Design And Research Of Proxy Signature Scheme Based On Lattice Hard Problem

Proxy signature is an extension of the traditional digital signature,which means that the signer needs to delegate his power by authorization.However,with the development of quantum computer research,proxy signature schemes which based on large integer factorization and discrete logarithm are facing great threats.Lattice cryptography as a typical post quantum cryptography,with simple operation,anti quantum attack,security depends on the quantum problem of average complexity and other characteristics,which provide security guarantee and theoretical support to construct lattice based cryptography scheme,lattice cryptography has become a hot topic of research in cryptography.In this paper,we proposed a lattice-based proxy signature.The main work is as follows:A proxy signature scheme consists of five stages: key generation,authorization certificate signature,authorization certificate verification,proxy signature and proxy signature verification.In the proxy signature scheme,combining partial proxy signature scheme and proxy signature scheme with certification,using the framework of partial proxy signature with the certificate,the proxy signature scheme can also improve the efficiency of the signature in the constraints of the proxy signer permissions.When designing the signature algorithm,the problem of small integer solution on the lattice is incorporated into the signature algorithm,so that the security of the proxy signature scheme can be reduced to the(SIS)problem.In the two phases of the authorization certificate signature and proxy signature,the private key information is hidden by using the reject sampling method in view of the private key leakage caused by introducing private key information in the signing process.Solving the problem of low efficiency of reject sampling by bimodal gaussion distribution,this distribution of introducing variables in the signature process from Gauss distribution to bimodal gauss distribution,reduce the rejection sampling rejected space,enhance the proxy signature certificate of authorization signature and proxy signature algorithm.In order to prove the security of the lattice based proxy signature scheme which we proposed,accroding to the non forgery,verifiability and strong non repudiation.In this paper,the unforgery is proved by forging ordinary digital signature,unauthorized attacker,forgery signature and malicious original signer forgery proxy signature one by one.The attacker forge a legal signature is reduced to the small integer solution problem(SIS)on the lattice.Finally,this paper compares and analyzes several other proxy signature schemes based on lattice,which shows that the scheme which we proposed reduces the length of signature and the length of public key.