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A quantum cipher supported by a secret key so called keyed communication inquantum noise (KCQ) is very attractive in implementing high speed keygeneration and secure data transmission. However, Yuen-2000 as a basic model ofKCQ has a difficulty to ensure the quantitative security evaluation because allphysical parameter for the cipher system is finite. Recently, an outline of ageneralized scheme so called coherent pulse position modulation(CPPM) to showthe rigorous security analysis is given, where the parameters are allowed to beasymptotical. This may open a new way for the quantum key distribution withcoherent states of considerable energy and high speed.  In this paper, we clarify a generation method of CPPM quantum signal by usinga theory of unitary operator and symplectic transformation, and show anasymptotic property of security and its numerical examples.

Coherent pulse position modulation quantum cipher supported by secret key