Open AccessA ( t, m, n )‐Group Oriented Secret Sharing Scheme
Author(s) -
Miao Fuyou,
Fan Yuanyuan,
Wang Xingfu,
Xiong Yan,
Badawy Moaman
Publication year - 2016
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2016.01.026
Subject(s) - secret sharing , chinese remainder theorem , homomorphic secret sharing , scheme (mathematics) , shamir's secret sharing , group (periodic table) , mathematics , computer science , authentication (law) , secure multi party computation , verifiable secret sharing , computer security , theoretical computer science , discrete mathematics , arithmetic , combinatorics , cryptography , set (abstract data type) , mathematical analysis , chemistry , organic chemistry , programming language
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.