  There is a great adventure of watermarking usage in the context of
conventional authentication since it does not require additional storage space
for supplementary metadata. However JPEG compression, being a conventional
method to compress images, leads to exact authentication breaking. We discuss a
semi-fragile watermarking system for digital images tolerant to JPEG/JPEG2000
compression. Recently we have published a selective authentication method based
on Zernike moments. But unfortunately it has large computational complexity and
not sufficiently good detection of small image modifications. In the current
paper it is proposed (in contrast to Zernike moments approach) the usage of
image finite differences and 3-bit quantization as the main technique. In order
to embed a watermark (WM) into the image, some areas of the Haar wavelet
transform coefficients are used. Simulation results show a good resistance of
this method to JPEG compression with $\mbox{\rm CR}\leq 30\%$ (Compression
Ratio), high probability of small image modification recognition, image quality
assessments $\mbox{\rm PSNR}\geq 40$ (Peak signal-to-noise ratio) dB and
$\mbox{\rm SSIM}\geq 0.98$ (Structural Similarity Index Measure) after
embedding and lower computation complexity of WM embedding and extraction. All
these properties qualify this approach as effective.
