Improved Analysis of Kannan’s Shortest Lattice

Abstract. The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since over twenty years. Kannan’s algorithm for solving the shortest vector problem (SVP) is in particular crucial in Schnorr’s celebrated block reduction algorithm, on which rely the best known generic attacks against the lattice-based encryption schemes mentioned above. In this paper we improve the complexity upper-bounds of Kannan’s algorithms. The analysis provides new insight on the practical cost of solving SVP, and helps progressing towards providing meaningful key-sizes.