On the effect of colluding eavesdroppers on secrecy capacity scaling

In a powerful secrecy attack, eavesdroppers can collude, i.e., they can share their observations. Securing information in such a scenario will be an even more challenging task compared to non-colluding case. We here analyze the effect of eavesdropper collusion on the achievable performance in both the path loss and ergodic multi-path fading models. We provide two results: 1) For the Poisson point process model in a random extended network, if the legitimate nodes have unit intensity (λ = 1) and the colluding eavesdroppers have an intensity of λ
e
= O((log n)
^−(2+p)
) for any p > 0, almost all of the nodes can achieve a secure rate of Ω(1/√n); I and 2) In the K-user Gaussian interference channel with E external colluding eavesdroppers, a secure degrees of freedom of η =[1/2−E/K]
⁺
per frequency-time slot is achievable for each user in the ergodic setting (in the absence of the eavesdropper channel state information).