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In this paper, the authors will study the question of performing arbitrary updates in secret sharing schemes when shares of unaffected parties shall remain unchanged. They will introduce a zonal transformation matrix in the lifetime of secret sharing schemes to simplify constructions of multi-time secret sharing schemes and propose management models that allow unlimited updates from arbitrary schemes without need for broadcasts. As an example, they give an efficient implementation bases on Shamir's threshold scheme which is ideal from a shareholder's point of view.
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