Research And Design Of Lattice-based Digital Signature Scheme

The development of quantum computers will bring serious security problems,and the traditional public-key cryptosystems will suffer great threats.Lattice-based cryptography is one of the most promising algorithms in the post-quantum era,and it is of great theoretical research value and significant to design digital signature schemes,the research hotspot in public-key cryptography,under the lattice difficulty problems.The proposed lattice-based digital signature schemes have the shortcoming of fewer types and large key length.In view of this,this paper proposes two types of signature schemes based on different basic algorithms as follows.(1)The traditional digital signature scheme based on certificate requires larger storage space than identity-based digital signature scheme.For that reason,this paper proposes an identity-based digital signature scheme from lattice using the bimodal gaussian distribution to achieve rejection sampling,which improves the rejection rate.In terms of security proof,its security can be statistically reduced to the Shortest Integer Solution problem on the lattice.After comparing with other signature schemes,the key length of this scheme is smaller,which has obvious advantages in the practical application.(2)Proxy signing enables the transfer of signing rights of the signer,and the final signature operation is performed by the proxy signer after authorization.This paper proposes a lattice-based proxy signature scheme,which adopts the fixed dimension basis delegation technology to control the length of the key.Comprehensive analysis and proof are carried out in terms of serval properties.Comparison with other schemes shows that this scheme has the smaller key length and the better completeness.What's more,the analysis on practical applications shows that this scheme has broad application prospects.