Algorithm of Basis reduction 張圻毓

Outline Algorithm Example

Algorithm Input : Linearly independent column vector f 1 ……f n Z n Output : A reduced basis (g 1 ……g n ) of the lattice L=Σ 1 ≦ i ≦ n Zf i Z n

Algorithm 1. for i =1,…,n do g i  f i compute the GSO G*,M Q n*n, i  2 2.while i ≦ n do 3. for j= i-1,i-2,…,1 do 4. g i  g i - 「 μ ij 」 g j update the GSO {replacement step}

Algorithm 5. if i>1 and then exchange g i-1 and g i and update the GSO, i  i-1 else i  i+1 6. return g 1,…,g n

Example