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Encrypted Secret Sharing and Analysis by Plaintext Randomization

  • Stephen R. Tate
  • Roopa VishwanathanEmail author
  • Scott Weeks
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7807)

Abstract

In this paper we consider the problem of secret sharing where shares are encrypted using a public-key encryption (PKE) scheme and ciphertexts are publicly available. While intuition tells us that the secret should be protected if the PKE is secure against chosen-ciphertext attacks (i.e., CCA-secure), formally proving this reveals some subtle and non-trivial challenges. We isolate the problems that this raises, and devise a new analysis technique called “plaintext randomization” that can successfully overcome these challenges, resulting in the desired proof. The encryption of different shares can use one key or multiple keys, with natural applications in both scenarios.

Keywords

Secret Sharing Access Structure Secret Share Scheme Trust Platform Module Oblivious Transfer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bellare, M., Boldyreva, A., Micali, S.: Public-key encryption in a multi-user setting: security proofs and improvements. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 259–274. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: Proceedings of the 38th Symposium on Foundations of Computer Science (FOCS), pp. 394–403 (1997)Google Scholar
  3. 3.
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: Proceedings of 42nd Symposium on Foundations of Computer Science (FOCS), pp. 136–145 (2001)Google Scholar
  4. 4.
    Canetti, R., Kushilevitz, E., Lindell, Y.: On the limitations of universally composable two-party computation without set-up assumptions. J. Crypt. 19(2), 135–167 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Cramer, R., Shoup, V.: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack. SIAM J. Comput. 33, 167–226 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Dwork, C., Naor, M., Reingold, O., Stockmeyer, L.: Magic functions: in memoriam: Bernard M. Dwork 1923–1998. J. ACM 50(6), 852–921 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM J. Comput. 25(1), 169–192 (1996)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the 19th Symposium on Theory of Computing (STOC), pp. 218–229 (1987)Google Scholar
  9. 9.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Gunupudi, V., Tate, S.R.: Generalized non-interactive oblivious transfer using count-limited objects with applications to secure mobile agents. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 98–112. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  11. 11.
    Hofheinz, D., Jager, T.: Tightly secure signatures and public-key encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 590–607. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  12. 12.
    Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. In: Proceedings of IEEE Globecom, pp. 99–102 (1987)Google Scholar
  13. 13.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Stephen R. Tate
    • 1
  • Roopa Vishwanathan
    • 1
    Email author
  • Scott Weeks
    • 2
  1. 1.Department of Computer ScienceUniversity of North Carolina at GreensboroGreensboroUSA
  2. 2.Department of Computer ScienceGeorge Mason UniversityFairfaxUSA

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