Hierarchical secret sharing schemes are known for the way the secret is shared among a group of participants that is partitioned into levels. We examine these schemes in terms of how easily they delete a secret after it is distributed or namely for cases where the reliability of data deletion depends on deletion of the indispensable participants' share. In this paper, we consider Tassa's idea of using formal derivatives and Birkhoff interpolation so that his method will work well even over finite fields of characteristic 2, then we devise a method for derivatives. As a result, we propose a fast (k, n) hierarchical secret sharing scheme applicable to any level and report the software implementation evaluation. Moreover, taking practical use into consideration, we cover the optimization specialized for a ({1, 3}, n) hierarchical secret sharing scheme.

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Several secret sharing schemes with low computational costs have been proposed. XOR-based secret sharing schemes have been reported to be a part of such low-cost schemes. However, no discussion has been provided on the connection between them and the properties of circulant matrices. In this paper, we propose several theorems of circulant matrices to discuss the rank of a matrix and then show that we can discuss XOR-based secret sharing schemes using the properties of circulant matrices. We also present an evaluation of our software implementation.