Secret Keys from Channel Noise

Hadi Ahmadi, Reihaneh Safavi–Naini

Meixiang Zhang, Xueqin Jiang, Yu‐Ting Huang

Physical-layer secret key generation is a meaningful approach to enhance the security of wireless links by taking advantages of wireless channels. However eavesdroppers may obtain the secret key bits if their channels become correlated to the legitimate channels. In this paper, to increase the mismatch rate at the eavesdroppers, we propose a new secret key generation scheme for polar coded multiple-input multiple-output (MIMO) systems by applying MIMO precoding and adding signal-like noise on the transmitted signals. Furthermore, considering the channel polarization phenomenon of polar codes, we propose to adaptively send messages that are used for secret key generation over the less reliable channel-bits of eavesdroppers. In addition, we propose to add randomness to messages to ensure that eavesdroppers are unable to generate the secret key bits even when their channels are highly correlated to the legitimate channels. Simulation results demonstrate that our proposed scheme prevents eavesdroppers to generate the secret key with an extremely high probability.

Himanshu Tyagi, Shun Watanabe

Yan Feng, Xueqin Jiang, Jia Hou +2 more

The classical secret-key agreement (SKA) scheme includes three phases: (a) advantage distillation (AD), (b) reconciliation, and (c) privacy amplification. Define the transmission rate as the ratio between the number of raw key bits obtained by the AD phase and the number of transmitted bits in the AD. The unidirectional SKA, whose transmission rate is 0 . 5, can be realized by using the original two-way wiretap channel as the AD phase. In this paper, we establish an efficient bidirectional SKA whose transmission rate is nearly 1 by modifying the two-way wiretap channel and using the modified two-way wiretap channel as the AD phase. The bidirectional SKA can be extended to multiple rounds of SKA with the same performance and transmission rate. For multiple rounds of bidirectional SKA, we have provided the bit error rate performance of the main channel and eavesdropper’s channel and the secret-key capacity. It is shown that the bit error rate (BER) of the main channel was lower than the eavesdropper’s channel and we prove that the transmission rate was nearly 1 when the number of rounds was large. Moreover, the secret-key capacity C s was from 0 . 04 to 0 . 1 as the error probability of channel was from 0 . 01 to 0 . 15 in binary symmetric channel (BSC). The secret-key capacity was close to 0 . 3 as the signal-to-noise ratio increased in the additive white Gaussian noise (AWGN) channel.

Ashish J. Khisti

The secret-key agreement problem over wiretap channels controlled by a state parameter is studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. In absence of public-discussion, our lower bound is strictly better than the best known lower bound for transmitting an independent secret message. This illustrates that the coding schemes for secret-key agreement are substantially different than secret-message transmission. For the special case of Gaussian channels, we establish the secret-key capacity when the legitimate receiver's signal-to-noise-ratio is greater than 0 dB. When a public discussion channel is available between the sender and the receiver, upper and lower bounds on the secret-key capacity are again established. These bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an independent noise condition.

Ueli M. Maurer, Renato Renner, Stefan Wolf