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Suppose t − 1 secrets s1,......,st − 1 have been recovered.
Suppose k − 1 secrets have been recovered which means that k − 1 additional equations are built.
In Harn-Hsu's work, any t − 1 shareholder can recover all k − 1 secrets with only one reconstructed secret.
It is proved that even k − 1 secrets have been reconstructed; any t − 1 shareholders still cannot get any information on the last secret.
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