# Threshold Changeable Secret Sharing Scheme and Its Application to Group Authentication

## TL;DR

This paper introduces a threshold changeable secret sharing scheme that enhances security by dynamically adjusting the threshold during secret reconstruction and applies it to efficient group authentication in mobile Internet applications.

## Contribution

It proposes a novel threshold changeable secret sharing scheme based on linear codes that does not rely on computational assumptions and achieves asymptotically perfect security.

## Key findings

- Threshold can be increased from t to all participants during reconstruction.
- Scheme achieves asymptotically perfect security without computational assumptions.
- Enables efficient m-to-m group authentication for mobile Internet applications.

## Abstract

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.