Numerical Stability Reduction Algorithm for NTRU Symplectic Lattice

Lattice-based reduction algorithm is an important algorithm for solving the shortest vector (SVP) problem in lattice theory. It plays an important role in analyzing the security of NRTU public-key cryptosystems. But it has the problem of low efficiency for high-dimensional NTRU lattice reduction. This paper analyzes the upper bound of the GSO coefficient of the symplectic reduction of NTRU lattices, optimizes the constraints of the semi-length reduction and proposes MS-LLL reduction algorithm. Based on the Householder transformation to solve the numerical stability of QR decomposition, the HMS-LLL algorithm is given, with its realization principle and process. The experimental results show that the time cost of the HMS-LLL algorithm is close to that of the S-LLL algorithm, and the quality of the output results is better.