An algorithm for finding a shortest vector in a two-dimensional modular lattice

AbstractLet 0 < a, b < d be integers with a ≠ b. The lattice Ld(a, b) is the set of all multiples of the vector (a, b) modulo d. An algorithm is presented for finding a shortest vector in Ld(a, b). The complexity of the algorithm is shown to be logarithmic in the size of d when the number of arithmetical operations is counted