Secure message transmission is of extreme importance in today's information-based society. Stream encryption is a practically important means to this end. This monograph is devoted to a new aspect of stream ciphers, namely the stability theory of stream ciphers, with the purpose of developing bounds on complexity which can form part of the basis for a general theory of data security and of stabilizing stream-cipher systems. The approach adopted in this monograph is new. The topic is treated by introducing measure indexes on the security of stream ciphers, developing lower bounds on these indexes, and establishing connections among them. The treatment involves the stability of boolean functions, the stability of linear complexity of key streams, the period stability of key streams, and the stability of source codes. Misleading ideas about stream ciphers are exposed and new viewpoints presented. The numerous measure indexes and bounds on them that are introduced here, the approach based on spectrum techniques, andthe ten open problems presented will all be useful to the reader concerned with analyzing and designing stream ciphers for securing data.