On the Equivalence of 2-Threshold Secret Sharing Schemes and Prefix Codes

  • Paolo D’Arco
  • Roberto De PriscoEmail author
  • Alfredo De Santis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11161)


Kmargodski et al. have shown an equivalence between \((2,\infty )\)-threshold secret sharing schemes (evolving schemes) and prefix codes for the integers. Their approach exploits the codewords of the prefix code to share the secret. In this paper we propose an alternative approach that exploits only the tree structure underlying the prefix code. The approach works equally well both for the finite case, that is for (2, n)-threshold schemes, and for the infinite case, that is for evolving 2-threshold schemes.


  1. 1.
    Blakley, G.R.: Safeguarding cryptographic keys. In: Merwin, R.E., Zanca, J.T., Smith, M. (eds.) Proceedings of the 1979 AFIPS National Computer Conference. AFIPS Conference Proceedings, vol. 48, pp. 313–317. AFIPS Press (1979)Google Scholar
  2. 2.
    Beimel, A.: Secret-sharing schemes: a survey. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011). Scholar
  3. 3.
    Benaloh, J., Leichter, J.: Generalized secret sharing and monotone functions. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 27–35. Springer, New York (1990). Scholar
  4. 4.
    Cascudo, I.P., Cramer, R., Xing, C.: Bounds on the threshold gap in secret sharing and its applications. IEEE Trans. Inf. Theory 59(9), 5600–5612 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, Hoboken (2006)zbMATHGoogle Scholar
  6. 6.
    D’Arco, P., De Prisco, R., De Santis, A., Perez Del Pozo, A., Vaccaro, U.: Probabilistic Secret Sharing. ManuscriptGoogle Scholar
  7. 7.
    Karchmer, M., Wigderson, A.: On span programs. In: Proceedings of the 8th IEEE Structure in Complexity Theory, pp. 102–111 (1993)Google Scholar
  8. 8.
    Komargodski, I., Naor, M., Yogev, E.: How to share a secret, infinitely. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 485–514. Springer, Heidelberg (2016). Scholar
  9. 9.
    Komargodski, I., Paskin-Cherniavsky, A.: Evolving secret sharing: dynamic thresholds and robustness. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 379–393. Springer, Cham (2017). Scholar
  10. 10.
    Ito, M., Saito, A., Nishizeki, T.: Secret sharing schemes realizing general access structure. In: Proceedings of the IEEE Global Telecommunication Conference, Globecom 1987, pp. 99–102 (1987). Journal version: Multiple assignment scheme for sharing secret. J. Cryptol. 6(1), 15–20 (1993)Google Scholar
  11. 11.
    Paskin-Cherniavsky, A.: How to infinitely share a secret more efficiently. IACR Cryptology ePrint Archive (2016).
  12. 12.
    Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Simmons, G.J., Jackson, W., Martin, K.M.: The geometry of shared secret schemes. Bull. ICA 1, 71–88 (1991)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Paolo D’Arco
    • 1
  • Roberto De Prisco
    • 1
    Email author
  • Alfredo De Santis
    • 1
  1. 1.Dipartimento di InformaticaUniversità di SalernoFiscianoItaly

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