A basic secret sharing scheme is defined to resist passive attacks only, which means that its security depends on the assumption that all parties involved run the protocols as prescribed by the scheme. After taking part in the distribution protocol, a non-qualified set of participants is not able to deduce (part of) the secret from their shares.
In many applications, however, a secret sharing scheme is also required to withstand active attacks. This is accomplished by verifiable secret sharing (VSS) schemes, as first introduced in 1985 [3]. Specifically, a VSS scheme is required to withstand the following two types of active attacks:
a dealer sending inconsistent or incorrect shares to some of the participants during the distribution protocol, and
participants submitting incorrect shares during the reconstruction protocol.
Clearly, Shamir's threshold scheme is not a VSS scheme, since it does not exclude either of these attacks.
A well-known example is Feldman's VSS scheme [4]....
This is a preview of subscription content, log in via an institution to check access.
References
Ben-Or, M., S. Goldwasser, and A. Wigderson (1988). “Completeness theorems for noncryptographic fault-tolerant distributed computation.” Proceedings of 20th Symposium on Theory of Computing (STOC'88). ACM Press, New York, 1–10.
Chaum, D., C. Crépeau, and I. Damgård (1988). “Multiparty unconditionally secure protocols.” Proceedings of 20th Symposium on Theory of Computing (STOC'88). ACM Press, New York, 11–19.
Chor, B., S. Goldwasser, S. Micali, and B. Awerbuch (1985). “Verifiable secret sharing and achieving simultaneity in the presence of faults.” Proceedings of 26th IEEE Symposium on Foundations of Computer Science (FOCS'85). IEEE Computer Society Press, Los Alamitos, CA, 383–395.
Feldman, P. (1987). “A practical scheme for non-interactive verifiable secret sharing.” Proceedings of 28th IEEE Symposium on Foundations of Computer Science (FOCS'87). IEEE Computer Society Press, Los Alamitos, CA, 427–437.
Fujisaki, E. and T. Okamoto (1998). “A practical and provably secure scheme for publicly verifiable secret sharing and its applications.” Advances in Cryptology—EUROCRYPT'98, Lecture Notes in Computer Science, vol. 1403, ed. K. Nyberg. Springer-Verlag, Berlin, 32–46.
Gennaro, R., S. Jarecki, H. Krawczyk, and T. Rabin (1999). “Secure distributed key generation for discrete-log based cryptosystems.” Advances in Cryptology—EUROCRYPT'99, Lecture Notes in Computer Science, vol. 1592, ed. J. Stern. Springer-Verlag, Berlin, 295–310.
Gennaro, R., S. Jarecki, H. Krawczyk, and T. Rabin (2003). “Secure applications of pedersens distributed key generation protocol.” Cryptographers' Track RSA 2003, Lecture Notes in Computer Science, vol. 2612, ed. M. Joye. Springer-Verlag, Berlin, 373–390.
Goldreich, O., S. Micali, and A. Wigderson (1987). “How to play any mental game—or—a completeness theorem for protocols with honest majority.” Proceedings of 19th Symposium on Theory of Computing (STOC'87). ACM Press, New York, 218–229.
Pedersen, T. (1991). “A threshold cryptosystem without a trusted party.” Advances in Cryptology—EUROCRYPT'91, Lecture Notes in Computer Science, vol. 547, ed. D.W. Davies. Springer-Verlag, Berlin, 522–526.
Pedersen, T.P. (1992). “Non-interactive and information-theoretic secure verifiable secret sharing.” Advances in Cryptology—CRYPTO'91, Lecture Notes in Computer Science, vol. 576, ed. J. Feigenbaum. Springer-Verlag, Berlin, 129–140.
Schoenmakers, B. (1999). “A simple publicly verifiable secret sharing scheme and its application to electronic voting.” Advances in Cryptology—CRYPTO'99, Lecture Notes in Computer Science, vol. 1666, ed. J. Wiener. Springer-Verlag, Berlin, 148–164.
Stadler, M. (1996). “Publicly verifiable secret sharing.” Advances in Cryptology—EUROCRYPT'96, Lecture Notes in Computer Science, vol. 1070, ed. U. Maurer. Springer-Verlag, Berlin, 190–199.
Young, A., and M. Yung (2001). “A PVSS as hard as discrete log and shareholder separability.” Public Key Cryptography—PKC'01, Lecture Notes in Computer Science, vol. 1992, ed. K. Kim. Springer-Verlag, Berlin, 287–299.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 International Federation for Information Processing
About this entry
Cite this entry
Schoenmakers, B. (2005). Verifiable Secret Sharing. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_452
Download citation
DOI: https://doi.org/10.1007/0-387-23483-7_452
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23473-1
Online ISBN: 978-0-387-23483-0
eBook Packages: Computer ScienceReference Module Computer Science and Engineering