Communications of the ACM
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Dynamic Threshold Scheme Based on the Definition of Cross-Product in an N-Dimentional Linear Space
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
A Generalized Secret Sharing Scheme With Cheater Detection
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
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For some secret sharing applications, the secret reconstructed is not revealed to the participants, and therefore, the secret/shadows can be repeatedly used without having to be changed. But for other applications, in which the secret reconstructed is revealed to participants, a new secret must be chosen and its corresponding shadows must be regenerated and then secretly distributed to participants again, in order to enforce the same secret sharing policy. This is inefficient because of the overhead in the generation and distribution of shadows. In this paper, an l-span secret sharing scheme for the general sharing policy is proposed to solve the secret/shadows regeneration problem by extending the life span of the shadows from 1 to l, i. e., the shadows can be repeatedly used for l times to generate l different secrets.