2 Search Results for "Kunihiro, Noboru"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.47
Quantum Programming in Polylogarithmic Time

Authors: Florent Ferrari, Emmanuel Hainry, Romain Péchoux, and Mário Silva

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the complexity class FBQPOLYLOG of functions approximable in polylogarithmic time with a quantum random access Turing machine. We introduce a quantum programming language with first-order recursive procedures, which provides the first programming language-based characterization of FBQPOLYLOG. Each program computes a function in FBQPOLYLOG (soundness) and, conversely, each function of this complexity class is computed by a program (completeness). We also provide a compilation strategy from programs to uniform families of quantum circuits of polylogarithmic depth and polynomial size, whose set of computed functions is known as qnc, and recover the well-known separation result FBQPOLYLOG ⊊ QNC.
Cite as

Florent Ferrari, Emmanuel Hainry, Romain Péchoux, and Mário Silva. Quantum Programming in Polylogarithmic Time. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ferrari_et_al:LIPIcs.MFCS.2025.47,
  author =	{Ferrari, Florent and Hainry, Emmanuel and P\'{e}choux, Romain and Silva, M\'{a}rio},
  title =	{{Quantum Programming in Polylogarithmic Time}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{47:1--47:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.47},
  URN =		{urn:nbn:de:0030-drops-241547},
  doi =		{10.4230/LIPIcs.MFCS.2025.47},
  annote =	{Keywords: Quantum programming languages, Polylogarithmic time, Quantum circuits, Implicit computational complexity}
}
Document
DOI: 10.4230/LIPIcs.ITC.2020.2
d-Multiplicative Secret Sharing for Multipartite Adversary Structures

Authors: Reo Eriguchi and Noboru Kunihiro

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

Abstract
Secret sharing schemes are said to be d-multiplicative if the i-th shares of any d secrets s^(j), j∈[d] can be converted into an additive share of the product ∏_{j∈[d]}s^(j). d-Multiplicative secret sharing is a central building block of multiparty computation protocols with minimum number of rounds which are unconditionally secure against possibly non-threshold adversaries. It is known that d-multiplicative secret sharing is possible if and only if no d forbidden subsets covers the set of all the n players or, equivalently, it is private with respect to an adversary structure of type Q_d. However, the only known method to achieve d-multiplicativity for any adversary structure of type Q_d is based on CNF secret sharing schemes, which are not efficient in general in that the information ratios are exponential in n. In this paper, we explicitly construct a d-multiplicative secret sharing scheme for any 𝓁-partite adversary structure of type Q_d whose information ratio is O(n^{𝓁+1}). Our schemes are applicable to the class of all the 𝓁-partite adversary structures, which is much wider than that of the threshold ones. Furthermore, our schemes achieve information ratios which are polynomial in n if 𝓁 is constant and hence are more efficient than CNF schemes. In addition, based on the standard embedding of 𝓁-partite adversary structures into ℝ^𝓁, we introduce a class of 𝓁-partite adversary structures of type Q_d with good geometric properties and show that there exist more efficient d-multiplicative secret sharing schemes for adversary structures in that family than the above general construction. The family of adversary structures is a natural generalization of that of the threshold ones and includes some adversary structures which arise in real-world scenarios.
Cite as

Reo Eriguchi and Noboru Kunihiro. d-Multiplicative Secret Sharing for Multipartite Adversary Structures. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{eriguchi_et_al:LIPIcs.ITC.2020.2,
  author =	{Eriguchi, Reo and Kunihiro, Noboru},
  title =	{{d-Multiplicative Secret Sharing for Multipartite Adversary Structures}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{2:1--2:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.2},
  URN =		{urn:nbn:de:0030-drops-121079},
  doi =		{10.4230/LIPIcs.ITC.2020.2},
  annote =	{Keywords: Secret sharing scheme, multiplicative secret sharing scheme, multipartite adversary structure}
}
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