The exchange of data is not limited to personal text information or information about institutions and governments, but includes digital media transferred via the Internet including everything, whether texts, images or videos and audio, or animation. These media need high-security protection and high speed during its transmission from one site to another. In this study, a new method is suggested for hiding a gray-level image within a larger color image based on the proposed steganography map that merged chaotic function and randomize function. The size of the chaos and randomize functions is 16 bytes. Experimental results obtained a successful method based on mean squared error, signal-to-noise ratio, peak signal noise rate, embedding capacity, entropy, and histogram. This method can rapidly hide and extract ciphertext in and from the gray image. The original image and the stego image are difficult to distinguish because the correlation between them is very close to 1, indicating that attackers cannot easily differentiate these images with the naked eye. This condition can successfully hide information on the Internet.