Grouped Secret Sharing Schemes Based on Lagrange Interpolation Polynomials and Chinese Remainder Theorem

Author:

Miao Fuyou1,Yu Yue1,Meng Keju1ORCID,Xiong Yan1,Chang Chin-Chen23

Affiliation:

1. University of Science and Technology of China, Hefei, Anhui, China

2. Feng Chia University, Taichung, Taiwan

3. Hangzhou Dianzi University, Hangzhou, China

Abstract

In a t , n threshold secret sharing (SS) scheme, whether or not a shareholder set is an authorized set totally depends on the number of shareholders in the set. When the access structure is not threshold, (t,n) threshold SS is not suitable. This paper proposes a new kind of SS named grouped secret sharing (GSS), which is specific multipartite SS. Moreover, in order to implement GSS, we utilize both Lagrange interpolation polynomials and Chinese remainder theorem to design two GSS schemes, respectively. Detailed analysis shows that both GSS schemes are correct and perfect, which means any authorized set can recover the secret while an unauthorized set cannot get any information about the secret.

Funder

National Key Research and Development Program of China

Publisher

Hindawi Limited

Subject

Computer Networks and Communications,Information Systems

Reference22 articles.

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4. On the asymptotic idealness of the asmuth-bloom threshold secret sharing scheme;C. C. Drăgan;Information Sciences,2018

5. Characterizing ideal weighted threshold secret sharing;A. Beimel

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1. On modular (CRT-based) secret sharing;Journal of Computer Virology and Hacking Techniques;2024-07-01

2. Multipartie Threshold Secret Sharing Scheme Based on Polynomial Interpolation;Pure Mathematics;2022

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