Study of the rate-distortion theory for Shannon cipher system

在本研究中，得到了香农密码系统的下列编码定理。情形1（保密信息离散，安全等级：保密信息条件密码的熵）(a)对于噪声较小的离散广播信道，确定了密码率R、密钥率R_k、安全等级h和普通接收机允许失真的可实现区域。(b)对于高斯窃听信道，确定了密码率R、密钥率R_k、安全等级h和普通接收机允许失真的可实现范围。(a)对于噪声较小的离散广播信道，导出了密码率R、密钥率R_k、安全等级D和普通接收机可接受失真的可达区域的内外边界。(b)对于高斯窃听信道，导出了密码率R、密钥率R_k、安全等级D和普通接收机允许失真的可实现区域的内外边界。(a)在无噪声信道的情况下，导出了密码率R、密钥率R_k、安全等级D和普通接收机允许失真的可达区域的内外边界。

In this study, the following coding theorems are obtained for the Shannon cipher system.Case 1 (Secret information : discrete, Security level : entropy of secret information conditioned cryptogram)(a) For the case of less-noisy discrete broadcast channel, the achievable region of cryptogram rate R,key rate R_k, security level h, and admissible distortion of regular receiver is determined.(b) For the case of the Gaussian wiretap channel, the achievable region of cryptogram rate R,key rate R_k security level h, and admissible distortion of regular receiver is determined.Case 2 (Secret information : continuous, Security level : attainable minimum distortion of wiretappers)(a) For the case of less-noisy discrete broadcast channel, inner and outer bounds of the achievable region of cryptogram rate R,key rate R_k, security level D,and admissible distortion of regular receiver are derived.(b) For the case of the Gaussian wiretap channel, inner and outer bounds of the achievable region of cryptogram rate R,key rate R_k, security level D,and admissible distortion of regular receiver are derived.Case 3 (Secret information : discrete, Security level : attainable minimum distortion of wiretappers)(a) For the case of noiseless channel, inner and outer bounds of the achievable region of cryptogram rate R,key rate R_k, security level D,and admissible distortion of regular receiver are derived.