In this research, we describe how to construct an efficient and
unconditionally secure verifiable threshold changeable scheme,
in which any participants can verify whether the share
given by the dealer is correct or not, in which the combiner can
verify whether the pooled shares are correct or not, and in which
the threshold can updated plural times to the values determined in
advance. An optimal threshold changeable scheme was defined and
given by Martin et.al., and an unconditionally secure verifiable
threshold scheme was by Pedersen. Martins' scheme is based on
Blakley's threshold scheme whereas Pedersen's is based on Shamir's.
Hence these two schemes cannot directly be combined. Then we first
construct an almost optimal threshold changeable scheme based on
Shamir's, and after that using Pedersen's scheme, construct a
unconditionally
secure verifiable threshold scheme in which the threshold can be
updated plural times, say N times. Furthermore, our method can
decrease the amount of information the dealer has to be publish,
comparing with simply applying Pedersen's scheme N times.
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