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Documents authored by Sahai, Amit

Document
DOI: 10.4230/LIPIcs.ITC.2022.10
Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC

Authors: Saikrishna Badrinarayanan, Yuval Ishai, Dakshita Khurana, Amit Sahai, and Daniel Wichs

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

Abstract
We provide counterexamples to the "dream" version of Yao’s XOR Lemma. In particular, we put forward explicit candidates for hard predicates, such that the advantage of predicting the XOR of many independent copies does not decrease beyond some fixed negligible function, even as the number of copies gets arbitrarily large. We provide two such constructions: - Our first construction is in the ideal obfuscation model (alternatively, assuming virtual black-box obfuscation for a concrete class of circuits). It develops a general framework that may be of broader interest, and allows us to embed an instance of a resettably-secure multiparty computation protocol into a one-way function. Along the way, we design the first resettably-secure multiparty computation protocol for general functionalities in the plain model with super-polynomial simulation, under standard assumptions. - The second construction relies on public-coin differing-inputs obfuscation (PCdiO) along with a certain form of hash-function security called extended second-preimage resistance (ESPR). It starts with a previously known counterexample to the dream direct-product hardness amplification based on ESPR, and uses PCdiO to upgrade it into a counterexample for the XOR lemma. Prior to our work, even completely heuristic counterexamples of this type were not known.
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Saikrishna Badrinarayanan, Yuval Ishai, Dakshita Khurana, Amit Sahai, and Daniel Wichs. Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{badrinarayanan_et_al:LIPIcs.ITC.2022.10,
  author =	{Badrinarayanan, Saikrishna and Ishai, Yuval and Khurana, Dakshita and Sahai, Amit and Wichs, Daniel},
  title =	{{Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{10:1--10:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.10},
  URN =		{urn:nbn:de:0030-drops-164885},
  doi =		{10.4230/LIPIcs.ITC.2022.10},
  annote =	{Keywords: XOR Lemma, Resettable MPC, Obfuscation}
}
Document
DOI: 10.4230/LIPIcs.ITC.2020.6
Expander Graphs Are Non-Malleable Codes

Authors: Peter Michael Reichstein Rasmussen and Amit Sahai

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
Any d-regular graph on n vertices with spectral expansion λ satisfying n = Ω(d³log(d)/λ) yields a O((λ^{3/2})/d)-non-malleable code for single-bit messages in the split-state model.
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Peter Michael Reichstein Rasmussen and Amit Sahai. Expander Graphs Are Non-Malleable Codes. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 6:1-6:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{rasmussen_et_al:LIPIcs.ITC.2020.6,
  author =	{Rasmussen, Peter Michael Reichstein and Sahai, Amit},
  title =	{{Expander Graphs Are Non-Malleable Codes}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{6:1--6:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.6},
  URN =		{urn:nbn:de:0030-drops-121114},
  doi =		{10.4230/LIPIcs.ITC.2020.6},
  annote =	{Keywords: Non-Malleable Code, Expander Graph, Mixing Lemma}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.82
Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption

Authors: James Bartusek, Yuval Ishai, Aayush Jain, Fermi Ma, Amit Sahai, and Mark Zhandry

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

Abstract
An affine determinant program ADP: {0,1}^n → {0,1} is specified by a tuple (A,B_1,…,B_n) of square matrices over ?_q and a function Eval: ?_q → {0,1}, and evaluated on x ∈ {0,1}^n by computing Eval(det(A + ∑_{i∈[n]} x_i B_i)). In this work, we suggest ADPs as a new framework for building general-purpose obfuscation and witness encryption. We provide evidence to suggest that constructions following our ADP-based framework may one day yield secure, practically feasible obfuscation. As a proof-of-concept, we give a candidate ADP-based construction of indistinguishability obfuscation (i?) for all circuits along with a simple witness encryption candidate. We provide cryptanalysis demonstrating that our schemes resist several potential attacks, and leave further cryptanalysis to future work. Lastly, we explore practically feasible applications of our witness encryption candidate, such as public-key encryption with near-optimal key generation.
Cite as

James Bartusek, Yuval Ishai, Aayush Jain, Fermi Ma, Amit Sahai, and Mark Zhandry. Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 82:1-82:39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bartusek_et_al:LIPIcs.ITCS.2020.82,
  author =	{Bartusek, James and Ishai, Yuval and Jain, Aayush and Ma, Fermi and Sahai, Amit and Zhandry, Mark},
  title =	{{Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{82:1--82:39},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.82},
  URN =		{urn:nbn:de:0030-drops-117679},
  doi =		{10.4230/LIPIcs.ITCS.2020.82},
  annote =	{Keywords: Obfuscation, Witness Encryption}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.8
Hierarchical Functional Encryption

Authors: Zvika Brakerski, Nishanth Chandran, Vipul Goyal, Aayush Jain, Amit Sahai, and Gil Segev

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
Functional encryption provides fine-grained access control for encrypted data, allowing each user to learn only specific functions of the encrypted data. We study the notion of hierarchical functional encryption, which augments functional encryption with delegation capabilities, offering significantly more expressive access control. We present a generic transformation that converts any general-purpose public-key functional encryption scheme into a hierarchical one without relying on any additional assumptions. This significantly refines our understanding of the power of functional encryption, showing that the existence of functional encryption is equivalent to that of its hierarchical generalization. Instantiating our transformation with the existing functional encryption schemes yields a variety of hierarchical schemes offering various trade-offs between their delegation capabilities (i.e., the depth and width of their hierarchical structures) and underlying assumptions. When starting with a scheme secure against an unbounded number of collusions, we can support arbitrary hierarchical structures. In addition, even when starting with schemes that are secure against a bounded number of collusions (which are known to exist under rather minimal assumptions such as the existence of public-key encryption and shallow pseudorandom generators), we can support hierarchical structures of bounded depth and width.
Cite as

Zvika Brakerski, Nishanth Chandran, Vipul Goyal, Aayush Jain, Amit Sahai, and Gil Segev. Hierarchical Functional Encryption. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 8:1-8:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{brakerski_et_al:LIPIcs.ITCS.2017.8,
  author =	{Brakerski, Zvika and Chandran, Nishanth and Goyal, Vipul and Jain, Aayush and Sahai, Amit and Segev, Gil},
  title =	{{Hierarchical Functional Encryption}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{8:1--8:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.8},
  URN =		{urn:nbn:de:0030-drops-81992},
  doi =		{10.4230/LIPIcs.ITCS.2017.8},
  annote =	{Keywords: Functional Encryption, Delegatable Encryption, Cryptography}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.29
Do Distributed Differentially-Private Protocols Require Oblivious Transfer?

Authors: Vipul Goyal, Dakshita Khurana, Ilya Mironov, Omkant Pandey, and Amit Sahai

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We study the cryptographic complexity of two-party differentially-private protocols for a large natural class of boolean functionalities. Information theoretically, McGregor et al. [FOCS 2010] and Goyal et al. [Crypto 2013] demonstrated several functionalities for which the maximal possible accuracy in the distributed setting is significantly lower than that in the client-server setting. Goyal et al. [Crypto 2013] further showed that "highly accurate" protocols in the distributed setting for any non-trivial functionality in fact imply the existence of one-way functions. However, it has remained an open problem to characterize the exact cryptographic complexity of this class. In particular, we know that semi-honest oblivious transfer helps obtain optimally accurate distributed differential privacy. But we do not know whether the reverse is true. We study the following question: Does the existence of optimally accurate distributed differentially private protocols for any class of functionalities imply the existence of oblivious transfer (or equivalently secure multi-party computation)? We resolve this question in the affirmative for the class of boolean functionalities that contain an XOR embedded on adjacent inputs. We give a reduction from oblivious transfer to: - Any distributed optimally accurate epsilon-differentially private protocol with epsilon > 0 computing a functionality with a boolean XOR embedded on adjacent inputs. - Any distributed non-optimally accurate epsilon-differentially private protocol with epsilon > 0, for a constant range of non-optimal accuracies and constant range of values of epsilon, computing a functionality with a boolean XOR embedded on adjacent inputs. Enroute to proving these results, we demonstrate a connection between optimally-accurate twoparty differentially-private protocols for functions with a boolean XOR embedded on adjacent inputs, and noisy channels, which were shown by Crépeau and Kilian [FOCS 1988] to be sufficient for oblivious transfer.
Cite as

Vipul Goyal, Dakshita Khurana, Ilya Mironov, Omkant Pandey, and Amit Sahai. Do Distributed Differentially-Private Protocols Require Oblivious Transfer?. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{goyal_et_al:LIPIcs.ICALP.2016.29,
  author =	{Goyal, Vipul and Khurana, Dakshita and Mironov, Ilya and Pandey, Omkant and Sahai, Amit},
  title =	{{Do Distributed Differentially-Private Protocols Require Oblivious Transfer?}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.29},
  URN =		{urn:nbn:de:0030-drops-63080},
  doi =		{10.4230/LIPIcs.ICALP.2016.29},
  annote =	{Keywords: Oblivious Transfer, Distributed Differential Privacy, Noisy Channels, Weak Noisy Channels}
}
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