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Secure message transmission on directed networks

Author

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  • Renault, Jérôme
  • Renou, Ludovic
  • Tomala, Tristan

Abstract

A sender wishes to transmit a secret to a receiver through a communication network, where some nodes are controlled by an adversary. We characterize the directed networks for which there exist ε-secret and ε-strongly secure communication protocols (∀ε>0): if all nodes are obedient the receiver learns the secret with probability at least 1−ε and no information is leaked (secrecy), and this property is maintained under every strategy of the adversary (security). For secrecy, a necessary and sufficient condition is that there is a directed path from the sender to the receiver, and for each possible adversarial coalition A, there is an undirected path from the sender to the receiver that contains no node in A. For security, a necessary and sufficient condition is that for every possible adversarial coalition A, the graph obtained by removing all nodes in A still has the previous property.

Suggested Citation

  • Renault, Jérôme & Renou, Ludovic & Tomala, Tristan, 2014. "Secure message transmission on directed networks," Games and Economic Behavior, Elsevier, vol. 85(C), pages 1-18.
  • Handle: RePEc:eee:gamebe:v:85:y:2014:i:c:p:1-18
    DOI: 10.1016/j.geb.2014.01.012
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    References listed on IDEAS

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    1. Ben-Porath, Elchanan & Kahneman, Michael, 1996. "Communication in Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 70(2), pages 281-297, August.
    2. Renou, Ludovic & Tomala, Tristan, 2012. "Mechanism design and communication networks," Theoretical Economics, Econometric Society, vol. 7(3), September.
    3. Tristan Tomala, 2011. "Fault Reporting in Partially Known Networks and Folk Theorems," Operations Research, INFORMS, vol. 59(3), pages 754-763, June.
    4. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
    5. Renou, Ludovic & Tomala, Tristan, 2012. "Mechanism design and communication networks," Theoretical Economics, Econometric Society, vol. 7(3), September.
    6. Tristan Tomala, 2008. "Probabilistic Reliability and Privacy of Communication Using Multicast in General Neighbor Networks," Post-Print hal-00464542, HAL.
    7. Forges, Francoise, 1990. "Universal Mechanisms," Econometrica, Econometric Society, vol. 58(6), pages 1341-1364, November.
    8. Renou, Ludovic & Tomala, Tristan, 2012. "Mechanism design and communication networks," Theoretical Economics, Econometric Society, vol. 7(3), September.
    9. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January.
    10. Renou, Ludovic & Tomala, Tristan, 2012. "Mechanism design and communication networks," Theoretical Economics, Econometric Society, vol. 7(3), September.
    11. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    12. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    13. Renou, Ludovic & Tomala, Tristan, 2012. "Mechanism design and communication networks," Theoretical Economics, Econometric Society, vol. 7(3), September.
    14. Renou, Ludovic & Tomala, Tristan, 2012. "Mechanism design and communication networks," Theoretical Economics, Econometric Society, vol. 7(3), September.
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    1. repec:eee:jetheo:v:175:y:2018:i:c:p:201-247 is not listed on IDEAS

    More about this item

    Keywords

    Secure communication; Protocols; Communication;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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