Research On Fully Secure Lattice-based Signature Schemes In The Standard Model

Digital signature scheme based on intractable lattice problems is a special kind of digital signature scheme.Compared with other digital signature schemes,it has more solid security guarantee.Digital signature scheme based on intractable lat-tice problems can withstand any algorithm attacks,including quantum computers.Additionally,the hardness of lattice problems under random instance is equivalent to the worst-case instance,this ensures the security of signature scheme in daily application.Since O.Goldreich et al.has given the first lattice-based signature schemes.The improved scheme of the lattice signatures has mostly focused on achieving short signatures and public key with strict security.First,there are two kinds of digital signature schemes on the lattice:one is in the standard model,the other is in the random oracle model.In this paper,we discusses the lattice signature schemes under the standard model.At present,the study of the lattice signature schemes under the standard model also focus on the above problems.Because the size of the verification key of a digital signature scheme can directly affect the efficiency of the scheme.Nowadays the verification key of the digital signature scheme still has a common problem of large size.In a general lattice,the verification key of signature schemes consist of the matrices in Zq,and we reduce the size of verification key by reducing the number of matrix.Our constructions are based on encryption from lattice,and a special partition function is used to construct a lattice signatures.This construction idea has a notable advantage:we can construct compatible algorithm groups based on improving partition functions to design signature schemes,and it can effectively reducing the size of verification keys.We combine the basic structural framework of the digital signature schemes with design ideas of the lattice based signatures in the standard model,use the modified partitioning function of S.Yamada and the predicate encoding scheme of S.Katsumata,to construct two lattice signature schemes provably fully secure with short public key,and the two schemes are all existentially unforgeable under adaptative chosen message attacks secure.Scheme one compares with the previous signature schemes in the standard models,the verification key consist of fewer matrices,and has higher security.Scheme two uses predicate coding technique to add parallelism on the basis of scheme one,which achieves the verification key consist of fewer matrices and higher efficiency.while ensuring that scheme two is still completely secure.At the same time,it is guaranteed that the scheme two is still fully secure.