@article{oai:ipsj.ixsq.nii.ac.jp:00210368,
 author = {Koji, Shima and Hiroshi, Doi and Koji, Shima and Hiroshi, Doi},
 issue = {3},
 journal = {情報処理学会論文誌},
 month = {Mar},
 note = {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.
------------------------------
This is a preprint of an article intended for publication Journal of
Information Processing(JIP). This preprint should not be cited. This
article should be cited as: Journal of Information Processing Vol.29(2021) (online)
DOI　http://dx.doi.org/10.2197/ipsjjip.29.266
------------------------------, 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.
------------------------------
This is a preprint of an article intended for publication Journal of
Information Processing(JIP). This preprint should not be cited. This
article should be cited as: Journal of Information Processing Vol.29(2021) (online)
DOI　http://dx.doi.org/10.2197/ipsjjip.29.266
------------------------------},
 title = {New Proof Techniques Using the Properties of Circulant Matrices for XOR-based (k, n) Threshold Secret Sharing Schemes},
 volume = {62},
 year = {2021}
}