Design Of New Multi-secret Sharing Schemes And Applications Of Local Secret Sharing Scheme In Blockchain

Shamir and Blakley proposed the secret sharing method firstly in 1979,and its theory and application have been refined for more than 40 years.Secret sharing,as a crucial cryptographic primitive,is also being applied to more and more cryptographic protocols as the importance of information security grows.In a secret sharing scheme,a trusted third party divides the secret into several shares using a predetermined method,and then distributes these shares to participants who match certain criteria,allowing them to combine their shares to retrieve the secret.This thesis expands on previous research by investigating the design of new multi-secret sharing schemes and applications of local secret sharing schemes in blockchain.The followings are the main research findings of this thesis:In Chapter 1,the research status and progress analysis of secret sharing schemes are introduced.In Section 1.1,firstly,we introduce the research progress of multipartite secret sharing schemes,especially the details of hierarchical secret sharing schemes and compartmented secret sharing schemes.Then we introduce the contents of secret sharing schemes related to this thesis,mainly verifiable multi secret sharing schemes,post quantum multi-stage secret sharing schemes and local secret sharing schemes.From the description above,the linear recursive sequence plays a very important role.Finally,we also introduce other secret sharing schemes that have been studied recently by many researchers.In Section 1.2,we introduce the main structure of this thesis.In Chapter 2,we introduce some basic concepts of secret sharing schemes used in this thesis and related linear recursive sequences.In Section 2.1,we mainly introduce Shamir threshold secret sharing scheme and its generalization,i.e.,Lai-Ding scheme.In Section 2.2,we mainly introduce the knowledge of non-homogeneous linear recursive sequences.The main contribution of this section is that we propose a general formula by summarizing the linear recursive sequences used in the existing literature,and divide them into two types,i.e.,Type-t and Type-l linear recursive sequences.In Chapter 3,we mainly use Type-t non-homogeneous linear recursive sequences and XTR public key encryption scheme to construct two new(k,l,m)verifiable multi secret sharing schemes.After analyzing the problems of existing schemes and attacking them,in this chapter,we propose two new multi-secret sharing schemes to overcome these defects.In addition,through security proof and comparison with existing schemes,it is found that our new schemes can achieve the same security by using shorter public key and private key lengths.At the same time,new proposed schemes are dynamic,verifiable and reusable multi-secret sharing schemes with computational security.In Chapter 4,we mainly use Type-t and Type-l non-homogeneous linear recursive sequences and Ajtai’s function to construct post-quantum multi-stage secret sharing schemes,which can recover multiple secrets in any order.Next,we analyze the security from three aspects: correctness,verifiability and privacy,and prove that new schemes are computationally secure secret sharing schemes.Through performance analysis,although new schemes increase storage consumption,they reduce time consumption.In addition,from the perspective of time consumption,the first two schemes proposed by us are better than the last two schemes.However,since Ajtai’s function is a lattice-based collision resistant function,our schemes are post-quantum,which can also be applied to more scenarios in the future.In Chapter 5,we mainly use Shamir threshold secret sharing scheme,Lai-Ding secret sharing scheme and locally recoverable codes to construct two local secret sharing schemes respectively,and construct a new distributed storage blockchain scheme based on one of them.The local secret sharing schemes proposed in this chapter eliminate the restriction on the number of peers in the blockchain in the previous scheme,and the two schemes can be applied to private blockchain,consortium blockchain and public blockchain respectively.Through analysis and comparison,although the new distributed storage blockchain scheme increases the storage consumption slightly,reduces the recovery communication consumption and enhances its robustness to peer failures.In Chapter 6,we summarize the research results of this thesis and introduce the problems to be considered in the future work.