In this paper, we present two new methods for authentication of digital images using invertible watermarking. While virtually all watermarking schemes introduce some small amount of non-invertible distortion in the image, the new methods are invertible in the sense that, if the image is deemed authentic, the distortion due to authentication can be removed to obtain the original image data. Two techniques are proposed: one is based on robust spatial additive watermarks combined with modulo addition and the second one on lossless compression and encryption of bit-planes. Both techniques provide cryptographic strength in verifying the image integrity in the sense that the probability of making a modification to the image that will not be detected can be directly related to a secure cryptographic element, such as a hash function. The second technique can be generalized to other data types than bitmap images. As an example, a lossless authentication method for JPEG files is presented and some results discussed. In the paper, we also explain that invertible authentication can only be achieved at the expense of not being able to authenticate every possible image. However, it is argued that all images that occur in practice can be authenticated. The techniques provide new information assurance tools for integrity protection of sensitive imagery, such as medical images or images viewed under non-standard conditions when usual criteria for visibility do not apply.