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This paper proposes a data-hiding technique for binary images in morphological transform domain for authentication purpose. To achieve blind watermark extraction, it is difficult to use the detail coefficients directly as a location map to determine the data-hiding locations. Hence, we view flipping an edge pixel in binary images as shifting the edge location one pixel horizontally and vertically. Based on this observation, we propose an interlaced morphological binary wavelet transform to track the shifted edges, which thus facilitates blind watermark extraction and incorporation of cryptographic signature. Unlike existing block-based approach, in which the block size is constrained by 3times3 pixels or larger, we process an image in 2times2 pixel blocks. This allows flexibility in tracking the edges and also achieves low computational complexity. The two processing cases that flipping the candidates of one does not affect the flippability conditions of another are employed for orthogonal embedding, which renders more suitable candidates can be identified such that a larger capacity can be achieved. A novel effective Backward-Forward Minimization method is proposed, which considers both backwardly those neighboring processed embeddable candidates and forwardly those unprocessed flippable candidates that may be affected by flipping the current pixel. In this way, the total visual distortion can be minimized. Experimental results demonstrate the validity of our arguments.