Open AccessChinese remainder theorem secret sharing in multivariate polynomials
Author(s) -
G. V. Matveev
Publication year - 2019
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika/žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-3956
pISSN - 2520-6508
DOI - 10.33581/2520-6508-2019-3-129-133
Subject(s) - chinese remainder theorem , secret sharing , mathematics , generalization , finite field , discrete mathematics , realization (probability) , remainder , ideal (ethics) , integer (computer science) , ring of integers , polynomial , polynomial ring , scheme (mathematics) , field (mathematics) , ring (chemistry) , combinatorics , algebraic number field , arithmetic , cryptography , pure mathematics , computer science , algorithm , mathematical analysis , philosophy , statistics , chemistry , organic chemistry , epistemology , programming language
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.