In this paper, we present a new digital signature for copyright protection of digital images. The proposed algorithm is designed to be more robust to both the compression (quantization) errors and the illegal signature attack by a third party. More specifically, to maximize the watermaking effect, we embed the watermark by randomly adding or subtracking a fixed number instead of executing the XORs. Also, to improve the reliability of the watermark detection, we extact the watermark only on some image blocks, which are less sensitive to the compression error. Futhermore, the unrecovered compression errors are further detected by the Hypothesis testing. The illegal signalture attack of a third party is also protected by using some probabilistic decisions of the MSE between the orignal image and the signed image. Experimental results show that the peroposed algorithm is more robust to the quantization errors and illegal signature attack by a third party.