Trojan Horse attacks can lead to unauthorized data flows and can cause either a confidentiality violation or an integrity violation. Existing solutions to address this problem employ analysis techniques that keep track of all subject accesses to objects, and hence can be expensive. In this paper we show that for an unauthorized flow to exist in an access control matrix, a flow of length one must exist. Thus, to eliminate unauthorized flows, it is sufficient to remove all one-step flows, thereby avoiding the need for expensive transitive closure computations. This new insight allows us to develop an efficient methodology to identify and prevent all unauthorized flows leading to confidentiality and integrity violations. We develop separate solutions for two different environments that occur in real life, and experimentally validate the efficiency and restrictiveness of the proposed approaches using real data sets.