Coin-Tossing Protocols. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 30:1-30:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bitansky_et_al:LIPIcs.ITCS.2020.30,
  author =	{Bitansky, Nir and Geier, Nathan},
  title =	{{On Oblivious Amplification of Coin-Tossing Protocols}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{30:1--30:13},
  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.2020.30},
  URN =		{urn:nbn:de:0030-drops-117150},
  doi =		{10.4230/LIPIcs.ITCS.2020.30},
  annote =	{Keywords: Coin Tossing, Amplification, Lower Bound, Santha Vazirani}
}
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