We consider a watermark application to assist in the integrity maintenance and verification of the associated images. There is a great benefit in using WM in the context of authentication since it does not require any additional storage space for supplementary metadata, in contrast with cryptographic signatures, for instance. However there is a fundamental problem in the case of exact authentication: How to embed a signature into a cover message in such a way that it would be possible to restore the watermarked cover image into its original state without any error? There are different approaches to solve this problem. We use the watermarking method consisting of modulo addition of a mark and investigate it in detail. Our contribution lies in investigating different modified techniques of both watermark embedding and detection in order to provide the best reliability of watermark authentication. The simulation results for different types of embedders and detectors in combination with the pictures of watermarked images are given.