Abstract
Harn has introduced a (t, n) threshold secret sharing scheme recently, in which shareholders’ shares are not disclosed in the secret reconstruction phase. The benefit is that the outside adversary cannot learn the secret even if it is recovered by more than t shareholders. Moreover, Harn has further extended this scheme into a multi-secret sharing scheme so that multiple secrets can be recovered individually at different stagies. Both schemes are claimed to achieve the perfectness property using heuristic arguments. However, in this paper, we show that the above claim is false and these schemes are not perfect. In the first scheme, the coalition of \(t-1\) shareholders can conclude that the secret is not uniformly distributed. And in the multi-secret sharing scheme, when the public parameters satisfy some special conditions, the coalition of \(t-1\) shareholders can even use the recovered secrets to preclude some possible values for the unrecovered secrets.
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