Secure message transmission is of extreme importance intoday's information-based society. Stream encryption is apractically important means to this end. This monograph isdevoted to a new aspect of stream ciphers, namely thestability theory of stream ciphers, with the purpose ofdeveloping bounds on complexity which can form part of thebasis for a general theory of data security and ofstabilizing stream-cipher systems.The approach adopted in this monograph is new. The topic istreated by introducing measure indexes on the security ofstream ciphers, developing lower bounds on these indexes,and establishing connections among them. The treatmentinvolves the stability of boolean functions, the stabilityof linear complexity of key streams, the period stability ofkey streams, and the stability of source codes. Misleadingideas about stream ciphers are exposed and new viewpointspresented.The numerous measure indexes and bounds on them that areintroduced here, the approach based on spectrum techniques,andthe ten open problems presented will all be useful tothe reader concerned with analyzing and designing streamciphers for securing data.