Two legitimate parties, referred to as Alice and Bob, wish to generate secret keys from the wireless channel in the presence of an eavesdropper, referred to as Eve, in order to use such keys for encryption and decryption. In general, the secret key rate highly depends on the coherence time of the channel. In particular, a straightforward method of generating secret keys in static environments results in ultra-low rates. In order to resolve this problem, we introduce a low-complexity method called induced randomness. In this method, Alice and Bob independently generate local randomness to be used together with the uniqueness of the wireless channel coefficients in order to enable high-rate secret key generation. In this work, two scenarios are considered: first, when Alice and Bob share a direct communication channel, and second, when Alice and Bob do not have a direct link and communicate through an untrusted relay. After exchanging the induced randomness, post-processing is done by Alice and Bob to generate highly-correlated samples that are used for the key generation. Such samples are then converted into bits, disparities between the sequences generated by Alice and Bob are mitigated, and the resulting sequences are then hashed to compensate for the information leakage to the eavesdropper and to allow consistency checking of the generated key bit sequences. We utilize semantic security measures and information-theoretic inequalities to upper bound the probability of successful eavesdropping attack in terms of the mutual information measures that can be numerically computed. Given certain reasonable system parameters this bound is numerically evaluated to be 2-31 and 2-10.57 in the first and the second scenario, respectively.

中文翻译：

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静态环境中的物理层密钥生成


两个合法方（称为 Alice 和 Bob）希望在窃听者（称为 Eve）存在的情况下从无线信道生成秘密密钥，以便使用这些密钥进行加密和解密。一般来说，密钥率很大程度上取决于信道的相干时间。特别是，在静态环境中生成密钥的直接方法会导致超低速率。为了解决这个问题，我们引入了一种称为诱导随机性的低复杂度方法。在此方法中，Alice 和 Bob 独立生成局部随机性，与无线信道系数的唯一性一起使用，以便实现高速密钥生成。在这项工作中，考虑了两种场景：第一，当 Alice 和 Bob 共享直接通信通道时；第二，当 Alice 和 Bob 没有直接链路并通过不可信中继进行通信时。交换诱导随机性后，Alice 和 Bob 进行后处理，生成用于密钥生成的高度相关的样本。然后将这些样本转换为比特，减少 Alice 和 Bob 生成的序列之间的差异，然后对所得序列进行散列，以补偿窃听者的信息泄漏，并允许对生成的密钥比特序列进行一致性检查。我们利用语义安全措施和信息论不等式，根据可数值计算的互信息测量来确定成功窃听攻击的概率。给定某些合理的系统参数，在第一种情况和第二种情况下，该界限在数值上分别评估为 2-31 和 2-10.57。