CN109787757A - A kind of non-uniform quantizing method in physical layer key generation process - Google Patents
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Abstract
A kind of non-uniform quantizing method in safety of physical layer key generation process, the wireless signal strength RSS measured between legitimate correspondence both sides are modeled as the dimensional gaussian distribution that related coefficient is ρ, and related coefficient indicates the inequality degree between both sides' measured value；Standardization is done to the RSS value that each measurement obtains；To the identical non-uniform quantizing of 13 broken line PCM quantization methods on [0,1] section of RSS cumulative distribution function, is done, quantifies inverse function of the endpoint value Jing Guo RSS cumulative distribution function and be mapped in the domain RSS, as the endpoint quantified to RSS.The present invention does non-uniform quantizing using channel information intensity RSS cumulative distribution, compared with uniform quantization, has lower bit mismatch rate, provides better basis for subsequent information reconciliation step.
Description
Technical field
The present invention relates to wireless communication and field of information security technology, and in particular in a kind of physical layer key generation process
Non-uniform quantizing method.
Background technique
With the continuous development of the communication technology, wireless communication gradually occupies consequence in human lives.Due to electricity
The opening in magnetic space and the radiativity of electromagnetic signal transmission, the signal of communication that carry important information are fully exposed to free sky
Between in and wireless communication protocol standardization so that mobile data in transmission process be easy by illegal user eavesdropping,
Most likely result in the leakage of the personal important information such as privacy of user, finance.In safety of physical layer communication, wireless communication is utilized
The reciprocity characteristic of time-division system can be generated and shared key by measuring and encoding between two radio nodes.Due to
The difference of the spatial position of listener-in and legitimate correspondence, wireless channel is also different therewith, therefore the wireless communication based on randomness
The key that road obtains has good randomness and confidentiality.The classical process for obtaining shared key includes channel measurement, amount
Change, information reconciles, secrecy enhancing.
Existing wireless network card is not necessarily to any modification, so that it may the wireless signal strength (RSS) of each frame is measured, so
RSS is the radio channel characteristic parameter most generally used.However, RSS is easier to obtain data, but this parameter provides wirelessly
The coarse information of channel, often has extracting that key bit rate is lower and higher bit mismatch rate.
Summary of the invention
In order to reduce the bit mismatch rate of quantized segment in key generation process, the invention proposes a kind of physical layer keys
Non-uniform quantizing method in generating process.
In order to solve the above technical problem, the present invention provides following technical solutions:
A kind of non-uniform quantizing method in physical layer key generation process, it is described to be generated based on safety of physical layer key
Journey the following steps are included:
1) channel measurement: legitimate correspondence both sides obtain the two by measuring the received signal strength of common signal channel
Between with time fluctuation wireless signal strength RSS value；
2) quantify: being a string of key bits, the RSS obtained to each measurement by measured value non-uniform quantizing method migration
Value passes through standardization；The cumulative distribution function of RSS, in its [0,1] section, according to 1/2,1/4,1/8,1/16 ... length
Degree is divided, endpoint value (0,1/2,3/4,7/8,15/16 ..., 1) inverse function Jing Guo RSS cumulative distribution function is mapped to RSS
In domain, as the endpoint quantified to RSS
3) information reconciliation: a kind of information reconciliation protocol of application abandons or corrects the difference of communicating pair key bit.
4) secrecy enhancing: abandoning the consistent bit in part or executes certain bits switch to strengthen key, increases key
Entropy and the local message that may be obtained in a upper information reconciliation step of fuzzy listener-in.
Further, the RSS that legitimate correspondence both sides measure is modeled as dimensional gaussian distribution, joint probability density function
For
Wherein, Ri,μi,I ∈ { A, B } respectively indicates each measurement of communicating pair Alice and Bob and obtains the random of RSS
Variable, corresponding mean value and variance；Correlation coefficient ρ is used to measure channel inequality degree, is defined as
According to the heterogeneite theorem of channel, the RSS that communicating pair measures within the coherence time of wireless channel should
It is identical；However, since the inconsistency of interchannel noise, the half-duplex property of wireless channel and physical device causes to measure
What is be worth is inconsistent；The size that reciprocity degree is indicated using related coefficient, when ρ=0 indicate uplink and downlink channel it is mutually indepedent, do not deposit
In reciprocity；The complete reciprocity of uplink and downlink channel is indicated as ρ=1.
Further, it is deduced bit mismatch rate closed solution when two level uniform quantizations；It is combined by deriving
Mathematica numerical integration calculates, it is indicated that four level uniform quantizations are a kind of bit mismatch rate highest quantization method, mistake
Journey is as follows:
The case where for the quantization of two level, the mean μ for the RSS that legitimate correspondence both sides Alice and Bob is received with oneself is
Quantify line of demarcation namely quantized interval is S0,i=(- ∞, μi], S1,i=(μi,+∞), i={ A, B }, with Alice's and Bob
In the two-dimensional Cartesian system that RSS is constituted, quantify in (S0,A,S1,B) and (S1,A,S0,B) section when, quantization bit is mismatch
, bit mismatch rate are as follows:
In formula,Wherein ρ is related coefficient, is used
To indicate the inequality degree of channel；
Wherein RNA、RNBIt is RA、RBIt is obtained after standardized normal distribution is handled, namely:
Wherein Ri,μi,I ∈ { A, B } respectively indicates the stochastic variable, corresponding mean value and variance of communicating pair RSS；
Four level are quantified, corresponding quantized interval uses Gray code, mismatch ratio are as follows:
In formula, cxAnd cyIndicate the endpoint variables divided to RSS；Pr(QRA≠QRB) indicate to Alice's and Bob
RSS is quantified, quantization bit QRA、QRBInconsistent probability；To the variable c in formulax、cyLocal derviation is sought respectively, and enabling it is 0,
After arranging, obtain
With
Wherein, complementary error function is defined as
According to symmetry, formula (6) and (7) are set up simultaneously, then cx=cy=c, therefore obtain
Numerical value calculating is carried out to formula (8) and is fitted, fit equation are as follows:
C=-2.3 ρ4+3.4ρ3-1.9ρ2+0.3ρ+0.66 (9)
Quantization threshold c when bit mismatch rate highest is substantially in [0.6,0.7] region, and amount when uniform quantization scheme
Change threshold valueIt falls in this section, so uniform quantization is a kind of highest amount of key mismatch ratio
Change method.
Further, for four level non-uniform quantizings, legitimate correspondence both sides Alice and Bob carries out the RSS received
After standard normalization processing, key mismatch ratio are as follows:
Wherein
It is calculated by Mathematica numerical integration, compared with the bit mismatch rate that uniform quantization method obtains, is proposed
Non-uniform quantizing method mismatch ratio be lower than uniform quantization method.
Design of the invention are as follows: existing wireless network card is not necessarily to any modification, so that it may measure the channel information of each frame
The value of intensity RSS, so RSS is the radio channel characteristic parameter most generally used.But there are problems, although RSS compares appearance
Data are easily obtained, but this method only provides the coarse information of wireless channel, it is lower often to extract key bit rate, and deposit
In higher bit mismatch rate.The radio signal strength measurement value RSS of Alice and Bob is modeled as the two dimension that related coefficient is ρ
Gaussian Profile, related coefficient indicate that both sides' measured value obtains inequality degree；Standardization is done to the RSS value that each measurement obtains；
On [0,1] section of RSS cumulative distribution function after processing, the identical non-uniform quantizing of 13 broken line PCM quantization methods is done, namely
Length according to 1/2,1/4,1/8,1/16 ... is quantified, endpoint value (0,1/2,3/4,7/8,15/16 ..., 1) it is tired by RSS
The inverse function of product distribution function is mapped in the domain RSS, as the endpoint quantified to RSS Gray code is used to the bit after quantization simultaneously, reduces bit mismatch rate.
The invention has the benefit that non-uniform quantizing is done using channel information intensity RSS cumulative distribution, with uniform quantization
It compares, there is lower bit mismatch rate, provide better basis for subsequent information reconciliation step.
Detailed description of the invention
Fig. 1 show four level any quantization schematic diagrames
Fig. 2 show four level quantization thresholds and bit mismatch rate relational graph
Fig. 3 show quantized interval schematic diagram corresponding to four level non-uniform quantizing schemes
Fig. 4 show the relational graph between different quantization methods and correlation coefficient ρ
Specific embodiment
With reference to the accompanying drawing, the invention will be further described.
Referring to Fig.1~Fig. 4, a kind of non-uniform quantizing method in physical layer key generation process, comprising the following steps:
1) channel measurement: legitimate correspondence both sides (referred to as Alice and Bob) pass through measurement common signal channel received signal strength,
And then obtain between the two with time fluctuation RSS value；
2) quantify: being a string of key bits by measured value quantization method migration；
3) information reconciliation: although the cross correlation of channel measurement can be improved using Signal Pretreatment algorithm, quantization
Inconsistent key bit is still had between Alice and Bob afterwards, namely there are bit mismatch rates.Information reconciliation can be used
Technology come correct both ends generation key bit difference；
4) secrecy enhancing: abandoning the consistent bit in part or executes certain bits switch to strengthen key, increases key
Entropy and the local message that may be obtained in a upper information reconciliation step of fuzzy listener-in.
The quantizing process of the step 2), namely a kind of non-uniform quantizing method is proposed, to reduce legitimate correspondence both sides
Between bit mismatch rate.
In the quantizing process, theory of random processes is pointed out: it is F that given one, which has cumulative distribution function,X(x)
Stochastic variable X, constructed fuction g (x)=FX (x), so that stochastic variable Y=g (X) obedience [0,1] is uniformly distributed namely Y=FX
(X)~U (0,1).Based on this, uniform quantization method is: it is assumed that the cumulative distribution function F of RSSX(x) it is known that [0,1] first-class
Every being divided into M section, then it is to the RSS received the endpoint for carrying out uniform quantization
HereIt is the inverse function of cumulative distribution function；RSS is modeled as Gaussian Profile, therefore constructed fuction is
Wherein complementary error function
Normal distribution is modeled as the RSS (unit dB) of Alice and Bob, i.e.,
i∈{A,B}；The RSS of down channel has heterogeneite thereon, is modeled as dimensional Gaussian point
Cloth, joint probability density function are
Wherein, Ri,μi,I ∈ { A, B } respectively indicates each measurement of communicating pair Alice and Bob and obtains the random of RSS
Variable, corresponding mean value and variance；Correlation coefficient ρ is used to measure channel inequality degree, and correlation coefficient ρ is defined as
Wherein E [X] expression does desired operation to stochastic variable X；
Here μi,I ∈ { A, B } respectively indicates the mean value and variance for receiving RSS of Alice and Bob.According to channel
Heterogeneite theorem, the uplink and downlink channel measurement of Radio Link should be identical；However, due to interchannel noise, wireless channel
The factors such as half-duplex property and the inconsistency of physical device cause the inconsistent of measured value, to there is quantization bit mismatch
Rate problem.Herein, the size of reciprocity degree is indicated using correlation coefficient ρ；Obviously, when ρ=0 indicates that uplink and downlink channel is mutual
It is independent, reciprocity is not present；The complete reciprocity of uplink and downlink channel is indicated as ρ=1.
The case where for the quantization of two level, the mean μ for the RSS that Alice and Bob are received with oneself are quantization line of demarcation,
Namely quantized interval is S0,i=(- ∞, μi],S1,i=(μi,+∞), i={ A, B }.The two dimension constituted with the RSS of Alice and Bob
In cartesian coordinate system, quantify in (S0,A,S1,B) and (S1,A,S0,B) section when, quantization bit is mismatch, the probability of mismatch
For；
In formula,Wherein ρ is related coefficient, is used
To indicate the inequality degree of channel；
Wherein RNA、RNBIt is RA、RBIt is obtained after standardized normal distribution is handled, namely:
Wherein Ri,μi,I ∈ { A, B } respectively indicates the stochastic variable, corresponding mean value and variance of communicating pair RSS.
Therefore the bit mismatch rate of two level quantization are as follows:
In present implementation, in the quantizing process, referring to Fig.1, for the quantization of four level, it is deduced quantization end
Relationship between point and mismatch ratio.Assuming that quantization encoding is Gray code, i.e. adjacent interval differs a bit.Corresponding quantization area
Between be encoded to " 00 ", " 01 ", " 11 " and " 10 ".R in Fig. 1NAAnd RNBBy formula (5) standardization.
If RNA∈(-∞,-cx) section, then Alice is encoded to " 00 ".At this time, it is assumed that RNB∈(-cy, 0), Bob coding
For " 01 ".Alice and Bob only one quantization bit is different, and their correspondence probability be Alice and Bob joint it is general
The half of integral of the rate density function on the section can more intuitively show that the bit of four level quantization loses referring to Fig.1
With rate are as follows:
To any correlation coefficient ρ, enable quantization threshold c value range be [0,3] (for Gaussian Profile, stochastic variable
Most values fall in this section), then formula (7) are substituted into, numerical integration is carried out by Mathematica software, is obtained such as Fig. 2 institute
The relation curve between quantization threshold and mismatch ratio under the cluster difference related coefficient shown.It can be seen that referring to Fig. 2 with amount
Change the increase of threshold value c, bit mismatch rate increases.When c is some value, bit mismatch rate is maximum, then reduces therewith.
For formula (7), key mismatch ratio is to variable cx,cyLocal derviation is sought respectively, and enabling it is 0.
After arranging, obtain
With
According to symmetry, if formula (8) and (9) are set up simultaneously, cx=cy=c, therefore obtain
Numerical value calculating is carried out to formula (10) and is fitted, fit equation are as follows:
C=-2.3 ρ4+3.4ρ3-1.9ρ2+0.3ρ+0.66 (9)
In conjunction with Fig. 2, formula (11) is indicated under different related coefficient, quantization threshold c when maximal bit mismatch ratio.Especially
When related coefficient is relatively small, quantization threshold when mismatch ratio maximum is substantially in [0.6,0.7] region, and uniform quantization scheme
When quantization threshold Fall in this section, thus uniform quantization be a kind of bit mismatch rate most
Big quantization method.
By the inspiration of 13 broken line non-uniform quantizings in Principle of Communication, when RSS amplitude is smaller, it is easy to be made an uproar by channel
Inconsistency of sound, receiving-transmitting sides component etc. influence, the bit after quantization be it is insecure, quantized interval should be larger；
Conversely, strong antijamming capability, the matching rate of bit is relatively high after quantization when RSS amplitude is larger, quantized interval can be with small by one
A bit.A kind of non-uniform quantizing method is proposed based on this in order to improve the matching rate and generating rate of bit.Alice and Bob
After being standardized to the RSS received, quantized interval is divided as shown in figure 3, wherein
Referring to Fig. 3, bit mismatch rate are as follows:
Wherein
It is calculated under the quantization of four level by Mathematica, the numerical integration of bit mismatch rate is as a result, as shown in Figure 4.
Figure 4, it is seen that the bit mismatch rate of the non-uniform quantizing method proposed is lower than in the case where identical related coefficient
Uniform quantization method.
Claims (4)
1. a kind of non-uniform quantizing method in physical layer key generation process, it is characterised in that: described to be based on safety of physical layer
Key generation process the following steps are included:
1) channel measurement: legitimate correspondence both sides are obtained between the two by measuring the received signal strength of common signal channel
With the wireless signal strength RSS value of time fluctuation；
2) quantify: being a string of key bits by measured value non-uniform quantizing method migration, the RSS value that each measurement obtains is passed through
Cross standardization；The cumulative distribution function of RSS, in its [0,1] section, according to 1/2,1/4,1/8,1/16 ... length into
Row divides, endpoint value (0,1/2,3/4,7/8,15/16 ..., 1) inverse function Jing Guo RSS cumulative distribution function is mapped to the domain RSS
In, as the endpoint quantified to RSS
3) information reconciliation: a kind of information reconciliation protocol of application abandons or corrects the difference of communicating pair key bit.
4) it secrecy enhancing: abandons the consistent bit in part or executes certain bits switch to strengthen key, increase the entropy of key
And the local message that fuzzy listener-in may obtain in a upper information reconciliation step.
2. the non-uniform quantizing method in a kind of physical layer key generation process as described in claim 1, it is characterised in that:
The RSS that legitimate correspondence both sides measure is modeled as dimensional gaussian distribution, and joint probability density function is
Wherein, Ri,μi,I ∈ { A, B } respectively indicates each measurement of communicating pair Alice and Bob and obtains the random change of RSS
Amount, corresponding mean value and variance；Correlation coefficient ρ is used to measure channel inequality degree, is defined as
Wherein E [X] expression does desired operation to stochastic variable X；
According to the heterogeneite theorem of channel, the RSS that communicating pair measures within the coherence time of wireless channel should be phase
With；However, since the inconsistency of interchannel noise, the half-duplex property of wireless channel and physical device causes measured value
It is inconsistent；The size that reciprocity degree is indicated using related coefficient, when ρ=0 indicates that uplink and downlink channel is mutually indepedent, there is no mutual
Yi Xing；The complete reciprocity of uplink and downlink channel is indicated as ρ=1.
3. the non-uniform quantizing method in a kind of physical layer key generation process as claimed in claim 2, it is characterised in that: push away
It is derived bit mismatch rate closed solution when two level uniform quantizations；Mathematica numerical integration is combined to calculate by deriving,
Point out that four level uniform quantizations are a kind of highest quantization method of bit mismatch rate, process is as follows:
The case where for the quantization of two level, the mean μ for the RSS that legitimate correspondence both sides Alice and Bob is received with oneself is quantization
Line of demarcation namely quantized interval are S0,i=(- ∞, μi], S1,i=(μi,+∞), i={ A, B }, with the RSS structure of Alice and Bob
At two-dimensional Cartesian system in, quantify in (S0,A,S1,B) and (S1,A,S0,B) section when, quantization bit is mismatch, bit
Mismatch ratio are as follows:
In formula,Wherein ρ is related coefficient, is used to table
Show the inequality degree of channel；
Wherein RNA、RNBIt is RA、RBIt is obtained after standardized normal distribution is handled, namely:
Wherein Ri,μi,I ∈ { A, B } respectively indicates the stochastic variable, corresponding mean value and variance of communicating pair RSS；
Four level are quantified, corresponding quantized interval uses Gray code, mismatch ratio are as follows:
In formula, cxAnd cyIndicate the endpoint variables divided to RSS；Pr(QRA≠QRB) indicate to the RSS of Alice and Bob into
Row quantization, quantization bit QRA、QRBInconsistent probability；
To the variable c in formulax、cyLocal derviation is sought respectively, and enabling it is 0, after arranging, is obtained
With
Wherein, complementary error function is defined as
According to symmetry, formula (6) and (7) are set up simultaneously, then cx=cy=c, therefore obtain
Numerical value calculating is carried out to formula (8) and is fitted, fit equation are as follows:
C=-2.3 ρ4+3.4ρ3-1.9ρ2+0.3ρ+0.66 (9)
Quantization threshold c when bit mismatch rate highest is substantially in [0.6,0.7] region, and quantization threshold when uniform quantization scheme
ValueIt falls in this section, so uniform quantization is a kind of highest quantization side of key mismatch ratio
Method.
4. the non-uniform quantizing method in a kind of physical layer key generation process as claimed in claim 3, it is characterised in that: right
In 4 level non-uniform quantizings, after legitimate correspondence both sides Alice and Bob carries out standard normal processing to the RSS received,
Key mismatch ratio are as follows:
Wherein,
It is calculated by Mathematica numerical integration, compared with the bit mismatch rate that uniform quantization method obtains, what is proposed is non-
The mismatch ratio of uniform quantization method is lower than uniform quantization method.
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