With the advent of Internet image authentication has become a central part of research in security. Since JPEG has recommended discrete cosine transform as one if the steps in image compression systems, a hash function which utilizes discrete cosine decomposition is desirable. In this paper, we propose a discrete cosine based hash function which distinguishes acceptable level of compression from image processing modifications such as Median filtering, Gaussian noise addition, and FMLR attack. To increase manipulation detection, we optimize the number of AC coefficients needed in smoothing.