2 Search Results for "Lin, Huijia"

Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2021.4
Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk)

Authors: Huijia (Rachel) Lin

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
Indistinguishability obfuscation, introduced by Barak et al. [Crypto 2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from the subexponential hardness of three well-founded assumptions. We prove the following. Theorem (Informal) Assume sub-exponential hardness for the following: - the Learning Parity with Noise (LPN) assumption over general prime fields 𝔽_p with polynomially many LPN samples and error rate 1/k^δ, where k is the dimension of the LPN secret, and δ > 0 is any constant; - the existence of a Boolean Pseudo-Random Generator (PRG) in NC⁰ with stretch n^(1+τ), where n is the length of the PRG seed, and τ > 0 is any constant; - the Decision Linear (DLIN) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exist. As a corollary, all cryptographic goals that can be achieved using indistinguishability obfuscation can now be achieved assuming the above three assumptions. This includes fully homomorphic encryption, functional encryption, multiparty non-interactive key-exchange, succinct garbled random access machine, and many others. This is joint work with Aayush Jain (UCLA and NTT Research) and Amit Sahai (UCLA).
Cite as

Huijia (Rachel) Lin. Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lin:LIPIcs.FSTTCS.2021.4,
  author =	{Lin, Huijia (Rachel)},
  title =	{{Indistinguishability Obfuscation from Well-Founded Assumptions}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.4},
  URN =		{urn:nbn:de:0030-drops-155154},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.4},
  annote =	{Keywords: Cryptography, indistinguishability obfuscation}
}
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-dev.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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