Research On Blockchain-based Threshold Signature And Threshold Signcryption

Traditional cryptosystems have relatively centralized permissions,and only the individual or entity in possession of the cryptographic permission can perform the corresponding cryptographic operation.Threshold cryptography can distribute these permission among multiple participants,and only the set of participants who reach the threshold value can complete the corresponding cryptographic operation,which can avoid the threat of attack or failure of a single participant and improve the security and reliability of the cryptographic system.With the widespread application and popularity of blockchain,threshold cryptography has attracted a lot of discussion and research in commercial applications and academic research,and the application of this technology has been extended from the original crypto e-currency to many fields such as Internet of Things,finance,and medical care,but it also faces new challenges in practical applications.The consensus mechanism of blockchain provides the necessary security for the whole system at the price of efficiency,and each node must process every transaction,which severely limits the processing ability of the system and tends to cause network congestion.In addition,the security of the blockchain is ensured by its data layer based on cryptography,which cannot break the security mechanism of the blockchain with the current computing capacity.However,the emergence of super quantum computers will break most of the current publickey cryptographic algorithms,so blockchain systems using traditional public-key cryptographic systems will be no longer secure.To address the problems of low computational efficiency,easy network congestion and inability to resist quantum computing attacks in the blockchain environment,this thesis presents a research on threshold signature and lattice threshold cryptographic schemes for the blockchain environment.Please see the following description for the main contents of this thesis.(1)A elliptic curve threshold signature for blockchain(BC-TECS)is proposed.BCTECS generates the public and private keys of users without the third-party trusted center,which is suitable for blockchain environment;uses shared key verification technology to ensure the honesty of participants;uses elliptic curve cryptosystem to achieve the higher security with shorter keys;adds and removes users when the shared key is changed,which satisfies the characteristics of strong liquidity of blockchain.This scheme has the characteristics of existential unforgeability and high efficiency.The work process of BCTECS in the traditional Bitcoin blockchain environment is given in the thesis.(2)A lattice threshold signature for blockchain(BC-LTSC)is proposed.BC-LTSC solves the problem of quantum computing attacks in the blockchain environment and can efficiently protect the privacy of users.Under the difficult assumptions of inhomogeneous small integer solution(ISIS)problem and learning with errors(LWE)problem,the scheme satisfies unforgeability,confidentiality and post-quantum security,and has high efficiency and low communication cost.An instance of BC-LTSC under the oracle data transmission model is given in the thesis.In summary,the two blockchain-based threshold cryptographic schemes proposed in this thesis can solve the problems in blockchain technology,improve the security and reliability of cryptosystems,and have important theoretical and application values.