In this paper, we propose a new perception based watermarking algorithm in binary document images for secure authentication purpose. Binary image watermarking with pixel flipping approach is a challenging problem, because flipping the black and white pixels in such simple images can bring noticeable visual distortion. A novel perceptual based model was proposed towards digital watermarking of binary images in the paper of A.T.S. Ho et al. (May 2004). The model estimates the distortion resulting from flipping of a pixel by finding the curvature-weighted distance difference (CWDD) measure between original and watermarked contour segments. In this paper, the reversible property of the CWDD measure is used towards designing a new authentication watermarking algorithm so that the possibility of any undetected modification to the watermarked image is removed. This algorithm embeds an authentication signature computed from the original image into itself after identifying an ordered set of low-distortion pixels. The same ordered set of pixels are correctly found in both the embedder and blind detector through the design of necessary conditions. The ability of the proposed authentication algorithm to detect any modification in the watermarked image is equivalent to the security of cryptographic authentication. The parity attack found in the previous block-wise data hiding methods in binary images is not possible in the proposed algorithm due to pixel-wise embedding of the authentication signature. Simulation results show the imperceptibility of the watermarking process and successful detection of content modifications.