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Documents authored by Pandey, Omkant

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.28
Improved Black-Box Constructions of Composable Secure Computation

Authors: Rohit Chatterjee, Xiao Liang, and Omkant Pandey

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We close the gap between black-box and non-black-box constructions of composable secure multiparty computation in the plain model under the minimal assumption of semi-honest oblivious transfer. The notion of protocol composition we target is angel-based security, or more precisely, security with super-polynomial helpers. In this notion, both the simulator and the adversary are given access to an oracle called an angel that can perform some predefined super-polynomial time task. Angel-based security maintains the attractive properties of the universal composition framework while providing meaningful security guarantees in complex environments without having to trust anyone. Angel-based security can be achieved using non-black-box constructions in max(R_OT,Õ(log n)) rounds where R_OT is the round-complexity of semi-honest oblivious transfer. However, current best known black-box constructions under the same assumption require max(R_OT,Õ(log² n)) rounds. If R_OT is a constant, the gap between non-black-box and black-box constructions can be a multiplicative factor log n. We close this gap by presenting a max(R_OT,Õ(log n)) round black-box construction. We achieve this result by constructing constant-round 1-1 CCA-secure commitments assuming only black-box access to one-way functions.
Cite as

Rohit Chatterjee, Xiao Liang, and Omkant Pandey. Improved Black-Box Constructions of Composable Secure Computation. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chatterjee_et_al:LIPIcs.ICALP.2020.28,
  author =	{Chatterjee, Rohit and Liang, Xiao and Pandey, Omkant},
  title =	{{Improved Black-Box Constructions of Composable Secure Computation}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.28},
  URN =		{urn:nbn:de:0030-drops-124351},
  doi =		{10.4230/LIPIcs.ICALP.2020.28},
  annote =	{Keywords: Secure Multi-Party Computation, Black-Box, Composable, Non-Malleable}
}
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.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}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.31
Block-Wise Non-Malleable Codes

Authors: Nishanth Chandran, Vipul Goyal, Pratyay Mukherjee, Omkant Pandey, and Jalaj Upadhyay

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

Abstract
Non-malleable codes, introduced by Dziembowski, Pietrzak, and Wichs (ICS'10) provide the guarantee that if a codeword c of a message m, is modified by a tampering function f to c', then c' either decodes to m or to "something unrelated" to m. In recent literature, a lot of focus has been on explicitly constructing such codes against a large and natural class of tampering functions such as split-state model in which the tampering function operates on different parts of the codeword independently. In this work, we consider a stronger adversarial model called block-wise tampering model, in which we allow tampering to depend on more than one block: if a codeword consists of two blocks c = (c1, c2), then the first tampering function f1 could produce a tampered part c'_1 = f1(c1) and the second tampering function f2 could produce c'_2 = f2(c1, c2) depending on both c2 and c1. The notion similarly extends to multiple blocks where tampering of block ci could happen with the knowledge of all cj for j <= i. We argue this is a natural notion where, for example, the blocks are sent one by one and the adversary must send the tampered block before it gets the next block. A little thought reveals that it is impossible to construct such codes that are non-malleable (in the standard sense) against such a powerful adversary: indeed, upon receiving the last block, an adversary could decode the entire codeword and then can tamper depending on the message. In light of this impossibility, we consider a natural relaxation called non-malleable codes with replacement which requires the adversary to produce not only related but also a valid codeword in order to succeed. Unfortunately, we show that even this relaxed definition is not achievable in the information-theoretic setting (i.e., when the tampering functions can be unbounded) which implies that we must turn our attention towards computationally bounded adversaries. As our main result, we show how to construct a block-wise non-malleable code (BNMC) from sub-exponentially hard one-way permutations. We provide an interesting connection between BNMC and non-malleable commitments. We show that any BNMC can be converted into a nonmalleable (w.r.t. opening) commitment scheme. Our techniques, quite surprisingly, give rise to a non-malleable commitment scheme (secure against so-called synchronizing adversaries), in which only the committer sends messages. We believe this result to be of independent interest. In the other direction, we show that any non-interactive non-malleable (w.r.t. opening) commitment can be used to construct BNMC only with 2 blocks. Unfortunately, such commitment scheme exists only under highly non-standard assumptions (adaptive one-way functions) and hence can not substitute our main construction.
Cite as

Nishanth Chandran, Vipul Goyal, Pratyay Mukherjee, Omkant Pandey, and Jalaj Upadhyay. Block-Wise Non-Malleable Codes. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chandran_et_al:LIPIcs.ICALP.2016.31,
  author =	{Chandran, Nishanth and Goyal, Vipul and Mukherjee, Pratyay and Pandey, Omkant and Upadhyay, Jalaj},
  title =	{{Block-Wise Non-Malleable Codes}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{31:1--31:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.31},
  URN =		{urn:nbn:de:0030-drops-63102},
  doi =		{10.4230/LIPIcs.ICALP.2016.31},
  annote =	{Keywords: Non-malleable codes, Non-malleable commitments, Block-wise Tampering, Complexity-leveraging}
}
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