Non-Interactive Dealer-Free Dynamic Threshold Secret Sharing Based on Standard Shamir’s SS for 5G Networks

Abstract

Wireless group communications and mobile computing have demonstrated its potential capacity in the next generation of mobile communication networks and wireless systems (5G), where devices have the particularity of being heterogeneous and so have different capabilities in terms of storage, computing, communication and energy. Conventional protocols are not suitable for 5G networks since this environment needs more flexible and simple protocols for secure group communications. Hence, how to realize the dynamical security is a big challenge for 5G networks. In data security management, the longer the system runs, the greater the attacker's capabilities become. A threshold changeable secret sharing scheme (TCSS) in which shares of a (t, n) SS generated by the dealer initially can be used to reconstruct the secret but having a larger thresholdj, (i.e., t <; j ≤ n), is a secure way to protect the secret for a longer period of time. A straightforward approach to design a non-interactive dealer-free TCSS is to let the dealer follow Shamir's SS to generate multiple shares for different thresholds, i, for i = t, t + 1, · · · , n. Using this approach, each shareholder needs to store n - t + 1 shares. In this article, we propose a non-interactive ⌈n-1/t⌉ dealer-free TCSS in which each shareholder only needs to store shares. Our proposed TCSS can t support standard Shamir's (t, n) SS. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. It is unconditionally secure and simpler than most of the existing schemes.

Keywords

• Dealer-free
• Lagrange interpolation
• non-interactive
• Shamir’s secret sharing scheme
• threshold changeable secret sharing scheme