A Novel Approximation Algorithm for the Shortest Vector Problem

Finding the shortest vector in a lattice is a NP-hard problem. The best known approximation algorithm for this problem is LLL algorithm with the approximation factor of $\alpha ^{\frac {n-1}{2}}$ , $\alpha \geq \frac {4}{3}$ , which is not a good approximation factor. This work proposes a new polynomial time approximation algorithm for the shortest lattice vector problem. The proposed method makes use of only integer arithmetic and does not require Gram-Schmidt orthogonal basis for generating reduced basis. The proposed method is able to obtain an approximation factor of $\frac {1}{(1-\delta)}$ , where $0 \leq \delta \lt 1$ .