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Data injection attacks to manipulate system state estimators on power grids are considered. A unified formulation for the problem of constructing attacking vectors is developed for linearized measurement models. Based on this formulation, a new low-complexity attacking strategy is shown to significantly outperform naive ℓ1 relaxation. It is demonstrated that it is possible to defend against malicious data injection if a small subset of measurements can be made immune to the attacks. However, selecting such subsets is a high-complexity combinatorial problem given the typically large size of electrical grids. To address the complexity issue, a fast greedy algorithm to select a subset of measurements to be protected is proposed. Another greedy algorithm that facilitates the placement of secure phasor measurement units (PMUs) to defend against data injection attacks is also developed. Simulations on the IEEE test systems demonstrate the benefits of the proposed algorithms.