In this paper, we present a novel reversible watermarking scheme for image authentication for JPEG/JPEG-2000 coded images. Since the watermarking scheme is reversible, the exact original image can be recovered from the watermarked image. The watermarking scheme makes use of finite state machine principles. The proposed scheme is asymmetric as the watermark extraction key is different than its embedding key. The algorithm is implemented and tested for its visual quality, compression overhead, execution time overhead and payload capacity. It is found that the algorithm has high visual quality, high payload capacity, low compression overhead and low execution time overhead.