Secret sharing protects a secret by distributing it to a group of participants/ nodes. The shared data,called shadows, are held by the nodes, and only certain authorized groups of nodes can reconstruct the secret from the shadows. In the (k, n) threshold secret sharing scheme, the secret is shared with n nodes, and more than k-1 nodes can collaborate to reconstruct the secret. There are many evolutions which involve threshold secret sharing, for examples, the proactive scheme, which periodically updates the shadows, and the mobile scheme, which can arbitrarily change the number of the nodes and the threshold. The size of the shadow is also an issue of interest: the sizes of the shadows which are held by a node are bigger, smaller than or equivalent to the secret. However, some schemes which have the size of the shadow smaller than the size of the secret do not have these advanced features. In this paper, we utilize polynomials and matrices to construct a new scheme, in which it not only has the property of having the size of the shadow smaller than the size of the secret, but also achieves proactive property. We apply furthermore the secret sharing to the verification systems when shopping to merchants for e-commerce.