Pairs of Values and the Chi-squared Attack

Secure digital communication techniques currently fall into one (or a combination) of three categories: cryptography, steganography, or watermarking. Each technique has different uses and different goals. Cryptography and steganography are generally used to transmit confidential information between two or more parties. Cryptography does so by using known mathematical formulas or techniques to encrypt a message. The encryption algorithm employs a secret key to map a meaningful message, say, a block of text, into a message that appears meaningless, such as a block of random characters. The message is then transmitted and decrypted at the receiving end using a companion key. This decryption algorithm maps the ciphertext (the encrypted message) back into the plaintext (the original message), which can be read directly. Theoretically, at least, the ciphertext can be decrypted only by someone who possesses the secret (decryption) key. In a secure system, only the intended recipient(s) and possibly the sender (in a symmetric system) possess the secret key. However, despite the fact that the content of the message is secure, an eavesdropper can, nonetheless, tell that a secret message is being sent. Steganography, on the other hand, is intended to disguise even the mere fact that a message is being transmitted between parties. To do so, steganography employs the use of a cover medium, often an image, audio file, video file, or some other digital medium that inherently contains redundancy or “noise.” In this sense, noise refers to data that are either meaningless or unnecessary to communicate information. The message is embedded into the cover medium such that it is imperceptible to anyone viewing or listening to the cover file. In theory, the message can be detected or extracted only by the intended recipient (or the sender) who knows both that a hidden message exists in the cover medium and how to extract the message. For a second layer of security and to make the message appear more like noise in the cover medium, the message is often encrypted before it is embedded. Watermarking, though similar to steganography in its implementation, differs from steganography in its intent. The goal of watermarking is to embed