  The security analysis of physical encryption protocol based on coherent pulse
position modulation(CPPM) originated by Yuen is one of the most interesting
topics in the study of cryptosystem with a security level beyond the Shannon
limit. Although the implementation of CPPM scheme has certain difficulty,
several methods have been proposed recently. This paper deals with the CPPM
encryption in terms of symplectic transformation, which includes a phase mask
encryption as a special example, and formulates a unified security analysis for
such encryption schemes. Specifically, we give a lower bound of Eve's symbol
error probability using reliability function theory to ensure that our proposed
system exceeds the Shannon limit. Then we assume the secret key is given to Eve
after her heterodyne measurement. Since this assumption means that Eve has a
great advantage in the sense of the conventional cryptography, the lower bound
of her error indeed ensures the security level beyond the Shannon limit. In
addition, we show some numerical examples of the security performance.
