A (t;w) threshold scheme over insecure channels

Secret sharing schemes can be used to facilitate distributed trust or shared control for critical activities (e.g., signing corporate cheques; opening bank vaults), by gating the critical action on cooperation by t of w users. The disadvatages of these schemes are ineffective key management and in parties communication, the share secret keys must remain secret at both end. In this paper, we propose a method to exchange a Shamir´s secret sharing over insecure channels to overcome these disadvantages. The algorithm complexity analysis shows that it is an efficient scheme in both space and time for constructing the share secret keys, recovering the message M from the threshold t of w people and encrypting the share secret keys. Since there is no efficient algorithm known of recovering pairs of share secret key (x_i, y_i) from corresponding ciphertext c_i, given the public information (n_i, e_i) of each person. Therefore, this scheme can be achieved the high security through the insecure communication channels.