Watermarking ciphers

In order to protect both the data confidentiality and legality, a concept of a watermarking cipher (also called a w-cipher) is defined. The main idea of this is as follows: the transformation of a plaintext $x$ by the composition of the encryption and decryption operations using some encryption and decryption keys yields a proper text $x'$ containing a unique watermark $w$. The encryption and decryption keys in the w-cipher are connected in some way with each other and with the given watermark $w$. In contrast with the ciphers usually studied in cryptography, the encryption function in a w-cipher is not compulsorily invertible. Thus in fact w-ciphers are not ciphers in the known sense of the word but the ciphers are w-ciphers of a certain partial type, and all terms, notions and notations related to ciphers are quite applicable to w-ciphers. It is shown how a data watermarking can be performed by applying a w-cipher in such a way that the concealment of a watermark into a plaintext is accomplished by this w-cipher either in the encryption or in the decryption processes. Some examples of w-ciphers constructed on the basis of symmetric stream ciphers are presented in the paper.