Randomness Required for Linear Threshold Sharing Schemes Defined over Any Finite Abelian Group

1. W. Adkins and S. Weintrab. Algebra, an approach via module theory. Springer-Verlag, NY, 1992.

   MATH  Google Scholar 

2. G. Blakley. “Safeguarding cryptographic keys.” In Proc. Nat. Computer Conf. AFPIPS Conf. Proc., 48 pp. 313–317, 1979.

   Google Scholar 

3. S. Blackburn, M. Burmester, Y. Desmedt, and P. Wild. “Efficient Multiplicative Sharing schemes”. In Advances in Cryptology-Eurocrypt’ 96, LNCS 1070, pp. 107–118, Springer-Verlag, 1996.

   Google Scholar 

4. C. Blundo, A. De Santis, and U. Vaccaro. “Randomness in Distribution Protocols”. Inform. Comput. pp. 111–139, 1996.

   Google Scholar 

5. C. Blundo, A. De Santis, R. De Simone,, and U. Vaccaro. “Tight Bounds on the Information rate of secret Sharing Schemes”. In Design, Codes and Cryptography, 11, pp. 107–122, 1997.

   Article  MATH  Google Scholar 

6. C. Blundo, A.G. Gaggia, and D. R. Stinson. “On the Dealer’s randomness Required in Secret Sharing Schemes”. In Design, Codes and Cryptography, 11, pp. 235–259, 1997.

   Article  MATH  MathSciNet  Google Scholar 

7. C. Blundo and B. Masucci. Randomness in Multi-Secret Sharing Schemes. In Journal of Universal Computer Science, Vol. 5, No. 7, 1999, pp. 367–389.

   MathSciNet  Google Scholar 

8. C. Blundo and B. Masucci. A note on the Randomness in Dynamic Threshold Scheme. In Journal of Computer Security, Vol. 7, No. 1, 1999, pp. 73–85.

   Google Scholar 

9. C. Boyd, Digital Multisignatures, Cryptography and coding, Clarendon Press, 1989, pp 241–246.

   Google Scholar 

10. R.M. Capocelli, A. De Santis, L. Gargano, and U. Vaccaro, “On the Size of Shares for secret Sharing Schemes” In Journal of Cryptology, 6, pp. 157–167, 1993.

    Article  MATH  Google Scholar 

11. L. Csirmaz. “The Size of a Share Must Be large”. In Journal of Cryptology, 10, pp. 223–231, 1997.

    Article  MATH  MathSciNet  Google Scholar 

12. L. Csirmaz. The dealer’s random bits in perfect sharing schemes In Studia Sci. Math. Hungar. 32(1996) pp. 429–437.

    MATH  MathSciNet  Google Scholar 

13. A. De Santis, Y. Desmedt, Y. Frankel, and M. Yung. “How to share a function”. In Proceedings of the twenty-sixth annual ACM Symp. Theory of Computing (STOC), pp. 522–533, 1994.

    Google Scholar 

14. A. De Santis, and B. Masucucci. “Multiple Ramp Schemes”. In IEEE Transns. on Inform. Theory, 45, no. 5, pp. 1720–1728, 1999.

    Article  MATH  Google Scholar 

15. Y. Desmedt. Society and group oriented cryptography: a new concept. In Advances of Cryptology-Crypto’ 87

    Google Scholar 

16. Y. Desmedt, G. Di Crescenzo, and M. Burmester. “Multiplicative non-abelian sharing schemes and their application to threshold cryptography”. In Advances in Cryptology-Asiacrypt’ 94, LNCS 917. pp. 21–32, Springer-Verlag, 1995.

    Chapter  Google Scholar 

17. Y. Desmedt and Y. Frankel. “Homomorphic zero-knowledge threshold schemes over any finite abelian group”. In Siam J. Disc. Math. vol 7, no. 4 pp. 667–679, SIAM, 1994.

    Article  MATH  MathSciNet  Google Scholar 

18. Y. Desmedt and S. Jajodia. Redistributing secret shares to new access structures and its applications. Tech. Report ISSE-TR-97-01, George Mason University, July 1997 ftp://isse.gmu.edu/pub/techrep/97.01.jajodia.ps.gz

19. Y. Desmedt, B. King, W. Kishimoto, and K. Kurosawa, “A comment on the efficiency of secret sharing scheme over any finite abelian group”, In Information Security and Privacy, ACISP’98 (Third Australasian Conference on Information Security and Privacy), LNCS 1438, 1998, 391–402.

    Chapter  Google Scholar 

20. Y. Frankel, Y. Desmedt, and M. Burmester. “ Non-existence of homomorphic general sharing schemes for some key spaces”, in Advances of Cryptology-Crypto’ 92, 740, 1992 pp 549–557

    Google Scholar 

21. Y. Frankel, P. Gemmel, P. Mackenzie, and M. Yung. “Proactive RSA”. In Advances of Cryptology-Crypto’ 97, 1997, LNCS 1294, Springer Verlag, 1997, p. 440–454.

    Chapter  Google Scholar 

22. Y. Frankel, P. Gemmel, P. Mackenzie, and M. Yung. “Optimal-Resilience Proactive Public-key Cryptosystems”. In Proc. 38th FOCS, IEEE, 1997, p. 384–393.

    Google Scholar 

23. R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin. “Robust and efficient sharing of RSA functions”. In Advances of Cryptology-Crypto’ 96, LNCS 1109, Springer Verlag, 1996, p. 157–172.

    Chapter  Google Scholar 

24. B. King. “Improved Methods to Perform Threshold RSA”. In Advances in Cryptology-ASIACRYPT 2000, LNCS 1976, Springer Verlag, 2000,p. 359–372.

    Chapter  Google Scholar 

25. H.L. Keng. Introduction to Number Theory. Springer Verlag, NY 1982

    MATH  Google Scholar 

26. T. Hungerford. Algebra. Springer-Verlag, NY, 1974.

    MATH  Google Scholar 

27. E. Karnin, J. Greene, and M. Hellman. “On secret sharing systems.” In IEEE Trans. Inform. Theory, 29(1), pp. 35–41, 1983.

    Article  MATH  MathSciNet  Google Scholar 

28. E. Kushilevitz and A. Rosen. A Randomness Rounds Tradeoff in Private Computation. In Advances in Cryptology-CRYPTO’ 94, LNCS 839, 1994 pp. 397–410.

    Google Scholar 

29. R. Lidl and G. Pilz. Applied Abstract Algebra. Springer Verlag, NY 1984

    MATH  Google Scholar 

30. R. Rivest, A. Shamir, and L. Adelman, A method for obtaining digital signatures and public key cryptosystems, Comm. ACM, 21(1978), pp 294–299.

    Article  Google Scholar 

31. A. Shamir, How to share a secret, Comm. ACM, 22(1979), pp 612–613.

    Article  MATH  MathSciNet  Google Scholar 

32. V. Shoup. “Practical Threshold Signatures”. In Advances in Cryptology-EU-ROCRYPT 2000, LNCS 1807, Springer Verlag 2000, p. 207–220.

    Google Scholar 

33. D. Stinson. Cryptography, Theory and practice. CRC Press, NY, 1995

    MATH  Google Scholar 

34. M. van Dijk. “A Linear Construction of secret Sharing Schemes”. In Design, Codes and Cryptography 12, pp. 161–201, 1997.

    Article  MATH  Google Scholar 

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