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Provably Secure Distributed Schnorr Signatures and a (t, n) Threshold Scheme for Implicit Certificates

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2119))

Abstract

In a (t, n) threshold digital signature scheme, t out of n signers must co-operate to issue a signature. We present an efficient and robust (t, n) threshold version of Schnorr’s signature scheme. We prove it to be as secure as Schnorr’s signature scheme, i.e., existentially unforgeable under adaptively chosen message attacks. The signature scheme is then incorporated into a (t,n) threshold scheme for implicit certificates. We prove the implicit certificate scheme to be as secure as the distributed Schnorr signature scheme.

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References

  1. M. Bellare and P. Rogaway. Random oracles are practical: a paradigm for designing efficient protocols. In First Annual ACM Conference on Computer and Communications Security, pages 62–73, 1993.

    Google Scholar 

  2. D. Brown. Implicitly certifying signatures securely. manuscript.

    Google Scholar 

  3. R. Gallant D. Brown and S. Vanstone. Provably secure implicit certificate schemes. In Financial Cryptography’ 01, to appear.

    Google Scholar 

  4. Y. G. Desmedt. Threshold cryptography. European Trans. on Telecommunications, 5(4):449–457, 1994.

    Article  MathSciNet  Google Scholar 

  5. P. Feldman. A practical scheme for non-interactive verifiable secret sharing. In 28th FOCS, pages 427–437, 1987.

    Google Scholar 

  6. S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM J. on Computing, 18/1:186–308, 1989.

    Article  MathSciNet  Google Scholar 

  7. R. Gennaro S. Jarecki H. Krawczyk and T. Rabin. Secure distributed key generation for discrete-log based cryptosystems. In Eurocrypt’ 99, pages 295–310, 1999.

    Google Scholar 

  8. S. K. Langford. Threshold DSS signatures without a trusted party. In Crypto’ 95, pages 397–409, 1995.

    Google Scholar 

  9. E. Okamoto, G. Davida, and M. Mambo. Some recent research aspects of threshold cryptography. In Workshop on Information Security Applications, 1997.

    Google Scholar 

  10. C. Park and K. Kurosawa. New elgamal type threshold digital signature scheme. IEICE Trans., E79-A:86–93, 1996.

    Google Scholar 

  11. T.P. Pedersen. Non-interactive and information-theoretic secure verifiable secret sharing. In Crypto’ 91, pages 129–140, 1991.

    Google Scholar 

  12. T.P. Pedersen. A threshold cryptosystem without a trusted party. In Eurocrypt’ 91, pages 522–526, 1991.

    Google Scholar 

  13. L. Pintsov and S. Vanstone. Postal revenue collection in the digital age. In Financial Cryptography’ 00, 2000.

    Google Scholar 

  14. D. Pointcheval and J. Stern. Security proofs for signature schemes. In Eurocrypt’ 96, pages 387–399, 1996.

    Google Scholar 

  15. C.P. Schnorr. Efficient signature generation by smart cards. Journal of Cryptology, 4:161–174, 1991.

    Article  MATH  Google Scholar 

  16. A. Shamir. How to share a secret. Communications of the ACM, 22:612–613, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. van Dijk. A linear construction of secret sharing schemes. Designs, Codes and Cryptography, 12:161–201, 1997.

    Article  MATH  Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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Stinson, D.R., Strobl, R. (2001). Provably Secure Distributed Schnorr Signatures and a (t, n) Threshold Scheme for Implicit Certificates. In: Varadharajan, V., Mu, Y. (eds) Information Security and Privacy. ACISP 2001. Lecture Notes in Computer Science, vol 2119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47719-5_33

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  • DOI: https://doi.org/10.1007/3-540-47719-5_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42300-3

  • Online ISBN: 978-3-540-47719-8

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