Lin Pin-Hsun, Janda Carsten R, Jorswieck Eduard A, Schaefer Rafael F
Information Theory and Communication Systems Department, Technische Universität Braunschweig, 38106 Braunschweig, Germany.
Information Theory and Applications Chair, Technische Universität Berlin, 10623 Berlin, Germany.
Entropy (Basel). 2020 Jun 18;22(6):679. doi: 10.3390/e22060679.
In order to make a warden, Willie, unaware of the existence of meaningful communications, there have been different schemes proposed including covert and stealth communications. When legitimate users have no channel advantage over Willie, the legitimate users may need additional secret keys to confuse Willie, if the stealth or covert communication is still possible. However, secret key generation (SKG) may raise Willie's attention since it has a public discussion, which is observable by Willie. To prevent Willie's attention, we consider the source model for SKG under a strong secrecy constraint, which has further to fulfill a stealth constraint. Our first contribution is that, if the stochastic dependence between the observations at Alice and Bob fulfills the strict more capable criterion with respect to the stochastic dependence between the observations at Alice and Willie or between Bob and Willie, then a positive stealthy secret key rate is identical to the one without the stealth constraint. Our second contribution is that, if the random variables observed at Alice, Bob, and Willie induced by the common random source form a Markov chain, then the key capacity of the source model SKG with the strong secrecy constraint and the stealth constraint is equal to the key capacity with the strong secrecy constraint, but without the stealth constraint. For the case of fast fading models, a sufficient condition for the existence of an equivalent model, which is degraded, is provided, based on stochastic orders. Furthermore, we present an example to illustrate our results.
为了使典狱长威利 unaware 有意义通信的存在，人们提出了不同的方案，包括隐蔽和秘密通信。当合法用户相对于威利没有信道优势时，如果仍然可能进行秘密或隐蔽通信，合法用户可能需要额外的密钥来迷惑威利。然而，密钥生成（SKG）可能会引起威利的注意，因为它有一个公开讨论，这是威利可以观察到的。为了防止威利的注意，我们考虑在强保密性约束下的 SKG 源模型，该模型还需要满足一个秘密约束。我们的第一个贡献是，如果爱丽丝和鲍勃观测值之间的随机依赖性相对于爱丽丝和威利或鲍勃和威利观测值之间的随机依赖性满足严格的更有能力标准，那么正的秘密密钥率与没有秘密约束时的相同。我们的第二个贡献是，如果由公共随机源在爱丽丝、鲍勃和威利处观测到的随机变量形成一个马尔可夫链，那么具有强保密性约束和秘密约束的源模型 SKG 的密钥容量等于具有强保密性约束但没有秘密约束的密钥容量。对于快衰落模型的情况，基于随机序提供了一个退化的等效模型存在的充分条件。此外，我们给出一个例子来说明我们的结果。
