Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in ?p Norm

In this work, we give provable sieving algorithms for the Shortest Vector Problem (SVP) and Closest (CVP) on lattices in ?p norm (1?p??). The running time obtain is better than existing algorithms. We a new linear procedure that works all main idea to divide space into hypercubes such each vector can be mapped efficiently sub-region. achieve complexity of 22.751n+o(n), which much less 23.849n+o(n) previous best algorithm. also introduce mixed procedure, where point hypercube within ball then quadratic sieve performed hypercube. This improves time, especially ?2 norm, 22.25n+o(n), while List Sieve Birthday algorithm has 22.465n+o(n). adopt our techniques approximation SVP CVP (1?p??) show 22.001n+o(n), have 23.169n+o(n).