Robust secret key extraction from channel secondary random process

TLDR: This paper proposes a new simple technique to generate the secret key that mitigates the effect of noise and exploits the estimated channel to generate a secondary random process SRP that is common between the two legitimate nodes.

Abstract: The vast majority of existing secret key generation protocols exploit the inherent randomness of the wireless channel as a common source of randomness. However, independent noise added at the receivers of the legitimate nodes affects the reciprocity of the channel. In this paper, we propose a new simple technique to generate the secret key that mitigates the effect of noise. Specifically, we exploit the estimated channel to generate a secondary random process SRP that is common between the two legitimate nodes. We compare the estimated channel gain and phase to a preset threshold. The moving differences between the locations at which the estimated channel gain and phase exceed the threshold are the realization of our SRP. We study the properties of our generated SRP and derive a closed form expression for the probability mass function of the realizations of our SRP. We simulate an orthogonal frequency division multiplexing system and show that our proposed technique provides a drastic improvement in the key bit mismatch rate between the legitimate nodes when compared with the techniques that exploit the estimated channel gain or phase directly. In addition to that, the secret key generated through our technique is longer than that generated by conventional techniques. Moreover, we compute the conditional probabilities used to estimate the secret key capacity. Copyright © 2016 John Wiley & Sons, Ltd.

Figures

Fig. 2: Flow chart of SRP creation for channel gain at Alice.

Fig. 6: Probabilities for channel phase SRP.

Fig. 8: Normalized key length as a function of SNR for our scheme vs. existing techniques.

Fig. 7: Entropy as a function of SNR for our scheme vs. existing techniques.

TABLE II: Simulation parameters

Fig. 1: Typical steps for SKG.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Robust secret key extraction from channel secondary random process" ?

In this paper, the authors propose a new simple technique to generate the secret key that mitigates the effect of noise. The authors study the properties of their generated SRP and derive a closed form expression for the probability mass function of the realizations of their SRP. The authors simulate an orthogonal frequency division multiplexing ( OFDM ) system and show that their proposed technique provides a drastic improvement in the key bit mismatch rate ( BMR ) between the legitimate nodes when compared to the techniques that exploit the estimated channel gain or phase directly. 

Q2. What is the advantage of the combined SRP technique?

The reduction in entropy resulting from their method which is associated with significant reduction in BMR has the advantage that less exchange of messages is needed in the subsequent phases of information reconciliation and privacy amplifications. 

Q3. What is the probability of overwriting the initial zero in Sg?

To find a closed form expression for the probability mass function of each entry in Jg , which the authors denote by P (Jg[i] = jg), the authors use the Lagrange interpolating polynomial formula [23]. 

Q4. What is the probability of success for the channel phase?

The channel phase, θ, follows a uniform distribution with probability density function defined as:f(θ) = 12π , for 0 ≤ θ ≤ 2π (16)Hence,pph = 1− γph 2π . 

Q5. What is the step to generate the SRP?

The steps to generate their SRP are:1) Both Alice and Bob use their estimated channel gain to estimate a threshold (γg) as:γAg = E[|ĤALS |] + α std(|ĤALS |) (8) γBg = E[|ĤBLS |] + α std(|ĤBLS |), (9)where E[.] is the mean operation, std(.) is the standard deviation operation and α is a design parameter ∈ [−1 : 1]. 

Q6. What is the effect of the frequency of channel propping on the secret key?

This implies that for the level crossing rate technique to achieve a reasonable key length, the frequency of channel propping should increase which decreases the throughput of the system. 

Q7. What is the typical step in the SKG technique?

In the first step, Alice and Bob exchange beacon signals, from which each estimates the physical layer characteristics that are used as common sources of randomness. 

Q8. What is the probability of overwriting the initial zero in jg?

the entry in Jg is 1 with probability lg(vg, ug) lg(vg + 1, ug + 1). • Case 3: the first (out of the two producing Jg entry) entry is zero and the second is a value of the NB randomvariable.