Research On Multi-level Secret Sharing Scheme And Its Application

As an important means of information protection,secret sharing(SS)is also known as password segmentation storage technology.Its application idea is to divide a secret into several sub shares and distribute them to different participants,ensuring that any participant cannot reconstruct the secret.Only when the participants collaborate to share the sub share information can the initial secret be restored.Based on this idea of secret splitting and reconstruction,the application of secret sharing technology in cryptographic schemes can effectively reduce the concentration of secrets,disperse the risk of information leakage,improve the fault-tolerance of the scheme,and achieve the goal of securely and accurately transmitting information.However,due to the complexity of the application environment,it is necessary to consider various issues when constructing secret sharing schemes.For example,if the permissions of members in the same organization are different,it is necessary to apply a scheme that can achieve a hierarchical structure.In response to this application requirement,this paper conducts research on encryption and decryption algorithms,hierarchical models,multi secret models,and application effects.The main work contents are as follows:(1)Based on the creation idea of the classic(t,n)secret sharing model,that is,encryption and decryption algorithms are mostly based on reciprocal algorithms,a verifiable secret sharing scheme based on calculus algorithms is proposed.This scheme achieves secret distribution by generating sub shares through polynomial differentiation,encrypts the transmission sub shares using RSA algorithm,and verifies the correctness of the reconstructed structure by generating public values through a secure hash function,providing some security guarantees for the scheme.In addition,the scheme can be executed in polynomial time,and the overall communication efficiency of the scheme is high.(2)In order to achieve personalized secret sharing among multiple levels of participants,that is,in the process of secret sharing,it is necessary to provide corresponding secret sharing thresholds based on the differences in permissions of participants at different levels.This paper proposes a multi-level secret sharing scheme with variable thresholds.This scheme utilizes a calculus algorithm and combines the uniqueness of the participant’s identity to generate corresponding public values,reducing the amount of information that needs to be encrypted for transmission;At the same time,considering the diversity of participants’ levels,corresponding thresholds are set for them.The higher the level,the more public values participants obtain,and the lower the threshold value they need to reach when recovering secrets,reflecting the priority diversity of participants at different levels;In addition,before sharing the secret,the distributor uses a secure hash function to generate a hash value and disclose it,so that after obtaining the reconstruction secret,participants can be verified by a one-way hash function to ensure that the reconstruction result is correct,which improves the security of the scheme to a certain extent.(3)In secret sharing schemes,in order to accomplish multiple secret sharing tasks synchronously or asynchronously,a large amount of data that requires secure channel transmission or a large number of public values are usually generated,requiring significant transmission or storage costs.To solve this kind of problem,a secure multi-level and multi-secret sharing scheme is proposed based on Chinese remainder theorem,XOR cryptographic algorithm,and calculus operation rules.This scheme uses a calculus algorithm to construct a general secret distribution polynomial for different secrets,and generates a corresponding number of polynomial values of different degrees for participants at different levels.Some of the user secret values are retained,and the remaining values are aggregated using the Chinese Remainder Theorem.This operation will generate a small number of secure public values and sub shares;Distributors use random values,XOR algorithms to encrypt and process secrets and disclose them;When reconstructing the corresponding secret,the sub participant needs to meet the corresponding threshold value of the layer,fully utilize the public value and a small amount of encrypted information to recover the key,then use the XOR algorithm to obtain the secret,and compare it with the hash value of the secret to verify that the secret is correct.