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Robust Threshold Schemes Based on the Chinese Remainder Theorem

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Progress in Cryptology – AFRICACRYPT 2008 (AFRICACRYPT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5023))

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Abstract

Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing.

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References

  1. Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE Trans. Information Theory 29(2), 208–210 (1983)

    Article  MathSciNet  Google Scholar 

  2. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proc. of First ACM Conference on Computer and Communications Security, pp. 62–73 (1993)

    Google Scholar 

  3. Blakley, G.: Safeguarding cryptographic keys. In: Proc. of AFIPS National Computer Conference (1979)

    Google Scholar 

  4. Boudot, F., Traoré, J.: Efficient publicly verifiable secret sharing schemes with fast or delayed recovery. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 87–102. Springer, Heidelberg (1999)

    Google Scholar 

  5. Chaum, D., Evertse, J.H., Van De Graaf, J.: An improved protocol for demonstrating possesion of discrete logarithm and some generalizations. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 127–141. Springer, Heidelberg (1988)

    Google Scholar 

  6. Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)

    Google Scholar 

  7. Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. ACM Trans. Inf. Syst. Secur. 3(3), 161–185 (2000)

    Article  Google Scholar 

  8. Desmedt, Y.: Some recent research aspects of threshold cryptography. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 158–173. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)

    Google Scholar 

  10. Desmedt, Y., Frankel, Y.: Shared generation of authenticators and signatures. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 457–469. Springer, Heidelberg (1992)

    Google Scholar 

  11. Desmedt, Y., Frankel, Y.: Homomorphic zero-knowledge threshold schemes over any finite abelian group. SIAM Journal on Discrete Mathematics 7(4), 667–679 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ding, C., Pei, D., Salomaa, A.: Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography. World Scientific, Singapore (1996)

    MATH  Google Scholar 

  13. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Information Theory 31(4), 469–472 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kaya, K., Selçuk, A.A.: Threshold cryptography based on Asmuth–Bloom secret sharing. Information Sciences 177(19), 4148–4160 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lysyanskaya, A., Peikert, C.: Adaptive security in the threshold setting: From cryptosystems to signature schemes. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 331–350. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  16. Paillier, P.: Public key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)

    Google Scholar 

  17. Poupard, G., Stern, J.: Security analysis of a practical on the fly authentication and signature generation. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 422–436. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Comm. ACM 21(2), 120–126 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  19. De Santis, A., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely? In: Proc. of STOC 1994, pp. 522–533 (1994)

    Google Scholar 

  20. Shamir, A.: How to share a secret? Comm. ACM 22(11), 612–613 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  21. Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  22. Wei, W., Trung, T., Magliveras, S., Hoffman, F.: Cryptographic primitives based on groups of hidden order. Tatra Mountains Mathematical Publications 29, 147–155 (2004)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Engineering, Bilkent University, Ankara, 06800, Turkey

    Kamer Kaya & Ali Aydın Selçuk

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  1. Kamer Kaya
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  2. Ali Aydın Selçuk
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Serge Vaudenay

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Kaya, K., Selçuk, A.A. (2008). Robust Threshold Schemes Based on the Chinese Remainder Theorem. In: Vaudenay, S. (eds) Progress in Cryptology – AFRICACRYPT 2008. AFRICACRYPT 2008. Lecture Notes in Computer Science, vol 5023. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68164-9_7

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  • DOI: https://doi.org/10.1007/978-3-540-68164-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68159-5

  • Online ISBN: 978-3-540-68164-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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