Changing thresholds in the absence of secure channels

The ways the threshold parameter can be modified after the setup of a secret sharing scheme is the main theme of this work. The considerations are limited to the case where there are no secure channels. First we motivate the problem and discuss methods of threshold change when the dealer is still active and can use broadcasting to implement the change required. Next we study the case when participants themselves initiate the change of threshold without the dealer's help. A general model for threshold changeable secret sharing is developed and two constructions are given. The first generic construction allows the design of a threshold changeable secret sharing scheme which can be implemented using the Shamir approach. The second construction is geometrical in nature and is optimal in terms of the size of shares. The work is concluded by showing that any threshold scheme can be given some degree of threshold change capability.