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To accelerate the algorithms for the dihedral hidden subgroup problem, wepresent a new algorithm based on algorithm SV(shortest vector). A subroutine isgiven to get a transition quantum state by constructing a phase filterfunction, then the measurement basis are derived based on the technique forsolving low density subset problem. Finally, the parity of slope is revealed bythe measurements on the transition quantum state. This algorithm takes O(n)quantum space and O(n^2) classical space, which is superior to existingalgorithms, for a relatively small n(n<6400),it takes (n^0.5)*(log(max aij))^3computation time, which is superior to 2^(O(n^0.5)).

A quantum algorithm for the dihedral hidden subgroup problem based on algorithm SV