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

Masking Property of Quantum Random Cipher with Phase Mask Encryption -Towards Quantum Enigma Cipher-