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PIR Codes from Combinatorial Structures

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Arithmetic of Finite Fields (WAIFI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13638))

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Abstract

A k-server Private Information Retrieval (PIR) code is a binary linear [m, s]-code admitting a generator matrix such that for every integer i with \(1\le i\le s\) there exist k disjoint subsets of columns (called recovery sets) that add up to the vector of weight one, with the single 1 in position i. As shown in [8], a k-server PIR code is useful to reduce the storage overhead of a traditional k-server PIR protocol. Finding k-server PIR codes with a small blocklength for a given dimension has recently become an important research challenge. In this work, we propose new constructions of PIR codes from combinatorial structures, introducing the notion of k-partial packing. Several bounds over the existing literature are improved.

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References

  1. Baker, R.D.: Partitioning the planes of \({\rm {AG}}_{2m}(2)\) into \(2\)-designs. Discret. Math. 15, 205–211 (1976)

    Article  MATH  Google Scholar 

  2. Beutelspacher, A.: On parallelisms in finite projective spaces. Geom. Dedicata. 3, 35–40 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bras-Amorós, M., Stokes, K.: The semigroup of combinatorial configurations. Semigroup Forum 84, 91–96 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Buratti, M., Stinson, D.R.: On resolvable Golomb rulers, symmetric configurations and progressive dinner parties. J. Algebraic Combin. 55, 141–156 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  5. Colbourn, C.J., Dinitz, J.H.: Handbook of Combinatorial Designs, Discrete Mathematics and Its Applications, Second Edition, Chapman & Hall/CRC (2007)

    Google Scholar 

  6. Davydov, A.A., Faina, G., Giulietti, M., Marcugini, S., Pambianco, F.: On constructions and parameters of symmetric configurations \(v_k\). Des. Codes Cryptogr. 80, 125–147 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kurz, S., Yaakobi, E.: PIR codes with short block length. Des. Codes Crypt. 89(3), 559–587 (2021). https://doi.org/10.1007/s10623-020-00828-6

    Article  MathSciNet  MATH  Google Scholar 

  8. Fazeli, A., Vardy, A., Yaakobi, E.: Codes for distributed PIR with low storage overhead. In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 2852–2856 (2015)

    Google Scholar 

  9. Fazeli, A., Vardy, A., Yaakobi, E.: PIR with low storage overhead: coding instead of replication. arXiv:1505.06241 (2015)

  10. Gévay, G.: Resolvable configurations. Discret. Appl. Math. 266, 319–330 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gezek, M., Mathon, R., Tonchev, V.D.: Maximal arcs, codes, and new links between projective planes of order 16. Electron. J. Combinat. 27 (2020)

    Google Scholar 

  12. Giulietti, M.: Line partitions of internal points to a conic in \({\rm {PG}}(2, q)\). Combinatorica 29(1), 19–25 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gropp, H.: Non-symmetric configurations with natural index. Discrete Math. 124, 87–98 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hirschfeld, J.W.P.: Projective Geometries Over Finite Fields, 2nd edn. Oxford Univ. Press, Oxford (1998)

    MATH  Google Scholar 

  15. Lin, H.Y., Rosnes, E.: Lengthening and extending binary private information retrieval codes. In: International Zurich Seminar on Information and Communication, pp. 113–117 (2018)

    Google Scholar 

  16. Skachek, V.: Batch and PIR codes and their connections to locally repairable codes, Network Coding and Subspace Designs, Cham, Switzerland, pp. 427–442 (2018)

    Google Scholar 

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Acknowledgments

This research was partially supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). The first author is funded by the project “Strutture Geometriche, Combinatoria e loro Applicazioni” (Fondo Ricerca di Base, 2019, University of Perugia). The third author is funded by the project “Metodi matematici per la firma digitale ed il cloud computing” (Programma Operativo Nazionale (PON) “Ricerca e Innovazione” 2014–2020, University of Perugia). The authors would like to thank Marco Buratti for his helpful suggestions.

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Authors and Affiliations

  1. Università degli Studi di Perugia, Perugia, Italy

    Massimo Giulietti, Arianna Sabatini & Marco Timpanella

Authors
  1. Massimo Giulietti
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  2. Arianna Sabatini
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  3. Marco Timpanella
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Correspondence to Marco Timpanella .

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Editors and Affiliations

  1. Department of Mathematics, University of Paris VIII, Paris, France

    Sihem Mesnager

  2. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Zhengchun Zhou

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Giulietti, M., Sabatini, A., Timpanella, M. (2023). PIR Codes from Combinatorial Structures. In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_10

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  • DOI: https://doi.org/10.1007/978-3-031-22944-2_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22943-5

  • Online ISBN: 978-3-031-22944-2

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