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Documents authored by Prabhakaran, Manoj M.

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Prabhakaran, Manoj M.

Document
DOI: 10.4230/LIPIcs.ICALP.2016.88
Rényi Information Complexity and an Information Theoretic Characterization of the Partition Bound

Authors: Manoj M. Prabhakaran and Vinod M. Prabhakaran

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

Abstract
In this work we introduce a new information-theoretic complexity measure for 2-party functions, called Rényi information complexity. It is a lower-bound on communication complexity, and has the two leading lower-bounds on communication complexity as its natural relaxations: (external) information complexity and logarithm of partition complexity. These two lower-bounds had so far appeared conceptually quite different from each other, but we show that they are both obtained from Rényi information complexity using two different, but natural relaxations: 1. The relaxation of Rényi information complexity that yields information complexity is to change the order of Rényi mutual information used in its definition from infinity to 1. 2. The relaxation that connects Rényi information complexity with partition complexity is to replace protocol transcripts used in the definition of Rényi information complexity with what we term "pseudotranscripts", which omits the interactive nature of a protocol, but only requires that the probability of any transcript given inputs x and y to the two parties, factorizes into two terms which depend on x and y separately. While this relaxation yields an apparently different definition than (log of) partition function, we show that the two are in fact identical. This gives us a surprising characterization of the partition bound in terms of an information-theoretic quantity. We also show that if both the above relaxations are simultaneously applied to Rényi information complexity, we obtain a complexity measure that is lower-bounded by the (log of) relaxed partition complexity, a complexity measure introduced by Kerenidis et al. (FOCS 2012). We obtain a sharper connection between (external) information complexity and relaxed partition complexity than Kerenidis et al., using an arguably more direct proof. Further understanding Rényi information complexity (of various orders) might have consequences for important direct-sum problems in communication complexity, as it lies between communication complexity and information complexity.
Cite as

Manoj M. Prabhakaran and Vinod M. Prabhakaran. Rényi Information Complexity and an Information Theoretic Characterization of the Partition Bound. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 88:1-88:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{prabhakaran_et_al:LIPIcs.ICALP.2016.88,
  author =	{Prabhakaran, Manoj M. and Prabhakaran, Vinod M.},
  title =	{{R\'{e}nyi Information Complexity and an Information Theoretic Characterization of the Partition Bound}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{88:1--88:14},
  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.2016.88},
  URN =		{urn:nbn:de:0030-drops-61970},
  doi =		{10.4230/LIPIcs.ICALP.2016.88},
  annote =	{Keywords: Information Complexity, Communication Complexity, R\'{e}nyi Mutual Information}
}

Prabhakaran, Manoj

Document
DOI: 10.4230/LIPIcs.ITC.2024.2
Communication Complexity vs Randomness Complexity in Interactive Proofs

Authors: Benny Applebaum, Kaartik Bhushan, and Manoj Prabhakaran

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract
In this work, we study the interplay between the communication from a verifier in a general private-coin interactive protocol and the number of random bits it uses in the protocol. Under worst-case derandomization assumptions, we show that it is possible to transform any I-round interactive protocol that uses ρ random bits into another one for the same problem with the additional property that the verifier’s communication is bounded by O(I⋅ ρ). Importantly, this is done with a minor, logarithmic, increase in the communication from the prover to the verifier and while preserving the randomness complexity. Along the way, we introduce a new compression game between computationally-bounded compressor and computationally-unbounded decompressor and a new notion of conditioned efficient distributions that may be of independent interest. Our solutions are based on a combination of perfect hashing and pseudorandom generators.
Cite as

Benny Applebaum, Kaartik Bhushan, and Manoj Prabhakaran. Communication Complexity vs Randomness Complexity in Interactive Proofs. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{applebaum_et_al:LIPIcs.ITC.2024.2,
  author =	{Applebaum, Benny and Bhushan, Kaartik and Prabhakaran, Manoj},
  title =	{{Communication Complexity vs Randomness Complexity in Interactive Proofs}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{2:1--2:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.2},
  URN =		{urn:nbn:de:0030-drops-205103},
  doi =		{10.4230/LIPIcs.ITC.2024.2},
  annote =	{Keywords: Interactive Proof Systems, Communication Complexity, Hash Functions, Pseudo-Random Generators, Compression}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.14
Homomorphic Indistinguishability Obfuscation and Its Applications

Authors: Kaartik Bhushan, Venkata Koppula, and Manoj Prabhakaran

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
In this work, we propose the notion of homomorphic indistinguishability obfuscation (HiO) and present a construction based on subexponentially-secure iO and one-way functions. An HiO scheme allows us to convert an obfuscation of circuit C to an obfuscation of C'∘C, and this can be performed obliviously (that is, without knowing the circuit C). A naïve solution would be to obfuscate C'∘iO(C). However, if we do this for k hops, then the size of the final obfuscation is exponential in k. HiO ensures that the size of the final obfuscation remains polynomial after repeated compositions. As an application, we show how to build function-hiding hierarchical multi-input functional encryption and homomorphic witness encryption using HiO.
Cite as

Kaartik Bhushan, Venkata Koppula, and Manoj Prabhakaran. Homomorphic Indistinguishability Obfuscation and Its Applications. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhushan_et_al:LIPIcs.ITCS.2024.14,
  author =	{Bhushan, Kaartik and Koppula, Venkata and Prabhakaran, Manoj},
  title =	{{Homomorphic Indistinguishability Obfuscation and Its Applications}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.14},
  URN =		{urn:nbn:de:0030-drops-195429},
  doi =		{10.4230/LIPIcs.ITCS.2024.14},
  annote =	{Keywords: Program Obfuscation, Homomorphisms}
}
Document
DOI: 10.4230/LIPIcs.ITC.2021.1
Group Structure in Correlations and Its Applications in Cryptography

Authors: Guru-Vamsi Policharla, Manoj Prabhakaran, Rajeev Raghunath, and Parjanya Vyas

Published in: LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021)

Abstract
Correlated random variables are a key tool in cryptographic applications like secure multi-party computation. We investigate the power of a class of correlations that we term group correlations: A group correlation is a uniform distribution over pairs (x,y) ∈ G² such that x+y ∈ S, where G is a (possibly non-abelian) group and S is a subset of G. We also introduce bi-affine correlation{s}, and show how they relate to group correlations. We present several structural results, new protocols and applications of these correlations. The new applications include a completeness result for black box group computation, perfectly secure protocols for evaluating a broad class of black box "mixed-groups" circuits with bi-affine homomorphisms, and new information-theoretic results. Finally, we uncover a striking structure underlying OLE: In particular, we show that OLE over 𝔽_{2ⁿ}, is isomorphic to a group correlation over ℤ_4^n.
Cite as

Guru-Vamsi Policharla, Manoj Prabhakaran, Rajeev Raghunath, and Parjanya Vyas. Group Structure in Correlations and Its Applications in Cryptography. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{policharla_et_al:LIPIcs.ITC.2021.1,
  author =	{Policharla, Guru-Vamsi and Prabhakaran, Manoj and Raghunath, Rajeev and Vyas, Parjanya},
  title =	{{Group Structure in Correlations and Its Applications in Cryptography}},
  booktitle =	{2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
  pages =	{1:1--1:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-197-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{199},
  editor =	{Tessaro, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.1},
  URN =		{urn:nbn:de:0030-drops-143208},
  doi =		{10.4230/LIPIcs.ITC.2021.1},
  annote =	{Keywords: Group correlations, bi-affine correlations, secure computation}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.24
The Bottleneck Complexity of Secure Multiparty Computation

Authors: Elette Boyle, Abhishek Jain, Manoj Prabhakaran, and Ching-Hua Yu

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
In this work, we initiate the study of bottleneck complexity as a new communication efficiency measure for secure multiparty computation (MPC). Roughly, the bottleneck complexity of an MPC protocol is defined as the maximum communication complexity required by any party within the protocol execution. We observe that even without security, bottleneck communication complexity is an interesting measure of communication complexity for (distributed) functions and propose it as a fundamental area to explore. While achieving O(n) bottleneck complexity (where n is the number of parties) is straightforward, we show that: (1) achieving sublinear bottleneck complexity is not always possible, even when no security is required. (2) On the other hand, several useful classes of functions do have o(n) bottleneck complexity, when no security is required. Our main positive result is a compiler that transforms any (possibly insecure) efficient protocol with fixed communication-pattern for computing any functionality into a secure MPC protocol while preserving the bottleneck complexity of the underlying protocol (up to security parameter overhead). Given our compiler, an efficient protocol for any function f with sublinear bottleneck complexity can be transformed into an MPC protocol for f with the same bottleneck complexity. Along the way, we build cryptographic primitives - incremental fully-homomorphic encryption, succinct non-interactive arguments of knowledge with ID-based simulation-extractability property and verifiable protocol execution - that may be of independent interest.
Cite as

Elette Boyle, Abhishek Jain, Manoj Prabhakaran, and Ching-Hua Yu. The Bottleneck Complexity of Secure Multiparty Computation. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{boyle_et_al:LIPIcs.ICALP.2018.24,
  author =	{Boyle, Elette and Jain, Abhishek and Prabhakaran, Manoj and Yu, Ching-Hua},
  title =	{{The Bottleneck Complexity of Secure Multiparty Computation}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.24},
  URN =		{urn:nbn:de:0030-drops-90288},
  doi =		{10.4230/LIPIcs.ICALP.2018.24},
  annote =	{Keywords: distributed protocols, secure computation, communication complexity}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.ICALP.2018.103
Brief Announcement: On Secure m-Party Computation, Commuting Permutation Systems and Unassisted Non-Interactive MPC

Authors: Navneet Agarwal, Sanat Anand, and Manoj Prabhakaran

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
A fundamental problem in the theory of secure multi-party computation (MPC) is to characterize functions with more than 2 parties which admit MPC protocols with information-theoretic security against passive corruption. This question has seen little progress since the work of Chor and Ishai (2001), which demonstrated difficulties in resolving it. In this work, we make significant progress towards resolving this question in the important case of aggregating functionalities, in which m parties P1,...,Pm hold inputs x1,...,xm and an aggregating party P0 must learn f(x1,...,xm). We give a necessary condition and a slightly stronger sufficient condition for f to admit a secure protocol. Both the conditions are stated in terms of an algebraic structure we introduce called Commuting Permutations Systems (CPS), which may be of independent combinatorial interest. When our sufficiency condition is met, we obtain a perfectly secure protocol with minimal interaction, that fits the model of Non-Interactive MPC or NIMPC (Beimel et al., 2014), but without the need for a trusted party to generate correlated randomness. We define Unassisted Non-Interactive MPC (UNIMPC) to capture this variant. We also present an NIMPC protocol for all functionalities, which is simpler and more efficient than the one given in the prior work.
Cite as

Navneet Agarwal, Sanat Anand, and Manoj Prabhakaran. Brief Announcement: On Secure m-Party Computation, Commuting Permutation Systems and Unassisted Non-Interactive MPC. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 103:1-103:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{agarwal_et_al:LIPIcs.ICALP.2018.103,
  author =	{Agarwal, Navneet and Anand, Sanat and Prabhakaran, Manoj},
  title =	{{Brief Announcement: On Secure m-Party Computation, Commuting Permutation Systems and Unassisted Non-Interactive MPC}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{103:1--103:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.103},
  URN =		{urn:nbn:de:0030-drops-91079},
  doi =		{10.4230/LIPIcs.ICALP.2018.103},
  annote =	{Keywords: Secure Multi-Party Computation, Combinatorial Characterization, Latin Hypercube, Permutation Hypercube Complex}
}
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