Secret Key Capacity under Maximal Leakage

Holger Boche, Rafael F. Schaefer, Sebastian Baur +1 more

Secret key generation refers to the problem of generating a common secret key without revealing any information about it to an eavesdropper. All users observe correlated components of a common source and can further use a noisy public channel for discussion, which is open to eavesdroppers. A related problem is that of secure authentication, which has structural similarities and connections to the first problem. For authentication, users need to be enrolled and securely authenticated while minimizing the privacy leakage rate. This paper studies the algorithmic computability of the forward secret key capacity and the secure authentication capacity. For the algorithmic computability, the concept of a Turing machine is used as it provides fundamental performance limits for today's digital computers. In this paper, it is shown that the forward secret key capacity with a noisy public channel is not computable and consequently, there is no algorithm that can simulate or compute the secret key capacity; even if there are no limitations on computational complexity and computing power. On the other hand, if the public channel is noiseless so that there are no rate constraints on the public communication, the secret key capacity is a computable continuous function, which is the strongest form of computability. A similar behavior is subsequently observed for the authentication problem: The secure authentication capacity under storage rate and privacy leakage rate constraints is not computable, while the case without privacy leakage rate constraints is computable.

Huimin Zhang, Yingbin Liang, Lifeng Lai +1 more

Amin Gohari, Onur Günlü, Gerhard G. Kramer

Hideichi Sasaoka, Hisato Iwai

Secret key agreement based on radio propagation characteristics attracts attention as a kind of the wireless physical layer security. However, there are few studies on drop of the secret key capacity by multiple spot eavesdropping. This paper derived theoretical formula of the secret key capacity in secret key agreement based on the complex channel coefficient. This paper also derived theoretical formula of the leakage information by multiple spot eavesdropping and showed that leakage information increased with the increase of the eavesdropping spot number. Validity of these theoretical formulas was confirmed by computer simulation. Then, this paper calculated the coefficient of correlation of the channel coefficient in the simple propagation environment and evaluated security of secret key agreement by calculating leakage information for multiple spot eavesdropping.

Vamoua Yachongka, Hideki Yagi, Yasutada Oohama

We analyze the fundamental trade-off of secret key-based authentication systems in the presence of an eavesdropper for correlated Gaussian sources. A complete characterization of the trade-off among secret-key, storage, and privacy-leakage rates of both generated and chosen secret models is provided. One of the main contributions is revealing that unlike the known results for discrete sources, there is no need for the second auxiliary random variable in characterizing the capacity regions for the Gaussian cases. In addition, it is shown that the strong secrecy for secrecy-leakage of the systems can be achieved by an information-spectrum approach, and the parametric expressions (computable forms) of the capacity regions are also derived.

Keming Tian, Gang Xin, Jian Zhang