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International Conference on Decision and Game Theory for Security

GameSec 2019: Decision and Game Theory for Security pp 152–163Cite as

Realistic versus Rational Secret Sharing

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11836))

Abstract

The study of Rational Secret Sharing initiated by Halpern and Teague regards the reconstruction of the secretin secret sharing as a game. It was shown that participants (parties) may refuse to reveal their shares and so the reconstruction may fail. Moreover, a refusal to reveal the share may be a dominant strategy of a party.

In this paper we consider secret sharing as a sub-action or subgame of a larger action/game where the secret opens a possibility of consumption of a certain common good. We claim that utilities of participants will be dependent on the nature of this common good. In particular, Halpern and Teague scenario corresponds to a rivalrous and excludable common good. We consider the case when this common good is non-rivalrous and non-excludable and find many natural Nash equilibria. We list several applications of secret sharing to demonstrate our claim and give corresponding scenarios. In such circumstances the secret sharing scheme facilitates a power sharing agreement in the society. We also state that non-reconstruction may be beneficial for this society and give several examples.

Yvo Desmedt thanks the Jonsson Endowment. He is also an Honorary Professor at University College London. A part of this research was done while Yvo Desmedt was visiting The University of Auckland, partially supported by Marsden Fund grant 3706352.

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Notes

  1. 1.

    Sometimes the acronym SMC is used.

References

  1. Beerliová-Trubíniová, Z., Hirt, M.: Perfectly-secure MPC with linear communication complexity. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 213–230. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_13

    Chapter  Google Scholar 

  2. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In Proceedings of the Twentieth Annual ACM Symposium Theory of Computing, STOC, 2–4 May 1988, pp. 1–10 (1988)

    Google Scholar 

  3. Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, pp. 313–317 (1979)

    Google Scholar 

  4. Boyd, C.: Digital multisignatures. In: Beker, H., Piper, F. (eds.) Cryptography and Coding, pp. 241–246. Clarendon Press, Oxford (1989)

    Google Scholar 

  5. Croft, R.A., Harris, S.P.: Public-key cryptography and re-usable shared secrets. In: Beker, H., Piper, F. (eds.) Cryptography and Coding, pp. 189–201. Clarendon Press, Oxford (1989)

    Google Scholar 

  6. Desmedt, Y.: A high availability internetwork capable of accommodating compromised routers. BT Technol. J. 24, 77–83 (2006)

    Article  Google Scholar 

  7. Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_28

    Chapter  Google Scholar 

  8. Desmedt, Y.G.: Threshold cryptography. Eur. Trans. Telecommun. 5, 449–457 (1994)

    Article  Google Scholar 

  9. Desmedt, Y.: Society and group oriented cryptography: a new concept. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 120–127. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-48184-2_8

    Chapter  Google Scholar 

  10. Desmedt, Y.: Some recent research aspects of threshold cryptography. In: Okamoto, E., Davida, G., Mambo, M. (eds.) ISW 1997. LNCS, vol. 1396, pp. 158–173. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0030418

    Chapter  Google Scholar 

  11. Desmedt, Y.: Unconditionally private and reliable communication in an untrusted network. In: Proceedings of IEEE Information Theory Workshop on Theory and Practice in Information-Theoretic Security, 16–19 October 2005, pp. 38–41 (2005)

    Google Scholar 

  12. Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. J. ACM 40, 17–47 (1993)

    Article  MathSciNet  Google Scholar 

  13. Garay, J., Katz, J., Maurer, U., Tackmann, B., Zikas, V.: Rational protocol design: cryptography against incentive-driven adversaries. In: 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS), pp. 648–657. IEEE (2013)

    Google Scholar 

  14. Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fact-track multiparty computations with applications to threshold cryptography. In: Proceedings of the Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 101–111 (1998)

    Google Scholar 

  15. Gordon, S.D., Katz, J.: Rational secret sharing, revisited. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 229–241. Springer, Heidelberg (2006). https://doi.org/10.1007/11832072_16

    Chapter  Google Scholar 

  16. Halpern, J., Teague, V.: Rational secret sharing and multiparty computation: extended abstract. In: Proceedings of the Thirty-sixth Annual ACM Symposium on Theory of Computing STOC ’04, New York, NY, USA, pp. 623–632. ACM (2004)

    Google Scholar 

  17. Kawachi, A., Okamoto, Y., Tanaka, K., Yasunaga, K.: General constructions of rational secret sharing with expected constant-round reconstruction. Comput. J. 60, 711–728 (2016)

    MathSciNet  Google Scholar 

  18. Kol, G., Naor, M.: Cryptography and game theory: designing protocols for exchanging information. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 320–339. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_18

    Chapter  MATH  Google Scholar 

  19. Kurosawa, K., Suzuki, K.: Truly efficient 2-round perfectly secure message transmission scheme. IEEE Trans. Inf. Theory 55, 5223–5232 (2009)

    Article  MathSciNet  Google Scholar 

  20. Liu, C.L.: Introduction to Combinatorial Mathematics. McGraw-Hill, New York (1968)

    MATH  Google Scholar 

  21. McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed-Solomon codes. Commun. ACM 24, 583–584 (1981)

    Article  MathSciNet  Google Scholar 

  22. Mishra, A., Mathur, R., Jain, S., Rathore, J.S.: Cloud computing security. Int. J. Recent Innovation Trends Comput. Commun. 1, 36–39 (2013)

    Google Scholar 

  23. Nojoumian, M., Stinson, D.R.: Socio-rational secret sharing as a new direction in rational cryptography. In: Grossklags, J., Walrand, J. (eds.) GameSec 2012. LNCS, vol. 7638, pp. 18–37. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34266-0_2

    Chapter  Google Scholar 

  24. Samuelson, P.A.: The pure theory of public expenditure. Rev. Econ. Stat. 36, 387–389 (1954)

    Article  Google Scholar 

  25. Samuelson, P.A.: Diagrammatic exposition of a theory of public expenditure. Rev. Econ. Stat. 37, 350–356 (1955)

    Article  Google Scholar 

  26. Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)

    Article  MathSciNet  Google Scholar 

  27. Shoham, Y., Tennenholtz, M.: Non-cooperative computation: boolean functions with correctness and exclusivity. Theoret. Comput. Sci. 343, 97–113 (2005)

    Article  MathSciNet  Google Scholar 

  28. Yao, A.C.: Protocols for secure computations. In 23rd Annual Symposium on Foundations of Computer Science (FOCS), pp. 160–164. IEEE Computer Society Press (1982)

    Google Scholar 

  29. Yao, A.C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science (FOCS), pp. 162–167 (1986). IEEE Computer Society Press

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, Richardson, USA

    Yvo Desmedt

  2. Department of Mathematics, University of Auckland, Auckland, New Zealand

    Arkadii Slinko

Authors
  1. Yvo Desmedt
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  2. Arkadii Slinko
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Correspondence to Arkadii Slinko .

Editor information

Editors and Affiliations

  1. University of Melbourne, Melbourne, VIC, Australia

    Tansu Alpcan

  2. Washington University in St. Louis, St. Louis, MO, USA

    Yevgeniy Vorobeychik

  3. University of Maryland, College Park, College Park, MD, USA

    John S. Baras

  4. KTH Royal Institute of Technology, Stockholm, Sweden

    György Dán

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Desmedt, Y., Slinko, A. (2019). Realistic versus Rational Secret Sharing. In: Alpcan, T., Vorobeychik, Y., Baras, J., Dán, G. (eds) Decision and Game Theory for Security. GameSec 2019. Lecture Notes in Computer Science(), vol 11836. Springer, Cham. https://doi.org/10.1007/978-3-030-32430-8_10

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  • DOI: https://doi.org/10.1007/978-3-030-32430-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-32429-2

  • Online ISBN: 978-3-030-32430-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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