Tightly Coupled Secret Sharing and Its Application to Group Authentication
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Group oriented applications are getting more and more popular in today's mobile Internet and call for secure and efficient (t,n) threshold secret sharing scheme (or (t,n)-SS) to meet their requirements. A (t,n)-SS divides a secret into n shares such that any t or more than t shares can recover the secret while less than t shares cannot. However, an adversary, even without a valid share, may obtain the secret by mounting Illegal Participant (IP) attack or Half Threshold Channel Cracking (HTCC) attack. Therefore, 1) the paper presents the notion and generic framework of (t,m,n)-Tightly Coupled Secret Sharing ((t,m,n)-TCSS). Prior to recovering the secret, it requires m (m > t) participants to form a tightly coupled group by each independently constructing a component with the share. All m components have to be used to recover the secret and thus both attacks can be thwarted more directly and simply. Furthermore, following the framework, threshold changeable secret sharing can also be easily constructed. 2) As an implementation of the framework, a linear code based (t,m,n)-TCSS scheme is proposed. Analyses show that the scheme can prevent IP, HTCC and (t-1)-Insider conspiring attacks with asymptotically perfect security. Moreover, it doesn't depend on any computational assumption and is more secure and efficient in storage, communication and computation when compared with related schemes. 3) Based on (t,m,n)-TCSS, a group authentication scheme is constructed, which allows a group user to authenticate whether all users are legal group members at once and thus provides efficient and flexible m-to-m authentication for group oriented applications.
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