Secret Key Capacity for Ergodic Correlated Sources

隆太郎 松本, Ryutaroh Matsumoto

Kouya Tochikubo, Tomohiko Uyematsu, Ryutaroh Matsumoto

Karl-Ludwig Besser, Eduard Axel Jorswieck

Tzu-Han Chou, Stark Christiaan Draper, A.M. Sayeed

This paper investigates generation of a secret key from a reciprocal wireless channel. In particular we consider wireless channels that exhibit sparse structure in the wideband regime and study the impact of sparsity on the secret key capacity. We explore this problem in two steps. First, we study key generation from a state-dependent discrete memoryless multiple source. The state of the source captures the effect of channel sparsity. Secondly, we consider a wireless channel model that captures channel sparsity and correlation between the legitimate users' channel and the eavesdropper's channel. Such dependency can significantly reduce the secret key capacity. According to system delay requirements, two performance measures are considered: (i) ergodic secret key capacity and (ii) outage probability. We show that in the wideband regime when a white sounding sequence is adopted, a sparser channel can achieve a higher ergodic secret key rate than a richer channel can. For outage performance, we show that if the users generate secret keys at a fraction of the ergodic capacity, the outage probability will decay exponentially in signal bandwidth. Moreover, a larger exponent is achieved by a richer channel.

Amin Gohari, Onur Günlü, Gerhard G. Kramer

Jun Muramatsu, Kazuyuki Yoshimura, P. DAVIS

Secret key agreement is a procedure for agreeing on a secret key by exchanging messages over a public channel when a sender, a legitimate receiver (henceforth referred to as a receiver), and an eavesdropper have access to correlated sources. Maurer [6] defined secret key capacity, which is the least upper bound of the key generation rate of the secret key agreement, and presented an upper and a lower bound for the secret key capacity. The advantage distillation capacity is introduced and it is shown that this quantity equals to the secret key capacity. Naive information theoretical expressions of the secret key capacity and the advantage distillation capacity are also presented. An example of correlated sources, for which an analytic expression of the secret key capacity can be obtained, is also presented.