Two-operation homomorphic perfect sharing schemes over rings. (English) Zbl 0984.94027
Summary: Two-operation homomorphic sharing schemes were introduced by Y. Frankel and Y. Desmedt [Lect. Notes Comput. Sci. 740, 549-557 (1993; Zbl 0809.94015)]. They proved that if the set of keys is a Boolean algebra or a finite field, then there does not exist a two-operation homomorphic sharing scheme. In this paper, it is proved that there do not exist perfect two-operation homomorphic sharing schemes over finite rings with identities. A necessary condition for the existence of perfect two-operation sharing schemes over finite rings without identities is given.
MSC:
| 94A62 | Authentication, digital signatures and secret sharing |
Citations:
Zbl 0809.94015References:
| [1] | Ito, M., Saito, A. and Nishizeki, T., Secret sharing scheme realizing general access structures, In Proc. IEEE Global Telecommunications Conf. Globecom’87, 1987, 99–102. |
| [2] | Benaloh, J. C., Secret sharing homomorphism: Keeping shares of a secret, Lecture Notes in Comput. Sci., 263, 1987, 251–260. · Zbl 0637.94013 · doi:10.1007/3-540-47721-7_19 |
| [3] | Desmedt, Y. and Frankel, Y., Threshold cryptosystems, Lecture Notes in Comput. Sci., 435, 1989, 307–315. · doi:10.1007/0-387-34805-0_28 |
| [4] | Desmedt, Y. and Frankel, Y., Shared generation of authenticators and signatures, Lecture Notes in Comput. Sci., 576, 1992, 457–469. · Zbl 0789.68048 · doi:10.1007/3-540-46766-1_37 |
| [5] | Hwang, H., Cryptosystems for group oriented cryptography, Lecture Notes in Comput. Sci., 473, 1991, 352–360. · Zbl 0825.94183 · doi:10.1007/3-540-46877-3_32 |
| [6] | Lain, C. S. and Harn, L., Generalized threshold cryptosystems, Lecture Notes in Comput. Sci., 739, 1993, 159–169. · Zbl 0808.94022 |
| [7] | Desmedt, Y. and Frankel, Y., Non-existence of homomorphic general sharing scheme for some key spaces, Lecture Notes in Comput. Sci., 740, 1993, 549–557. · Zbl 0809.94015 · doi:10.1007/3-540-48071-4_39 |
| [8] | Ma, C. G. and Zhang, C., Classification of ideal two-operation homomorphic threshold schemes over Zn and the Galois Ring GR (Pe, n), Appl. Math.-JCU, 1998, 13(2): 217–222. · Zbl 1053.94555 |
| [9] | Xie, B. J., Abstract Algebra, Shanghai Science and Technology Press, Shanghai, 1982. · Zbl 0608.00002 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
