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arXiv 1504.04239cs.ITmath.IT
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具有安全率测度的保密通信

Secrecy Communication with Security Rate Measure

Lei Yu, Houqiang Li, Weiping Li

摘要:

提出了一种基于率失真理论的新的保密性度量。它被命名为\emph{security rate},它是在目标失真水平内重建源所需的附加速率的最小值(下确界),对于窃听器具有任何正概率。它表示从窃听器接收到的信息到任何解密重建的信息度量(比特)的最小距离(其中解密被定义为具有某种正可能性的目标失真水平内的重建)。根据信源编码定理,在给定失真度$D_{E}$和窃听器接收到的(加密)消息$M$的情况下,它等价于一个基于失真的模糊性$\mathop{\min}\limits _{p\left(v^{n}|s^{n},m\right):Ed\left(S^{n},V^{n}\right)\le D_{E}}\frac{1}{n}I\left(S^{n};V^{n}|M\right)$,可以看作是模糊性$\frac{1}{n}H\left(S^{n}|M\right)$在有损解密情况下的直接扩展.本文在无损通信的Shannon密码系统中研究了它,其中信源从发送者秘密地、无损地传输到合法的接收者,同时也被窃听者窃听。我们刻画了秘密密钥率、信源编码率、窃听失真和安全率(基于失真的含糊度)的容许域。由于安全率等于基于失真的模糊度,并且模糊度是基于失真的模糊度的特殊情况(具有汉明失真度量和$D_{E}=0$),这给出了最大模糊度的含义的答案。

英文摘要:

We introduce a new measure on secrecy, which is established based on rate-distortion theory. It is named \emph{security rate}, which is the minimum (infimum) of the additional rate needed to reconstruct the source within target distortion level with any positive probability for wiretapper. It denotes the minimum distance in information metric (bits) from what wiretapper has received to any decrypted reconstruction (where decryption is defined as reconstruction within target distortion level with some positive possibility). By source coding theorem, it is equivalent to a distortion-based equivocation $\mathop{\min}\limits _{p\left(v^{n}|s^{n},m\right):Ed\left(S^{n},V^{n}\right)\le D_{E}}\frac{1}{n}I\left(S^{n};V^{n}|M\right)$ which can be seen as a direct extension of equivocation $\frac{1}{n}H\left(S^{n}|M\right)$ to lossy decryption case, given distortion level $D_{E}$ and the received (encrypted) message $M$ of wiretapper. In this paper, we study it in Shannon cipher system with lossless communication, where a source is transmitted from sender to legitimate receiver secretly and losslessly, and also eavesdropped by a wiretapper. We characterize the admissible region of secret key rate, coding rate of the source, wiretapper distortion, and security rate (distortion-based equivocation). Since the security rate equals the distortion-based equivocation, and the equivocation is a special case of the distortion-based equivocation (with Hamming distortion measure and $D_{E}=0$), this gives an answer for the meaning of the maximum equivocation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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