Algorithms for self-synchronizing ciphers

Necessary conditions are determined for a self-synchronizing steam cipher algorithm to be secure. The stream cipher encryption hardware considered consists of a keystream generator, an exclusive-OR gate to combine the keystream and the binary coded message stream, and circuits to establish initial cryptographic synchronization. The security of the system is based on the use of secret cryptographic keys which must be transmitted to the receiver in advance over a secure route. It is shown that the algorithm (when expressed as a logic function) should be correlation-immune, permutation-immune, and nonlinear in its arguments. An example of a 125-stage 7th-order correlation-immune function is given, and its resistance to cryptanalysis is evaluated