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In our earlier work , we proposed for the first time that the perceptual video encryption be performed at the transformation stage by selecting one out of multiple unitary transforms according to the encryption key. In this letter, we aim to design some more efficient transforms to be used in this framework. Two criteria are followed for designing such transforms: 1) they are significantly different from discrete cosine transform (DCT) or discrete sine transform (DST), and 2) the resulted coding efficiency is exactly the same to what can be achieved by using DCT or just falls very slightly. As a result, we find that these transforms are actually derived by the sign-flipping on some node-variables in the flow-graph structure of DCT - a special case of the plane-based rotations (by π or 180°). Extensive simulations based on the H.264 codec are performed to demonstrate their effectiveness through both objective and subjective assessments. Finally, we present the security analysis to show the resistance of our algorithms to different types of attacks.