Simple and efficient threshold changeable secret sharing.

Shamir's (t, n) threshold secret sharing (SS) is one of the most important cryptographic primitives in various security applications designed to protect highly sensitive information, such as intellectual property and network security. A dealer in a (t, n) threshold SS divides the secret into n shares such that with t or more than t of these shares, the secret can be retrieved; but with less than t of these shares, no information of the secret can be revealed. In order to adapt the dynamic environment in various applications, the threshold changeable SS (TCSS) allows the threshold of the original secret to be dynamically adjusted. Note that Shamir's original SS is unable to achieve this property. In the literature, most existing TCSS schemes are suffering from limitations that either it requires a trusted dealer to generate and distribute new shares, or requires interactions among shareholders to generate new shares. In this paper, we propose a novel idea to construct a dealer-free and non-interactive TCSS based on pairwise keys between users. Research papers related to pairwise key distribution schemes have been published over last 40 years and it has become one of fundamental tools used in design of cryptographic solutions. First, we show that our idea can be used to construct a scheme for anonymously releasing data and a secure multiparty computation scheme. Both schemes are very simple and security analysis can be understood easily. Second, we demonstrate that a TCSS can also be designed based on same approach. Our design of TCSS is novel and it can be applied to convert any existing SS into a TCSS.