Patwari

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Patwari et al. presents a framework, called high rate uncorrelated bit extraction (HRUBE), which interpolates the signal first. After that it is decorrelated by transformation. In the last step a multi-bit quantization is used, where several Bits are quanitzed at once. This can reach 22 Bits/s with a inconsistency of 2.2%.

Introduction

Secret key can be calculated by two parties via Radio-Channel. With the raising entropy in calculations (caused by external influences like the texture of the room, noise), the solution of the calculations get better. E.g. reflections have a big influence on a good result. In addition to that the reciprocity of the channel, the fact, that both parties can notice the identical parameters at the same time in the channel, lead to better results. The fact, that the signal is different in every location, helps to exchange a secret. The problem is, that the channel offers reciprocity, but the measurement does not. In this case both parties get different results. This is caused by bigger noise on the channel, or by different hardware, which is used by the communicating partners. The secret (in Bits) has to be calculated out of the received signals. This is done with a quantizer. In this page we will describe the quantizer by Patwari et al.


Adversary Modell

For the presented modell of Patwari et al. it is assumed, that there is a passive attacker, that only listens and calculates. The attacker is not able to attack one party directly. The attacker is allowed zu listen to each communication between parties Aand B. Furthermore the attacker is allowed to make measurements of the channel from himself to A and to B, while A and B do Measurements of channels A to B or B to A. The attacker knows the algorithm to extract the keys including their parameters. It is assumed, that the attacker is not in close proximity, while A and B are calculating the key. This ensures, that the attacker measures an uncorrelated channel. Another assumption is, that the attacker is not able to jam the communicationchannel between A and B. Furthermore the attacker cannot do a MITM Attack against A or B.

Description

The measured signal is transferred with three methods to the resulting Bitstring (shared secret). In the beginning the signle signals are interpolated (see following paragraph). In detail: After receiving of signals there is a delay, which offers the opportunity, that measurments of party A and B, which are not done simultaneously, are now simultaneously again. After that the result of the interpolation is decorrelated with the de-correlation transformation. The result is a vecotr with uncorrelated components, which is caluculated through the Karhunen-Loeve Transformation over the previous measurements. In the third and final step the values of the vector are converted to Bits with a quantization (multi-bit adaptive quantization (MAQ), which is equals the final result. This uses communication between A and B again, so that these get the same results.

Fractional Interpolation Filtering

Since the sending of signals from A to B and from B to A cannot be parallel(due to the omnipresent minimal time variance, because most transceivers cannot parallel send and receive), it is attempted, with the help of the fractional interpolation (the interpolation in parts), to simulate, that signals are parallel sent or parallel measured. Patwari et al. wanted to reach a constant sending rate, so the set Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/wikimedia.org/v1/":): {\displaystyle T_{R,x} = T_{R,y} = T_R} . With the usage of a farrow filter [1], delays can be built in. As parameter the filter takes the value of the delay for the certain patry, as well as the measurements of the party. The delay of party A equals the formula Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/wikimedia.org/v1/":): {\displaystyle μ_a = 1/2 * (((t_b(i) - t_a(i)) / T_R);} for party B Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/wikimedia.org/v1/":): {\displaystyle μ_b = 1-μ_a} . The filter leads to:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/wikimedia.org/v1/":): {\displaystyle h_c = [\frac{\mu_c^3}6-\frac{\mu_c}6,-\frac{\mu_c^3}2+\frac{\mu_c^3}2+\mu_c,\frac{\mu_c^3}2-\mu_c^2-\frac{\mu_c}2,-\frac{\mu_c^3}6+\frac{\mu_c^2}2-\frac{\mu_c}3]^T}

c is here a placeholder for party A or B. Output are Vectors Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/wikimedia.org/v1/":): {\displaystyle x_a(i)} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/wikimedia.org/v1/":): {\displaystyle x_b(i)} .
  1. C.Farrow "A continuously variable digital delay element"