Unordered Multisecret Sharing Based on Generalized Chinese Remainder Theorem

Xiaoping Li,Chin-Chen Chang,Hefeng Chen,Yanjun Liu

doi:10.1155/2020/6073721

Abstract

Multisecret sharing schemes have been widely used in the area of information security, such as cloud storage, group authentication, and secure parallel communications. One of the issues for these schemes is to share and recover multisecret from their shareholders. However, the existing works consider the recovery of multisecret only when the correspondences between the secrets and their shares are definite. In this paper, we propose a multisecret sharing scheme to share and recover two secrets among the participants based on the generalized Chinese Remainder Theorem (GCRT), where the multisecret and their shares are unordered. To overcome the leakage of information, we propose an improved scheme including the improved sharing phase and the recovery phase. The improved scheme has not only a more secure performance but also a lower computation complexity. The conditions for recovery failure and success are also explored.

Highlights

Secret sharing plays a critical role in numerous applications, such as in threshold cryptography, access control, cloud computing, data hiding, and digital watermarking [1,2,3]
In a secret-sharing scheme (SS), a dealer divides a secret into several pieces and shares them among the shareholders
It shows that the secret can be recovered by any no less than t shares, while the recovery failure with fewer than t shares

Summary

Introduction

Secret sharing plays a critical role in numerous applications, such as in threshold cryptography, access control, cloud computing, data hiding, and digital watermarking [1,2,3]. For a (t, n) SS with threshold t, a secret s is divided into n pieces to be sheared among n shareholders by a dealer It shows that the secret can be recovered by any no less than t shares, while the recovery failure with fewer than t shares. E authors presented a public shift scheme to obtain the true pieces and used the proper one-way function to reconstruct the secrets stage-by-stage in a predetermined order For this scheme, it needs a large number of public values. The scheme presented in [15] is of one-time use To overcome this drawback, a one-way hash functionbased multiuse threshold secret-sharing scheme was proposed in [17].

Unordered Multisecret Sharing and the Generalized CRT

Unordered Multisecret-Sharing Scheme

Improved Unordered MultisecretSharing Scheme

Conclusions