We present a new image-authentication algorithm based on binary-quantified double random-phase encoding (DRPE) and a discrete cosine transformation (DCT) domain watermarking scheme. The image is encrypted using a DRPE scheme, in which only the phase part of the encoded image is preserved. Then, this phase image is quantified to become a binary image by giving 0 to these phase values that are less than 0 and setting others to 1. Then, the quantified binary image is secretly inserted into a host image with a DCT-domain watermarking algorithm. During image authentication, the receiver gets the binary image from the watermarked image using an inverse DCT operation and codes 0 values as -pi and values of 1 as pi to create a phase image. Finally, the input image is decoded from the retrieved phase image based on a double random phase decryption technique and is further authenticated using a nonlinear cross-correlation method. The present image-authentication algorithm offers an additional layer of system security because the hidden binary image reveals no information that is from the original image. Moreover, the image decrypted from the retrieved phase image cannot be easily recognized with naked eyes. However, it can be successfully authenticated by nonlinear cross-correlation, even in the face of attacks including noise attacks, filtering attacks, partial occlusion attacks, or geometric transformation attacks to the watermarked image. Our simulation results demonstrated the capability of the proposed image-authentication technique.