In this paper, we propose a verifiable multi-secret sharing scheme. Some secrets are protected by distributing them among many participants, whereby only an authorized group of participants can reconstruct the secrets. In our scheme, the secret will change periodically and the dealer will periodically publish some of the information to increase the robustness of system, in addition, the participants can verify the information which they have received. Each participant holds only one permanent, private secret, and some of them use it during different time periods to reconstruct the corresponding shared secrets without revealing their own private information. Because some public information is renewed in our scheme, the old information has nothing to do with the next secret. We also compare our scheme to the same technique-based studies in the fields promoting the benefits we achieve in this paper.

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In recent years, the ubiquity of communication networks speed up the development of wireless network and the Internet applications. In addition to the common service provided by the telecommunication enterprise, how to connect some distinct users to form a network which allow them to deal with their own works is a popular topic that many scholars engage in, [1] [2] [8]. When constructing the network, the key management is the most important problem that each system has to solve. There are many key agreement protocols which are non-hierarchical. However, the hierarchy is ubiquitous in our real life. In this paper, we have achieved a verifiable hierarchical key derivation scheme using the elliptic curve cryptography and the bilinear mapping function which can achieve the same security level but use less bit number when comparing to the RSA system.

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