Research On NTRU Digital Signature Scheme

With the rapid development of cloud computing,big data and computer net-work technology,cryptography is developing rapidly.In the public key cryptosys-tem,digital signature is a very important algorithm.Digital signature ensures the integrity of message transmission,identifies and authenticates the sender's iden-tity,and prevents the transmission of messages Repudiation occurs in the trans-action.The goal of network security is to play an important role in e-commerce and e-government,Digital signature scheme has broad research background.But with the emergence of quantum computer,professor shor put forward t A discrete logarithm cryptographic signature scheme(shor algorithm).Curren-t RSA public key digital signature algorithm and its application based on the signature scheme of discrete logarithm will be broken down by quantum compu-tation and find a effective digital signature schemes against quantum attacks are needed.Lattice signature scheme has the advantages of simple calculation,high efficiency,quantum resistance and the difficulty from worst case to avaerage case.As the main candidate of signature scheme in post quantum cryptography era.In this paper,we mainly construct a digital signature scheme based on the one-way difficulty function of lattice.However,there is a certain distance between the lattice based digital signature scheme and the practical application At present,the implementation efficiency of digital signature scheme is poor due to the length of secret key and signature.In order to solve the above problems,this paper focuses on the design a digital signature scheme with smaller secret key and signature length.The main contributions of this paper are as follows:1.First of all,a trapdoor based on NTRU is proposed.Considering that NTRU has strong structure,small storage space and efficient algorithm,NTRU is selected as short base.After a simple linear transformation,another set of lattice bases is generated as the public key.Compared with the previous trapdoor generation algorithm on lattice,this scheme is more efficient and practical,and the difficulty of generating one-way function is high.The length of open lattice base generated by the new algorithm is smaller and the quality of the generated notch gate is better.2.LWE inversion and Gaussian sampling algorithm are applied to NTRU based trapdoor.LWE difficulty problem plays an important role in the design of lattice cryptosystem.The difficulty problem of LWE can be transformed from quantum protocol to the shortest linear independent vector problem(SIVP)and the shortest approximate vector problem(Gapsvp).There are effective algorithms to solve the LWE problem of open lattice base.We design Gaussian sampling algorithm by using one-way notch gate function.The original image size of this algorithm is short and efficient.3.In this paper,we construct a lattice based post quantum digital signature scheme.Under the random oracle model,the scheme satisfies the unforgeability attack under the chosen ciphertext.In the digital signature stage,the public lattice is used as the public secret key for encryption.In the digital decryption stage,the Gaussian sampler is used to sample the preimage for message verifica-tion,It needs lower computational complexity,more practical and shorter secret key.