Binary Additive Counter Stream Ciphers

Although a number of block ciphers have been designed and are available in the public domain, they are usually used in one of the four modes: the cipher block chaining mode, the cipher feedback mode, the output feedback mode, and the counter mode. In all these cases, a stream cipher is actually used, as any block cipher used in any of these modes becomes a stream cipher. Stream ciphers are preferred, as they can destroy statistical properties of natural languages to some extent. The objective of this paper is to provide the state-of-the-art of a special type of stream ciphers, called binary additive counter stream ciphers, by surveying known results in the literature, deriving design criteria, and presenting experimental results. Two examples of binary additive counter stream ciphers are analysed in details, and are used to illustrate that it is possible to construct a practical stream cipher with many security properties. The security of the two ciphers with respect to known plaintext attacks is proven to be equivalent to the computational complexity of two number-theoretic problems. This is the first time that the security of a cipher with respect to known plaintext attacks is proved to be equivalent to the computational complexity of a mathematical problem.