Several Practical Multi-secret Sharing Scheme

In 1979, Shamir and Blakley proposed the threshold secret sharing scheme, which can realize the decentralized management of the sharing secret. The design of this sharing scheme can not only prevent the abuse of power, but also increase the security of the sharing secret. To solve the problem of sharing multiple secrets among many participants, the multi-secret sharing scheme was proposed. After that, many scholars did research on multi-secret sharing, which has achieved fruitful results. With the high socialization and commercialization of the information, how to design a safe and practical multi-secret sharing scheme is becoming the focus of research.This article firstly does research on the development of cryptography, the status of key management in the cryptographic system, and the secret sharing scheme which is one of the important means of key management. Then especially discusses the multi-secret sharing scheme, and discovers that the existing multi-secret sharing schemes have not considered the following aspects:(1) participant's weight:the position and power of different people in key management are different. (2) sharing secret's security level:according to the security level to classify the secrets, then based on specific application requirement to reconstruct the sharing secrets. (3) verification and dynamism:the scheme can prevent the external attacks and internal fraud, and allow the participants to be added or deleted dynamically. Moreover, the structure can be updated dynamically according to the security requirement.The main results are as follows:1. To solve the management problem of different-level secrets in some database system, based on the elliptic curve cryptosystem, a multi-stage secret sharing scheme among multiple organizations is proposed, which owns the advantage of a secret sharing scheme on access structure and the feature that the sharing secret can be restored in order in a multi-stage secret sharing scheme. Secret shadow is selected by the participant himself, which can not only reduce the dealer's computation cost, but also efficiently prevent the dealer providing the wrong information. In this scheme, any information can be communicated without a secure channel. Moreover, the scheme has the characteristic of verifiability. 2. To solve the management problem of multiple secrets in practical application, based on the existing schemes and combined with the idea of multi-secret sharing scheme, a dynamic multi-group secret sharing scheme is proposed. The dealer could adjust the threshold value depending on the sharing secret's secure level. The degree of the polynomial is low. The proposed scheme can prevent the participant from cheating without special verification algorithm. Therefore, the computational complexity of this scheme is lower and the efficiency is higher.3. To solve the problems in practical application involving both weighted participants and date's security level, based on Chinese remainder theorem, a hierarchical secret sharing scheme among weighted participants is proposed. The proposed scheme takes participants' weight into consideration and recovers many different-level secrets in one time by using the idea of multi-secret sharing. In the implementation phase, the participant set whose weight reaches a certain threshold value can restore the secrets of the corresponding rank and the following rank. Moreover, it needs not to choose a new polynomial in the distribution phase. The scheme can adjust the sharing secret according to the practical requirement.4. To solve the problems in practical application involving both weighted participants and adversary structure, based on Chinese remainder theorem, a secret sharing scheme constructed on adversary structure is proposed. The scheme has both reconstruction property and confidentiality property, which can efficiently prevent attacking from external attackers and cheating from internal fraud. Any information can be delivered in the form of plaintext, so the secure channel is unnecessary. The scheme allows participants to be added or deleted dynamically; the secret and adversary structure can be renewed without renewing the secret share of every participant.