Sure Interpolation and Its Application to Hierarchical Threshold Secret Sharing Scheme

Abstract

A threshold secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret. Threshold secret sharing is useful in management of cryptographic keys. Based on Birkhoff interpolation, Tassa has proposed an ideal hierarchical threshold secret sharing scheme. Then based on Sure interpolation and participants' identity, we present another ideal hierarchical threshold secret sharing scheme. Sure interpolation is simple and easy interpolation method to use in hierarchical threshold secret sharing scheme. At last, we analyze the ideal threshold secret sharing scheme based on Sure interpolation, which is more easy and simple to compute and implement in the real life.