Computers can be authenticated using automatically combined images. During an authentication process, a server transmits an image to a client. The transmitted image is combined with a stored image using a randomly selected logical operator to generate a combined image. The combined image is transmitted back to the server. The server has a copy of the transmitted image and the stored image and generates a series of template combined images using different logical operators selected from a set of logical operators to determine whether any of the template combined images match the received combined image. If the received combined image matches one of the template combined images, the user is authenticated.