Certificate-based Linearly Homomorphic Signature And Its Applications

With the vigorous development of 5G and the Internet of Things,users have increasingly higher wireless communication requirements.How to ensure data security in open networks has become a hot spot in both academia and industry.Cryptography provides the guarantee of confidentiality and authentication for solving security issues in networks.Digital signature is one of the most critical technologies for data authentication,which can ensure the integrity and authenticity of data.With the continuous advancement of network technology and applications,different application requirements have led to the birth of various signature schemes with special properties.The linearly homomorphic signature is just a representative of such digital signatures.Linearly homomorphic signature is essentially used to sign a subspace,the messages should be converted as vectors in a subspace.The signer only needs to sign a set of basis vectors when signing a subspace.The signatures of all vectors in the subspace can be derived from this set of basis vectors' signatures without using the private key.Linearly homomorphic signatures can be used in network coding and cloud storage to verify data integrity and authenticity.Currently,there are still some issues to be addressed in the research of linearly homomorphic signatures.Firstly,the existing schemes require high computational costs in signing and verification,which has higher requirements for the device's computing power.Secondly,most of the available schemes rely on traditional public key cryptosystem,identity-based public key cryptosystem,or certificateless public key cryptosystem.They suffer from the heavy cost of certificate management,key escrow,or the requirement of a secret channel for key distribution.The configuration process is cumbersome.The certificate-based public key cryptosystem does not have the above defects and is easy to be deployed.Therefore,this thesis will focus a systematic study on the theory and application of certificate-based linearly homomorphic signature scheme.Firstly,it introduces linearly homomorphic signature into the setting of certificate-based cryptosystem.The formal definition and security model of certificate-based on linearly homomorphic signature are presented based on certificate-based digital signature and the characteristics of linearly homomorphic signature.And then it puts forward the security concept of unforgeability of the certificatebased linearly homomorphic signature schemes under adaptively chosen subspace and adaptively chosen identity attacks.Secondly,it constructs two certificate-based linearly homomorphic signature schemes CBLHS-? and CBLHS-?.CBLHS-? focuses on reducing the signer's computational cost in signature generation.For signing a vector,CBLHS-? only needs one exponent computation over a group.While the CBLHS-? focuses on reducing the computational cost in signature verification.It requires no bilinear pairing operation with a constant computation cost independent of the dimension of the vectors.The security of the two schemes is proved in the security model based on co-CDH assumption and k-CAA assumption,respectively.Meanwhile,the efficiency of the two schemes is verified via theoretical and experiment analysis.Thirdly,the applications of CBLHS-? and CBLHS-? in network coding are investigated.The certificate-based linearly homomorphic signature scheme can be applied in network coding to prevent pollution attacks.The intermediate routing node in the network can verify the data packet's integrity and ensure secure data transmission.The CBLHS-? does not require the signer to have high computing power,so it is more suitable for IoT devices with limited computing power.However,this scheme requires a higher computational cost in signature verification.It will require intermediate routing nodes with better computing power to maintain good communication performance.As CBLHS-? is efficient in verification,it is easy to deploy in practical applications since it does not require intermediate routing devices to have better computing power.So it is more suitable for scenarios that require higher communication performance,such as electronic medical systems.Finally,it also studies how to use the certificate-based linearly homomorphic signature to solve the data integrity auditing problem.The third-party auditor can probabilistically detect the integrity of the data stored in the cloud storage provider through the challenge-response protocol upon downloading a small amount of data blocks.It devises two certificate-based data integrity auditing protocols CBDIAP-? and CBDIAP-? for different application scenarios.CBDIAP-? allows third-party auditors to audit the data without storing auditing information.CBDIAP-? is proposed for the pay-asyou-go business model,which allows the trusted third-party auditor to regularly audit the data and return the result to the user.Certificate-based linearly homomorphic signature schemes can be used in network coding to prevent pollution attacks and guarantee the data integrity and authenticity.Besides,it improves communication efficiency and promotes network coding technology into practical application.For data security in cloud storage,the practical certificatebased data integrity auditing protocol can be constructed from the certificate-based linearly homomorphic signature scheme.Therefore,the research on the certificate-based linearly homomorphic scheme and its applications has a significant theoretical and practical value.