Research On Verifiable Secret Sharing Based On Linear Recursion

Since the secret sharing scheme has been put forward,it has been receiving much attention from the information security community.The secret sharing scheme has been widely used in distributed cryptosystem and tolerance intrusion tolerance system,because it can solve the problem of overly centralized power and fault tolerance.In recent years,secret sharing schemes adapted to various application requirements have been put forward successively,such as verifiable secret sharing scheme,secret sharing based on linear recursive,secret sharing scheme based on general access structure,distributed secret sharing scheme,etc.In secret sharing schemes,there is a problem that key distributors and participants may be untrustworthy.Therefore,the researchers focus on the verification of the participants' key share,the enhancement of the efficiency of the participants' verification and the design of a highly efficient secret sharing scheme without third parties.In most secret sharing schemes,it is assumed that the number and access structure of the participants are unchanged before the reconstruction of the secret,which does not have the characteristics of dynamic changes in the participants and access structures.The increase or decrease of the participants,the change of access structure and the update of the key may result in the re-implementation of the key allocation algorithm,and the allocation algorithm is degraded into one time use,which restricts the application of the secret sharing scheme.This paper focuses on verifiable secret sharing and its application based on recursive equation.The main research work and results are as follows:(1)A verifiable secret sharing algorithm based on a new verifiable algorithm and a new verifying method is proposed.By improving the point addition operation of elliptic curve groups,a new verifiable algorithm is proposed based on the elliptic curve on the ring,referring to the RSA authentication method.By introducing the double parameters monotonically trapping gate function and making it conform to the requirements of the linear recursive sequence,a verification method is designed with only one time verification.Based on the proposed verification method,and combined with a linear recursive sequence,we design a linear recursive verifiable multi-key sharing scheme.In key distribution,this method is simple and does not need to calculate polynomial functions.The parameters needed to be published are less.(2)A verifiable dynamic secret sharing scheme is designed based on linear recursive equation.In order to solve the problem of the main key disclosure caused by participant exit in the secret sharing scheme based on Lagrange's interpolation formula,we introduce the general access structure instead of the(t,n)threshold structure,and further combine the key allocation algorithm of the proposed homogeneous linear recursive equation to construct a verifiable dynamic secret sharing scheme with a bilinear pairings on the elliptic curve.Verifiable dynamic secret sharing scheme,has the advantages of small key space,simple allocation algorithm and less public parameters.(3)The verification of orderly multi-step secret sharing scheme is proposed and is used in a key distribution scheme for access control system.For practical applications,there is a problem that participants with different privilege sizes,but high privilege have a relatively small set.Combined with the features of ordered multi-steps,an orderly multi-step secret sharing scheme based on linear recursive verifiability is designed.It is applicable to scenarios with different permissions between participants or different key levels.Based on this,a key distribution scheme for access control system is designed.