Research On Improved Lattice-based Linear Homomorphic Signature Algorithm

Since quantum computers can break classical cryptography algorithms,it is become more important and important to design cryptography algorithms anti quantum computer attacks in the coming times of quantum computers.Some lattice problems such as the Short Integer Solution problem(SIS),the Learning With Errors problem(LWE)are difficult to solve by quantum computers.Lattice cryptography algorithms are viewed as a type of secure cryptography algorithms with resistance to quantum computing attacks.Hence,research about lattice cryptography algorithms become more and more important for protecting information security in the post-quantum era.Linearly homomorphic signature algorithms have wide application in the network coding and cloud computation.This thesis proposes a lattice-based linearly homomorphic signature algorithm with shorter signatures and public keys and proves that this linear homomorphic signature algorithm is secure in the standard model based on it is difficult to solve the short integer solution problem.Specifically,compared with the previous secure linear homomorphic signature algorithm in the standard model,the linear homomorphic signature algorithm proposed in this thesis is of the following strengths: The signature is a 2u-dimensional vector,and the previous signature is a(r + 1)u-dimensional vector(r and u are integer numbers).The length of signature obtained in this way is much shorter;the public key of the linear homomorphic signature proposed in this thesis is r fewer n*u matrix,so that the length of the public key is greatly reduced;the calculation is converted from the splicing of multiple matrices to the linear calculation of multiple matrices,and the dimension of the matrix is reduced from(r + 1)u-dimension to 2udimension,so the calculation speed is faster.