IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2018-d836545.html
   My bibliography  Save this article

Optimal Shadow Allocations of Secret Sharing Schemes Arisen from the Dynamic Coloring of Extended Neighborhood Coronas

Author

Listed:
  • Raúl M. Falcón

    (Department Applied Mathematics I, School of Architecture, Universidad de Sevilla, 41012 Sevilla, Spain)

  • Nagaraj Mohanapriya

    (PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, Tamil Nadu, India)

  • Venkitachalam Aparna

    (PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, Tamil Nadu, India)

Abstract

Every t -dynamic proper n -coloring of a graph G describes a shadow allocation of any ( n , t + 1 ) -threshold secret sharing scheme based on G , so that, after just one round of communication, each participant can either reconstruct the secret, or obtain a different shadow from each one of his/her neighbors. Thus, for just one round of communication, this scheme is fair if and only if the threshold is either less than or equal to the minimum degree of G , or greater than or equal to its maximum degree. Despite that the dynamic coloring problem has widely been dealt with in the literature, a comprehensive study concerning this implementation in cryptography is still required. This paper delves into this topic by focusing on the use of extended neighborhood coronas for modeling communication networks whose average path lengths are small even after an asymptotic growth of their center and/or outer graphs. Particularly, the dynamic coloring problem is solved for any extended neighborhood corona with center path or star, for which we establish optimal shadow allocations of any (fair) threshold secret sharing scheme based on them. Some bounds are also established for the dynamic chromatic number of any extended neighborhood corona.

Suggested Citation

  • Raúl M. Falcón & Nagaraj Mohanapriya & Venkitachalam Aparna, 2022. "Optimal Shadow Allocations of Secret Sharing Schemes Arisen from the Dynamic Coloring of Extended Neighborhood Coronas," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2018-:d:836545
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2018/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/12/2018/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. Rajkumar & S. Muthuraman, 2021. "Structural and spectral properties of the generalized corona networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-30, April.
    2. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    3. Ramon Ferrer i Cancho & Christiaan Janssen & Ricard V. Solé, 2001. "The Topology of Technology Graphs: Small World Patterns in Electronic Circuits," Working Papers 01-05-029, Santa Fe Institute.
    4. Zhang, Xiaoyu & Xu, Maochao & Da, Gaofeng & Zhao, Peng, 2021. "Ensuring confidentiality and availability of sensitive data over a network system under cyber threats," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nie, Tingyuan & Fan, Bo & Wang, Zhenhao, 2022. "Complexity and robustness of weighted circuit network of placement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    2. Samrachana Adhikari & Beau Dabbs, 2018. "Social Network Analysis in R: A Software Review," Journal of Educational and Behavioral Statistics, , vol. 43(2), pages 225-253, April.
    3. Wang, Xiaojie & Slamu, Wushour & Guo, Wenqiang & Wang, Sixiu & Ren, Yan, 2022. "A novel semi local measure of identifying influential nodes in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Lin, Dan & Wu, Jiajing & Xuan, Qi & Tse, Chi K., 2022. "Ethereum transaction tracking: Inferring evolution of transaction networks via link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    5. Ferreira, D.S.R. & Ribeiro, J. & Oliveira, P.S.L. & Pimenta, A.R. & Freitas, R.P. & Dutra, R.S. & Papa, A.R.R. & Mendes, J.F.F., 2022. "Spatiotemporal analysis of earthquake occurrence in synthetic and worldwide data," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    6. Qinghu Liao & Wenwen Dong & Boxin Zhao, 2023. "A New Strategy to Solve “the Tragedy of the Commons” in Sustainable Grassland Ecological Compensation: Experience from Inner Mongolia, China," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    7. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    8. Daniel Reisinger & Fabian Tschofenig & Raven Adam & Marie Lisa Kogler & Manfred Füllsack & Fabian Veider & Georg Jäger, 2024. "Patterns of stability in complex contagions," Journal of Computational Social Science, Springer, vol. 7(2), pages 1895-1911, October.
    9. Gregory Gutin & Tomohiro Hirano & Sung-Ha Hwang & Philip R. Neary & Alexis Akira Toda, 2021. "The effect of social distancing on the reach of an epidemic in social networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(3), pages 629-647, July.
    10. Jie, Ke-Wei & Liu, San-Yang & Sun, Xiao-Jun & Xu, Yun-Cheng, 2023. "A dynamic ripple-spreading algorithm for solving mean–variance of shortest path model in uncertain random networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    11. Yu Gong & Xiaojiang Xu & Changping Zhao & Tobias Schoenherr, 2024. "Multi-Tier Supply Chain Learning Networks: A Simulation Study Based on the Experience-Weighted Attraction (EWA) Model," Sustainability, MDPI, vol. 16(10), pages 1-25, May.
    12. Divakaruni, Anantha & Zimmerman, Peter, 2023. "The Lightning Network: Turning Bitcoin into money," Finance Research Letters, Elsevier, vol. 52(C).
    13. Leto Peel & Tiago P. Peixoto & Manlio De Domenico, 2022. "Statistical inference links data and theory in network science," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    14. Chen, Feng & Wu, Bin & Lou, Wen-qian & Zhu, Bo-wen, 2024. "Impact of dual-credit policy on diffusion of technology R & D among automakers: Based on an evolutionary game model with technology-spillover in complex network," Energy, Elsevier, vol. 303(C).
    15. Xiaodi Ni & Lijun Yang, 2024. "Mapping Salience and Trajectory: On How to Situate Literary Translators in Publishing Legends of the Condor Heroes With Visualization," SAGE Open, , vol. 14(2), pages 21582440241, May.
    16. Abderrahim Zannou & Abdelhak Boulaalam & El Habib Nfaoui, 2020. "SIoT: A New Strategy to Improve the Network Lifetime with an Efficient Search Process," Future Internet, MDPI, vol. 13(1), pages 1-23, December.
    17. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    18. Jingsha He & Yue Li & Nafei Zhu, 2023. "A Game Theory-Based Model for the Dissemination of Privacy Information in Online Social Networks," Future Internet, MDPI, vol. 15(3), pages 1-17, February.
    19. Jianning Su & Julian Allagan & Shanzhen Gao & Olumide Malomo & Weizheng Gao & Ephrem Eyob, 2024. "Dominion on Grids," Mathematics, MDPI, vol. 12(21), pages 1-13, October.
    20. Qian, Qian & Feng, Hairong & Gu, Jing, 2021. "The influence of risk attitude on credit risk contagion—Perspective of information dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2018-:d:836545. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.