This paper presents in detail the foundation of security theory for ``Quantum stream cipher based on Holevo-Yuen theory". This type of cipher is a technology that provides information-theoretic security (ITS) to optical data transmission by randomizing ultrafast optical communication signals with quantum noise. In general, a quantitative security of ITS is discussed in terms of unicity distance in Shannon theory. However, the quantum version requires modeling beyond the Shannon model of random cipher to utilize the characteristics of the physical layer. Therefore, as first step, one has to develop a generalized unicity distance theory and apply it to evaluation of security. Although a complete theoretical formulation has not yet been established, this paper attempts to give a primitive structure of a generalization of Shannon random cipher and shows that the realization of this is generalized quantum stream cipher. In addition, we introduce several implementation methods of the generalized quantum stream ciphers and their security performances.