| As an important algorithm in public key cryptography,digital signature can provide message authentication,message integrity and nonrepudiation of electronic documents.It is widely used in many fields such as business and financial industries.At present,the security of the proposed digital signature schemes is mostly based on the traditional number theory problems such as discrete logarithm and large integer factorization,but these problems have been proved to be no longer secure under the quantum computer.In order to cope with the advent of the quantum era,there is an urgent need to study some signature schemes that can resist quantum computer attacks,so the lattice-based digital signature has attracted more and more attention.The security of lattice-based digital signature scheme is mainly based on the difficulty of small integer solution problem and learning with errors in random case,so it can resist the attack of quantum computer.Moreover,lattice-based digital signature has the protocol relationship from the worst case to the random case that other signature systems do not have,which ensures the security of the signature scheme to a great extent.This paper mainly studies the digital signature scheme based on NTRU lattice and the strong designated verifier signature scheme based on lattice.Because the proposed lattice based digital signature scheme has large key,long signature length and long signature time.Therefore,in order to reduce the key and signature length of the signature scheme and improve the implementation efficiency of the scheme,this paper mainly makes the following contributions:First,because NTRU lattice has the advantages of quantum resistance,strong structure,simple algorithm,and small access space,this paper constructs a new digital signature scheme on NTRU lattice,and gives the correctness analysis of the scheme.The security of the scheme is mainly based on the nearest vector problem(CVP)on NTRU lattice,which can resist the attack of quantum computing.The scheme selects the base on the NTRU lattice as the short base,which simplifies the signature process,improves the signature speed,and makes the signature more efficient.More importantly,the scheme introduces multiple disturbance factors,which effectively prevent the leakage of the signature value during the signature process,thereby preventing the leakage of private key information and improving the security of the scheme.Secondly,this paper proposes a lattice-based strong designated verifier signature scheme,which uses a trapdoor generation algorithm and Gaussian sampling algorithm proposed by Micciancio and Peikert,which simplifies the way to obtain the signature private key in the signature.The speed of signature is greatly improved,making the signature scheme in this paper more efficient.And based on the improved short integer solution(SIS)problem,under the standard model,it is proved that the scheme is existentially unforgeable under the adaptive choice message attack,and the nontransferability of the scheme is proved based on the learning with errors(LWE)problem.Privacy of the signer’s identity.Finally,the signature scheme is applied to the data integrity audit mechanism in cloud computing,only an authorized third party can verify the data,which effectively protects the privacy of users. |
