Comment on Two schemes for Secure Outsourcing of Linear Programming
Abstract
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 c^{T}x, subject to Ax=b, x>0. Instead, they studied a peculiar form: minimize c^{T}x, 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2015
- DOI:
- 10.48550/arXiv.1511.06470
- arXiv:
- arXiv:1511.06470
- Bibcode:
- 2015arXiv151106470C
- Keywords:
-
- Computer Science - Cryptography and Security
- E-Print:
- 4 pages