A (t, m, n)-Group Oriented Secret Sharing Scheme

• Published in: Chinese Journal of Electronics Vol. 25; no. 1; pp. 174 - 178
• Main Authors: Miao, Fuyou, Fan, Yuanyuan, Wang, Xingfu, Xiong, Yan, Badawy, Moaman
• Format: Journal Article
• Language: English
• Published: Published by the IET on behalf of the CIE 01.01.2016
• Subjects: (t, n)‐SS scheme; (t,m, n)‐group oriented secret sharing scheme; (t,m,n)‐GOSS scheme; Chinese remainder theorem; Group oriented; private key cryptography; Randomized components; secret reconstruction; share allocation; Share protection; Threshold secret sharing; tightly‐coupled group; (t,m, n)-group oriented secret sharing scheme; Chinese remainder theorem; secret reconstruction; Share protection; tightly-coupled group; RC; randomized components; Group oriented; private key cryptography; (t,m,n)-GOSS scheme; share allocation; (t, n)-SS scheme; Threshold secret sharing
• ISSN: 1022-4653; 2075-5597
• DOI: 10.1049/cje.2016.01.026

Basic (t, n)-Secret sharing (SS) schemes share a secret among n shareholders by allocating each a share. The secret can be reconstructed only if at least t shares are available. An adversary without a valid share may obtain the secret when more than t shareholders participate in the secret reconstruction. To address this problem, the paper introduces the notion and gives the formal definition of (t, m, n)-Group oriented secret sharing (GOSS); and proposes a (t, m, n)-GOSS scheme based on Chinese remainder theorem. Without any share verification or user authentication, the scheme uses Randomized components (RC) to bind all participants into a tightly coupled group, and ensures that the secret can be recovered only if all m (m≥t) participants in the group have valid shares and release valid RCs honestly. Analysis shows that the proposed scheme can guarantee the security of the secret even though up to m−1 RCs or t−1 shares are available for adversaries. Our scheme does not depend on any assumption of hard problems or one way functions.