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On the shannon cipher system with a capacity-limited key-distribution channel

机译:在具有容量受限密钥分配通道的香农密码系统上

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摘要

We consider the Shannon cipher system in a setting where the secret key is delivered to the legitimate receiver via a channel with limited capacity. For this setting, we characterize the achievable region in the space of three figures of merit: the security (measured in terms of the equivocation), the compressibility of the cryptogram, and the distortion associated with the reconstruction of the plaintext source. Although lossy reconstruction of the plaintext does not rule out the option that the (noisy) decryption key would differ, to a certain extent, from the encryption key, we show, nevertheless, that the best strategy is to strive for perfect match between the two keys, by applying reliable channel coding to the key bits, and to control the distortion solely via rate-distortion coding of the plaintext source before the encryption. In this sense, our result has a flavor similar to that of the classical source-channel separation theorem. Some variations and extensions of this model are discussed as well.
机译:我们考虑将Shannon密码系统设置为通过有限容量的信道将密钥传递给合法接收者的环境。对于此设置,我们在三个品质因数的空间内描述可实现区域的特征:安全性(根据等值度量),密码的可压缩性以及与重建纯文本源有关的失真。尽管对明文进行有损重构并不能排除(嘈杂的)解密密钥在一定程度上与加密密钥有所不同的选择,但我们仍然表明,最好的策略是争取两者之间的完美匹配通过对密钥位应用可靠的信道编码,并仅在加密之前通过明文源的速率失真编码来控制失真,就可以控制密钥。从这个意义上讲,我们的结果具有类似于经典源通道分离定理的风味。还讨论了该模型的一些变体和扩展。

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