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International Conference on Information Security

ISC 2003: Information Security pp 122–136Cite as

Distributed RSA Signature Schemes for General Access Structures

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2851))

Abstract

In a distributed digital signature scheme, a set of participants shares a secret information that allows them to jointly compute a valid signature for any given message. These systems are said to be robust if they can tolerate the presence of some dishonest players.

Up to now, most of the proposed schemes consider only threshold structures: the system tolerates the presence of less than t corrupted players, and the subsets of players who can sign a message are those with k or more players, where k ≥ t.

We propose a framework which is more general than the threshold one, considering a general access structure of players allowed to sign and a general family of dishonest players that the scheme can tolerate. If these structures satisfy some conditions, we can design a distributed and secure RSA signature scheme for this setting. Our construction generalizes the threshold scheme of Shoup [23]. We also present some examples of non-threshold structures for which our scheme can be efficiently applied.

This work was partially supported by Spanish Ministerio de Ciencia y Tecnología under project TIC 2000-1044.

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References

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

    Google Scholar 

  2. Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. D. Boneh and M. Franklin, vol. 1294, pp. 425–439. Springer, Heidelberg (1997)

    Google Scholar 

  3. Brickell, E.F.: Some ideal secret sharing schemes. Journal of Combinatorial Mathematics and Combinatorial Computing 9, 105–113 (1989)

    MathSciNet  Google Scholar 

  4. Catalano, D., Gennaro, R., Halevi, S.: Computing inverses over a shared secret modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 190–206. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Canetti, R., Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Adaptive security for threshold cryptosystems. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 98–115. Springer, Heidelberg (1999)

    Google Scholar 

  6. Cramer, R., Fehr, S.: Optimal black-box secret sharing over arbitrary Abelian groups. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 272–287. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Damgård, I., Koprowski, M.: Practical threshold RSA signatures without a trusted dealer. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 152–165. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. Fouque, P.A., Stern, J.: Fully distributed threshold RSA under standard assumptions. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 310–330. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Frankel, Y., Desmedt, Y.: Parallel reliable threshold multisignature. Technical Report TR-92-04-02, University of Wisconsin-Milwaukee (1992)

    Google Scholar 

  12. Frankel, Y., Gemmell, P., MacKenzie, P., Yung, M.: Proactive RSA. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 440–454. Springer, Heidelberg (1997)

    Google Scholar 

  13. Frankel, Y., MacKenzie, P., Yung, M.: Robust efficient distributed RSA-key generation. In: Proceedings of STOC 1998, pp. 663–672 (1998)

    Google Scholar 

  14. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust and efficient sharing of RSA functions. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 157–172. Springer, Heidelberg (1996)

    Google Scholar 

  15. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust Threshold DSS signatures. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 354–371. Springer, Heidelberg (1996)

    Google Scholar 

  16. Goldwasser, S., Micali, S., Rivest, R.: A digital signature scheme secure against adaptative chosen-message attacks. SIAM Journal of Computing 17 (2), 281–308 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  17. Harn, L.: Group oriented (t, n) threshold digital signature scheme and digital multisignature. IEE Proceedings on Computation and Digital Technologies 141 (5), 307–313 (1994)

    Article  MATH  Google Scholar 

  18. Hirt, M., Maurer, U.: Complete characterization of adversaries tolerable in secure multi-party computation. In: Proceedings of PODC 1997, pp. 25–34 (1997)

    Google Scholar 

  19. Pedersen, T.: A threshold cryptosystem without a trusted party. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991)

    Google Scholar 

  20. Rabin, T.: A simplified approach to threshold and proactive RSA. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 89–104. Springer, Heidelberg (1998)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Chapter  Google Scholar 

  24. Simmons, G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1988)

    Google Scholar 

  25. Simmons, G.J., Jackson, W., Martin, K.: The geometry of secret sharing schemes. Bulletin of the ICA 1, 71–88 (1991)

    MATH  MathSciNet  Google Scholar 

  26. Stinson, D.R., Strobl, R.: Provably secure distributed Schnorr signatures and a (t, n) threshold scheme for implicit certificates. In: Varadharajan, V., Mu, Y. (eds.) ACISP 2001. LNCS, vol. 2119, pp. 417–434. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C. Jordi Girona, 1-3, Mòdul C3, Campus Nord, 08034, Barcelona, Spain

    Javier Herranz, Carles Padró & Germán Sáez

Authors
  1. Javier Herranz
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  2. Carles Padró
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  3. Germán Sáez
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Editor information

Editors and Affiliations

  1. Information Security Institute, Queensland University of Technology, GPO Box 2434, Qld 4001, Brisbane, Australia

    Colin Boyd

  2. Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, BS34 8QZ, Bristol, UK

    Wenbo Mao

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Herranz, J., Padró, C., Sáez, G. (2003). Distributed RSA Signature Schemes for General Access Structures. In: Boyd, C., Mao, W. (eds) Information Security. ISC 2003. Lecture Notes in Computer Science, vol 2851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10958513_10

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  • DOI: https://doi.org/10.1007/10958513_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20176-2

  • Online ISBN: 978-3-540-39981-0

  • eBook Packages: Springer Book Archive

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