Chinese remainder theorem secret sharing in multivariate polynomials
Keywords:
secret sharing, equiresidual ideals, equiprojectable sets, Chinese remainder theorem
Supporting Agencies
I thank T. Galibus and N. Shenets for their valuable comments. I also want to thank to V. Matulis for his help in preparation the paper.
Abstract
This paper deals with a generalization of the secret sharing using Chinese remainder theorem over the integers to multivariate polynomials over a finite field. We work with the ideals and their Gröbner bases instead of integer moduli. Therefore, the proposed method is called GB secret sharing. It was initially presented in our previous paper. Now we prove that any threshold structure has ideal GB realization. In a generic threshold modular scheme in ring of integers the sizes of the share space and the secret space are not equal. So, the scheme is not ideal and our generalization of modular secret sharing to the multivariate polynomial ring is more secure.
References
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Published
2019-11-25
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Short Communications
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How to Cite
[1]
Matveev, G.V. 2019. Chinese remainder theorem secret sharing in multivariate polynomials. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Nov. 2019), 129–133. DOI:https://doi.org/10.33581/2520-6508-2019-3-129-133.
