Comment on Two schemes for Secure Outsourcing of Linear Programming

Recently, Wang et al. [IEEE INFOCOM 2011, 820-828], and Nie et al. [IEEE AINA 2014, 591-596] have proposed two schemes for secure outsourcing of large-scale linear programming (LP). They did not consider the standard form: minimize cx, subject to Ax = b,x ≥ 0. Instead, they studied a peculiar form: minimize cx, subject to Ax = b,Bx ≥ 0, where B is a non-singular matrix. In this note, we stress that the proposed peculiar form is unsolvable and meaningless. The two schemes have confused the functional inequality constraints Bx ≥ 0 with the nonnegativity constraints x ≥ 0 in the linear programming model. But the condition x ≥ 0 is indispensable to the simplex method. Therefore, both two schemes failed.