Abstract
In a k out of n threshold signature scheme the secret key is distributed to n participants, so that any subset B of participants, with |B| ≥ k, can combine their shares to form a signature, while any subset of cardinality ≤ k−1 gain no information about the signature. In democratic organizations the number of users vary temporally while maintaining the relationship k = ⌊n/2⌋+1. The manner in which a legislature votes is similar to a threshold signature scheme, and the power to sign is similar to possessing shares to sign. The transfer of power to sign is an integral part of democracy. In recent work, redistribution schemes have been developed that allow one to vary the threshold k and the number of users n. However, these solutions require parties to delete their shares, which is often an unrealistic assumption. Here we provide a model for democratic bodies and solve the related problem of assuring an orderly and verifiable transfer of power as the size of the body varies.
Chapter PDF
Similar content being viewed by others
Keywords
References
G. Blakly. “Safeguarding cryptographic keys. ” In Proc. Nat. Computer Conf. AFPIPS Conf. Proc., 48. pages 313–317, 1979.
D. Boneh and M. Franklin. “Efficient generators of shared RSA keys” In Advances of Cryptology–Crypto’97, LNCS 1294, Springer-Verlag, pages 425–439, 1997.
D. Chaum. “Zero-knowledge Undeniable Signatures” In Advances of Cryptology - Eurocrypt’90, Springer- Verlag, LNCS 413,pages 458464.
D. Chaum, J.H. Evertse, and J. van de Graff. “An improved protocol for demonstrating possession of discrete logarithms and some generalizations ” In Advances of Cryptology-Eurocrypt’87, LNCS 304, Springer-Verlag, pages 127–141, 1988.
Y. Desmedt and Y. Frankel. “Homomorphie zero-knowledge threshold schemes over any finite Abelian group ” SIAM J. on Discrete Math., vol.7, no. 4 pages 667–679, 1994.
Y. Desmedt and S. Jajodia. Redistributing secret shares to new access structures and its applications. Tech. Re-port ISSE-TR-97–01, George Mason University, July 1997. ftp://isse.gmu.edu/pub/techrep/97_01 jajodia.ps.gz.
Y. Frankel and Y. Desmedt. “Classification of ideal homorphic threshold schemes over finite Abelian groups, In Advances in Cryptology- Eurocrypt’92, Springer- Verlag, pages 25–34, 1992.
Y. Frankel, P. Gemmel, P. MacKenzie, and M. Yung. “Optimal Resilience Proactive Public Threshold Cryptography ” In 38th Annual Symp. on the Foundations of Computer Science, IEEE Computer Society Press, 1997.
E. Karnin, J. Greene, and M. Hellman. “On secret sharing systems. ” IEEE Tr. Inform. Theory, 29(1), pages 35–41, 1983.
R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin. “Robust and efficient sharing of RSA functions” In Advances in Cryptology–Crypto ‘86,. Lecture Notes in Computer Science 1109, Springer Verlag, pages 157–172, 1996.
R. Rivest, A. Shamir, and L. Adelman. “A method for obtaining digital signatures and public key cryptosystems. ” Commun. ACM, 21, pages 120–126, 1978.
A. Shamir. “How to share a secret ” Commun. ACM, 22, pages 612–613, Nov., 1979.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Desmedt, Y., King, B. (1999). Verifiable Democracy. In: Preneel, B. (eds) Secure Information Networks. IFIP — The International Federation for Information Processing, vol 23. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35568-9_4
Download citation
DOI: https://doi.org/10.1007/978-0-387-35568-9_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-6487-1
Online ISBN: 978-0-387-35568-9
eBook Packages: Springer Book Archive