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Documents authored by Ananth, Prabhanjan

Document
DOI: 10.4230/LIPIcs.ITCS.2024.6
Pseudorandom Strings from Pseudorandom Quantum States

Authors: Prabhanjan Ananth, Yao-Ting Lin, and Henry Yuen

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

Abstract
We study the relationship between notions of pseudorandomness in the quantum and classical worlds. Pseudorandom quantum state generator (PRSG), a pseudorandomness notion in the quantum world, is an efficient circuit that produces states that are computationally indistinguishable from Haar random states. PRSGs have found applications in quantum gravity, quantum machine learning, quantum complexity theory, and quantum cryptography. Pseudorandom generators, on the other hand, a pseudorandomness notion in the classical world, is ubiquitous to theoretical computer science. While some separation results were known between PRSGs, for some parameter regimes, and PRGs, their relationship has not been completely understood. In this work, we show that a natural variant of pseudorandom generators called quantum pseudorandom generators (QPRGs) can be based on the existence of logarithmic output length PRSGs. Our result along with the previous separations gives a better picture regarding the relationship between the two notions. We also study the relationship between other notions, namely, pseudorandom function-like state generators and pseudorandom functions. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes. Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states.
Cite as

Prabhanjan Ananth, Yao-Ting Lin, and Henry Yuen. Pseudorandom Strings from Pseudorandom Quantum States. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ananth_et_al:LIPIcs.ITCS.2024.6,
  author =	{Ananth, Prabhanjan and Lin, Yao-Ting and Yuen, Henry},
  title =	{{Pseudorandom Strings from Pseudorandom Quantum States}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{6:1--6:22},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.6},
  URN =		{urn:nbn:de:0030-drops-195348},
  doi =		{10.4230/LIPIcs.ITCS.2024.6},
  annote =	{Keywords: Quantum Cryptography}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.4
Pre-Constrained Encryption

Authors: Prabhanjan Ananth, Abhishek Jain, Zhengzhong Jin, and Giulio Malavolta

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
In all existing encryption systems, the owner of the master secret key has the ability to decrypt all ciphertexts. In this work, we propose a new notion of pre-constrained encryption (PCE) where the owner of the master secret key does not have "full" decryption power. Instead, its decryption power is constrained in a pre-specified manner during the system setup. We present formal definitions and constructions of PCE, and discuss societal applications and implications to some well-studied cryptographic primitives.
Cite as

Prabhanjan Ananth, Abhishek Jain, Zhengzhong Jin, and Giulio Malavolta. Pre-Constrained Encryption. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ananth_et_al:LIPIcs.ITCS.2022.4,
  author =	{Ananth, Prabhanjan and Jain, Abhishek and Jin, Zhengzhong and Malavolta, Giulio},
  title =	{{Pre-Constrained Encryption}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.4},
  URN =		{urn:nbn:de:0030-drops-156001},
  doi =		{10.4230/LIPIcs.ITCS.2022.4},
  annote =	{Keywords: Advanced encryption systems}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2011.241
Rainbow Connectivity: Hardness and Tractability

Authors: Prabhanjan Ananth, Meghana Nasre, and Kanthi K. Sarpatwar

Published in: LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

Abstract
A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such that G is (strongly) rainbow connected. In this paper we study the rainbow connectivity problem and the strong rainbow connectivity problem from a computational point of view. Our main results can be summarised as below: 1) For every fixed k >= 3, it is NP-Complete to decide whether src(G) <= k even when the graph G is bipartite. 2) For every fixed odd k >= 3, it is NP-Complete to decide whether rc(G) <= k. This resolves one of the open problems posed by Chakraborty et al. (J. Comb. Opt., 2011) where they prove the hardness for the even case. 3) The following problem is fixed parameter tractable: Given a graph G, determine the maximum number of pairs of vertices that can be rainbow connected using two colors. 4) For a directed graph G, it is NP-Complete to decide whether rc(G) <= 2.
Cite as

Prabhanjan Ananth, Meghana Nasre, and Kanthi K. Sarpatwar. Rainbow Connectivity: Hardness and Tractability. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 241-251, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{ananth_et_al:LIPIcs.FSTTCS.2011.241,
  author =	{Ananth, Prabhanjan and Nasre, Meghana and Sarpatwar, Kanthi K.},
  title =	{{Rainbow Connectivity: Hardness and Tractability}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{241--251},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Chakraborty, Supratik and Kumar, Amit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.241},
  URN =		{urn:nbn:de:0030-drops-33535},
  doi =		{10.4230/LIPIcs.FSTTCS.2011.241},
  annote =	{Keywords: Computational Complexity, Rainbow Connectivity, Graph Theory, Fixed Parameter Tractable Algorithms}
}
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