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The Shannon cipher system with a guessing wiretapper

机译：带有猜测窃听器的Shannon密码系统

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The Shannon theory of cipher systems is combined with recent work on guessing values of random variables. The security of encryption systems is measured in terms of moments of the number of guesses needed for the wiretapper to uncover the plaintext given the cryptogram. While the encrypter aims at maximizing the guessing effort, the wiretapper strives to minimize it, e.g., by ordering guesses according to descending order of posterior probabilities of plaintexts given the cryptogram. For a memoryless plaintext source and a given key rate, a single-letter characterization is given for the highest achievable guessing exponent function, that is, the exponential rate of the pth moment of the number of guesses as a function of the plaintext message length. Moreover, we demonstrate asymptotically optimal strategies for both encryption and guessing, which are universal in the sense of being independent of the statistics of the source. The guessing exponent is then investigated as a function of the key rate and related to the large-deviations guessing performance.
机译：香农密码系统理论与最近关于猜测随机变量值的工作相结合。加密系统的安全性是根据窃听者揭露给定密码的明文所需的猜测次数来衡量的。虽然加密器旨在最大化猜测努力，但是窃听者努力例如通过根据给定密码的明文的后验概率的降序对猜测进行排序来使它最小化。对于无内存的纯文本源和给定的密钥速率，将为可实现的最高猜测指数函数提供单字母特征，即，猜测次数的p矩的指数比率与明文消息长度的函数。此外，我们展示了用于加密和猜测的渐近最优策略，它们在独立于源统计信息的意义上是通用的。然后，将猜测指数作为关键速率的函数进行调查，并与大偏差猜测性能相关。

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