The protocols for member expansion in secret sharing schemes are very useful for key management in dynamic topology networks. In order to reduce the computation complexity of the existed protocols for member expansion in secret sharing schemes, a new protocol is proposed based on the problem of elliptic curve discrete logarithm. This paper examines fifteen most recent patens that were awarded in the area of secret sharing. Unlike traditional detailed patent reviews that are focused on applying the simple secret sharing method, the proposed protocol has the following merits: 1) there is no trust center ; 2) only requesting broadcast 2t +1 times to generate the sub-secret for the new participant and the new participant can verify the truth of the sub-secret; 3) the old participants can verify the new sub-secret by the noninteractive zero-knowledge proof protocol; 4) In the sub-secret generation stage, not only sub-secrets of old participants but also the sub-secret of new participant is secure. Compared to the existed protocols, the proposed protocol has lower computational complexity and less communications. Therefore, the proposed protocol has higher performance and is suitable for resource-constrained terminals of dynamic networks.