Threshold Changeable Secret Sharing Scheme and Its Application to Group Authentication
This addresses security vulnerabilities in group-oriented applications like mobile Internet by providing a more secure and efficient authentication method, though it is incremental as it builds on existing secret sharing concepts.
The paper tackles the problem of adversaries impersonating shareholders to recover secrets in threshold secret sharing schemes by proposing a threshold changeable secret sharing (TCSS) scheme using linear code, which increases the threshold during reconstruction and achieves asymptotically perfect security without computational assumptions. It also applies this to create a group authentication scheme for efficient m-to-m authentication in group-oriented applications.
Group oriented applications are getting more and more popular in mobile Internet and call for secure and efficient secret sharing (SS) scheme to meet their requirements. A $(t,n)$ threshold SS scheme 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 impersonating a shareholder to recover the secret with $t$ or more legal shareholders. Therefore, this paper uses linear code to propose a threshold changeable secret sharing (TCSS) scheme, in which threshold should increase from $t$ to the exact number of all participants during secret reconstruction. The scheme does not depend on any computational assumption and realizes asymptotically perfect security. Furthermore, based on the proposed TCSS scheme, 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.