CN111246463B - Covert communication method based on skew parameter of alpha stable distribution random process - Google Patents
Covert communication method based on skew parameter of alpha stable distribution random process Download PDFInfo
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Abstract
A hidden communication method based on skew parameters in an alpha stable distribution random process is characterized in that a skewed alpha stable distribution random sequence is used as a carrier, and hidden bits transmitted by legal users modulate the polarity of the skew of the carrier sequence in front and back half bit periods to enable the absolute values of the carrier sequences to be the same but the polarities of the carrier sequences to be opposite, so that hidden signals in the whole bit period have the characteristic of symmetrical alpha stable distribution; the covert signal transmitted by this method is very similar to the symmetric alpha-stationary distributed interference present in many wireless communication networks, so that the presence of covert communication is not easily perceived by an eavesdropper. The invention provides an estimation formula of skewness with very small calculation amount and deduces a corresponding probability density function to obtain a bit error rate formula, and indicates the relationship between the bit error rate and the characteristic index, the skewness and the sample number. The invention has the advantages of easy realization, low requirement on the computing performance of equipment and better concealment.
Description
Technical Field
The invention relates to the technical field of wireless communication and information security, in particular to a covert communication method based on skewness parameters of an alpha stable distribution random process.
Background
In daily life, communication technologies such as LTE, 5G, wiFi, and the like are becoming increasingly common. Currently and in the future, the issue of protecting the communication security involved in personal privacy, property data, etc. is receiving increasing attention. One approach is to encrypt the network connection between the transport layer and the application layer through SSL and TLS. However, another problem is introduced during encryption, and encryption technology encrypts plaintext into a bunch of messy codes and reminds an eavesdropper that important information exists in transmitted data. Another method is to use a covert communication method, so that the transmitted covert signal has a random characteristic similar to that of environmental interference, and an eavesdropper cannot distinguish the source of noise (from the covert signal transmitted by a legitimate user or the environmental interference under multiple users). Therefore, the existence of hidden transmission of a legal user cannot be detected under the strict monitoring of an eavesdropper, and the transmitted information is not cracked, so that the key that the important information of the user is not eavesdropped is realized.
Many documents state that in wireless networks such as ad hoc, wi-Fi, cellular and LET, multiple access interference follows a symmetrical alpha-stationary distribution rather than the generally assumed gaussian (normal) distribution. The invention provides a hidden communication method hidden in environmental interference by utilizing skewness parameters in alpha stable distribution.
Disclosure of Invention
In order to overcome the defects of the prior art and enable a legal user to realize the safe transmission of the covert data, the invention provides a covert communication method based on an alpha stable distribution random process skew parameter, which is easy to realize, has low requirement on the calculation performance of equipment and has better concealment.
The invention provides the following technical scheme:
a hidden communication method based on alpha stable distribution random process skewness parameter comprises information hiding processing of a sending end of a hidden communication system and information recovery processing of a receiving end of the hidden communication system;
the information hiding processing of the sending end of the covert communication system comprises the following steps:
1-1: a stationarity distribution noise generator is used to generate a random distribution sequence following an alpha stationarity distribution with a characteristic index of alpha and a skewness of beta, denoted as S (alpha, beta), in a bit period T b Has N random sequences, marked as { X k ，k＝1，...，N}；
1-2: the masked bit b, encoded by Manchester, at an intermediate time of each bit period, i.e. T b At/2, a jump occurs; if b =1, a transition is made from low level to high level; if b =0, the level jumps from high level to low level, the single polarity and the double polarity are changed, and unipolar '0' and unipolar '1' are respectively changed into bipolar '-1' and bipolar '+1';
1-3: the random sequence output by the stably distributed noise generator is multiplied by the reversed '-1' of single and double polarity, and the polarity of the skewness is changed, namely the random sequence of S (alpha, -beta) distribution is obtained; multiplied by '+1', still a random sequence of S (α, β) distribution;
thus, if the concealment bit b =0, the random sequence s of the first half bit period 0 ＝{-X k K = 1...., N/2} is a random sequence obeying S (α, - β) distribution, and a random sequence S of the second half bit period 1 ＝{X k K = N/2.., N } is a random sequence that follows a distribution of S (α, β); conversely, if the concealed bit b =1, the random sequence s of the first half bit period 0 ＝{X k K = 1.... N/2} is a random sequence that follows S (α, β) distribution, and a random sequence S of the second half of the bit period 1 ＝{X k K = N/2.., N } is a random sequence that follows a S (α, - β) distribution;
the information recovery processing of the covert communication system receiving end comprises the following steps:
2-1: in the case of synchronization, the receiving end is in one bit period T b After demultiplexing the received N random sequences, dividing the N random sequences into 2 sequences with the length of N/2, namely r = [ r ] 0 ，r 1 ](ii) a Then make a pair of r 1 X (-1) processing such that the skewness sign is the same for the first and second half bit periods; then multiplexing, combining the 2 random sequences with the length of N/2 into a random sequence with the length of N, and recording the random sequence as a random sequence with the length of N
Under ideal channel, i.e. without attenuation, delay and noise, it is obvious that
2-2: from length N
In the random sequence, an estimate of the parameter skewness is estimated>
The estimated value of skewness is
2-3: by hard decision, obtainEstimation to concealed bits
The hard decision rule is:
further, the estimated value of skewness
Has a probability density function of
In the formula (I), the compound is shown in the specification,
on the basis, the estimator is an approximate unbiased estimation obtained by numerical integration through mathematic mathematical tool software, and when the characteristic index alpha tends to 1 or 2, the variance becomes large, and the performance of the estimator is deteriorated.
Still further, when the hidden bits '0', '1', etc. are at equal probability, the bit error rate ρ under the ideal channel is
Wherein Pr (e) represents the probability of event Pr (e); sign (t) is a sign function, which is defined as
The error function Erf (z) is defined as
The equation indicates the relationship between the bit error rate and the characteristic index α, the skew β and the number of samples N.
Further, in the case of an additive white Gaussian noise channel, the divergence ratio is defined as
Where gamma is the divergence of the alpha plateau,
the bit error rate is reduced with the increase of the divergence ratio, but a bit error rate platform exists, and when the divergence ratio tends to be infinite, the value of the bit error rate platform is the bit error rate of an ideal channel. The technical conception of the invention is as follows: a covert communication system includes a covert transmitter and a receiver. At a transmitting end, concealed bits modulate the skewness beta parameter of alpha stably distributed random noise; at the receiving end, the skewness beta value is estimated, and therefore the hidden bits are recovered.
The transmitter in the covert communication system has '0' for covert bits b, transmits S (alpha, -beta) distributed random distribution noise in the first half bit period, and transmits S (alpha, beta) distributed random distribution noise in the second half bit period; for the masked bit b of '1', the first half of the bit period is transmitted with the randomly distributed noise of S (α, β) distribution, and the second half of the bit period is transmitted with the randomly distributed noise of S (α, - β) distribution. Each bit period has a total of { X } k K = 1.., N samples of alpha-stationary random process. The skewness of the N/2 samples before and after the N samples is different, but noise with symmetrical alpha stable distribution is presented in the whole bit period, namely the skewness beta of the whole sample is 0, and the noise is similar to the environmental noise which is subjected to symmetrical alpha stable distribution in a wireless network.
A receiver in the covert communication system obtains a synchronous position through the fraction low-order covariance; obtaining the estimated value of skewness from the received N samples of one bit period through symbol fraction low-order moment
And obtaining the estimation of the hidden bit through hard decision. />
The hidden signal transmitted by the invention is similar to the environmental interference in the wireless network, i.e. an eavesdropper cannot easily distinguish whether the received signal is the environmental interference or the hidden signal, and the hidden signal has strong concealment. In addition, the structure of the covert communication system is unknown to the eavesdropper, which increases the difficulty of hacking by the eavesdropper.
Before the structure of a covert communication system is given, an alpha stable distribution is introduced. The random process has no closed probability density function expression and is defined by its characteristic function as
Φ X (t)＝exp[-iδt-|σt| α (1-iβsign(t)ξ(t，α))]
Here exp [ ·]An exponential function is defined as the function of the exponent,
the constant alpha is belonged to (0, 2)]Called characteristic index (characteristic exponent), beta e [ -1,1]Called skewness (shewness), σ ∈ R + Called scale, γ = σ α Called divergence (dispersion) and δ ∈ R as position (location). Note that the alpha stable distribution is S (α, β, σ, δ), and in the present invention, δ =0, σ =1, and is abbreviated as S (α, β) unless otherwise specified. If a random variable X obeys an alpha stable distribution, it is marked as X-S (alpha, beta).
The hidden bit to be transmitted is converted into an alpha stable distribution random sequence with opposite skewness symbols in the front half bit period and the rear half bit period, but the whole sequence presents the characteristic of symmetrical alpha stable distribution, is similar to the environmental interference in a wireless network, and is insensitive to an eavesdropper, so that the aim of hidden communication is fulfilled.
The invention has the beneficial effects that: the skewness estimation method based on the symbolic score low-order moment has low calculation complexity, and is suitable for calculating the Internet of things and the likeIn weaker equipment; gives the skewness
The probability density function formula and the bit error rate formula of the covert communication system obtain the performance of the covert communication system.
Drawings
Fig. 1 is a block diagram of a covert communication system.
Fig. 2 shows the fractional low-order covariance when α =1.43, β =0.5, and N = 400.
Fig. 3 is a graph of the estimator probability density function for α =1.43, β =0.8, N = 1000.
Fig. 4 is the mean of the estimators at α < 1, N = 1000.
Fig. 5 shows the variance of the α < 1, N =1000 estimator.
Fig. 6 shows the bit error rate for an ideal channel with a =0.5 and different numbers of samples.
Fig. 7 shows the bit error rate for α =0.5 for different numbers of samples in an additive white gaussian noise channel.
Detailed Description
The present invention will now be described in detail with reference to the accompanying drawings.
Referring to fig. 1-7, a covert communication method based on alpha stable distribution random process skewness parameter includes information hiding processing at the transmitting end of covert communication system and information recovery processing at the receiving end of covert communication system,
the information hiding processing of the sending end of the covert communication system comprises the following steps:
1-1: generating a randomly distributed sequence obeying an S (alpha, beta) distribution with a steadily distributed noise generator, with a bit period of T b At a T b Has N random sequences, marked as { X k ，k＝1，...，N}；
1-2: the masked bit b, encoded by Manchester, at an intermediate time of each bit period, i.e. T b At/2, a jump occurs, if b =1, from low level to high level; if b =0, the level is changed from high level to low levelChanging the unipolar '0' and '1' into bipolar '1' and '1', respectively;
1-3: the random sequence output by the stably distributed noise generator is multiplied by the '-1' of the single and double polarity transformation, and the polarity of the skewness is changed, namely the random sequence of S (alpha, -beta) distribution is obtained; multiplied by '+1', still a random sequence of S (α, β) distribution;
thus, if the concealment bit b =0, the random sequence s of the first half bit period 0 ＝{-X k K = 1...., N/2} is a random sequence obeying S (α, - β) distribution, and a random sequence S of the second half bit period 1 ＝{X k K = N/2.., N } is a random sequence that follows a distribution of S (α, β); conversely, if the concealed bit b =1, the random sequence s of the first half bit period 0 ＝{X k K = 1.... N/2} is a random sequence that follows S (α, β) distribution, and a random sequence S of the second half of the bit period 1 ＝{X k K = N/2.., N } is a random sequence that follows a S (α, - β) distribution;
the information recovery processing of the covert communication system receiving end comprises the following steps:
2-1: in the case of synchronization, the receiving end is in one bit period T b The received N random sequences are r = [ r = [ r ] 0 ，r 1 ]From the description of the transmitting end, it can be seen that, no matter whether the hidden bit is '0' or '1', the skewness sign of the half bit period before and after transmission is opposite, therefore, r is done at the receiving end 1 Processing x (-1) to make the skewness sign of the front and back half bit periods the same, where the demultiplexing divides the N random sequences into 2 random sequences with length N/2, and the multiplexing is just opposite, and combines the 2 random sequences with length N/2 into one random sequence with length N;
after multiplexing, it is recorded as
In the ideal channel, i.e., in the absence of fading, delay, and noise, it is apparent that there is a->
2-2: from length N
Evaluation of a parameter in a random sequence that estimates skewness>
The estimated value of skewness is
2-3: obtaining estimates of concealed bits using hard decisions
The hard decision rule is:
referring to fig. 2, a covert communication method based on an alpha stable distribution random process skewness parameter synchronously adopts a method of fractional low-order covariance. For random sequences of length N that obey S (alpha, beta) distribution { X k K =1,.., N }, the fractional low-order covariance is defined as:
wherein N is 1 ＝max(0，-k)，N 2 = min (N-k, N), a + b < α, p-th order of the symbol of the random variable X, defined as X <p> ＝sign(X)|X| p
Fig. 2 shows the fractional low-order covariance map of the signal of step 1-3, i.e. transmitted into the channel by the concealment system, where α =1.43, β =0.5, N =400, a = b = α/4. As can be seen from the figure, the fractional low order covariance is maximum only when k =0, i.e. full synchronization; in addition, fractional low order covariance is small; in particular, k = ± 400, ± 800, i.e., ± 1, ± 2 bit periods, no periodicity occurs. This means that an eavesdropper cannot determine the bit period of covert communication by the periodicity of the fractional low-order moments.
Referring to fig. 3, a probability density function curve of the estimator when α =1.25, β =0.8, n =1000 is given. The expression of the estimator and the probability density function thereof is specifically derived as follows:
if the random variables X-S (alpha, beta), the sign fraction low order moment is
Wherein E [ X ]]Is the expectation of a random variable X; gamma function
p.epsilon (-2, -1) U (-1, alpha). If p =0, then
Using ensemble averaging
Surrogate statistical mean E [ sign (X)]Obtaining an estimate of skewness
Is composed of
From the central limit theorem, S 0 Subject to a normal distribution with a mean value of
With a second order origin moment of
Thus, its variance is
That is to say S 0 Has a probability density function of
Known as S 0 Probability density function of
Then it is found based on the relevant theorem in the random process>
Is based on the probability density function->
Is composed of
Referring to fig. 4 and 5, the mean and variance of the estimator for a number of samples N =1000 and a characteristic index α < 1 are given. The mean value expression is
The variance is expressed as
These two expressions have no closed solution, but can be numerically calculated using mathematic mathematical software. As can be seen from the view in figure 4,
belonging to unbiased estimation. As can be seen from fig. 5, when the characteristic index α tends to 1, the variance becomes large and the performance of the estimator deteriorates. The same holds true for α > 2.
Referring to fig. 6, the bit error rate in the ideal channel for different numbers of samples N is given when α = 0.5. Based on the probability density function of the known estimator, the bit error rate rho of the hidden bit with equal probability of '0', '1' and the like can be directly obtained by combining the rule of hard decision
Simulation results show that the skew degree and the number of samples are increased, and the bit error rate can be reduced. Meanwhile, the simulation result is very consistent with the theoretical derivation.
Referring to fig. 7, the bit error rate for the additive white gaussian noise channel for different number of samples N and skewness is given for α = 0.5. Since the alpha-stationary random process does not have variance (power) in the conventional sense, the divergence is used to define the signal-to-noise ratio, called the divergence ratio, defined as
Where γ is the divergence of the alpha plateau, γ G Is the divergence of the gaussian noise and is,
is the gaussian noise power. It can be seen from the graph that under the condition of low divergence ratio, the bit error rate is higher, that is, the influence of gaussian noise on the estimator is larger; on the other hand, when the divergence is relatively large, there is an error bit rate platform (error floor), that is, no matter how high the divergence ratio is, the bit error rate can not be reduced any more. This is because the limit at this time is the ideal channel, so the bit error rate plateau value is the error ratio of the ideal channelSpecific rate. />
Claims (4)
1. A covert communication method based on skew parameters of an alpha stable distribution random process is characterized in that: the method comprises the steps of information hiding processing of a sending end of the covert communication system and information recovery processing of a receiving end of the covert communication system;
the information hiding processing of the sending end of the covert communication system comprises the following steps:
1-1: a stationarity distribution noise generator is used to generate a random distribution sequence following an alpha stationarity distribution with a characteristic index of alpha and a skewness of beta, denoted as S (alpha, beta), in a bit period T b Has N random sequences, marked as { X k ,k＝1,…,N}；
1-2: the masked bit b, encoded by Manchester, at an intermediate time of each bit period, i.e. T b At/2, a jump occurs; if b =1, a transition is made from low level to high level; if b =0, the level jumps from high level to low level, the single polarity and the double polarity are changed, and unipolar '0' and unipolar '1' are respectively changed into bipolar '-1' and bipolar '+1';
1-3: the random sequence output by the stably distributed noise generator is multiplied by the reversed '-1' of single and double polarity, and the polarity of the skewness is changed, namely the random sequence of S (alpha, -beta) distribution is obtained; multiplied by '+1', still a random sequence of S (α, β) distribution;
thus, if the concealment bit b =0, the random sequence s of the first half bit period 0 ＝{-X k K =1, \ 8230;, N/2} is a random sequence obeying a distribution of S (α, - β), a random sequence of the second half of the bit period S 1 ＝{X k K = N/2, ..., N } is a random sequence obeying a distribution of S (α, β); conversely, if the concealed bit b =1, the random sequence s of the first half bit period 0 ＝{X k K =1, ..., N/2} is a random sequence obeying the distribution of S (α, β), and S is a random sequence of the second half of the bit period 1 ＝{X k K = N/2, ..., N } is a random sequence obeying a distribution of S (α, - β);
the information recovery processing of the covert communication system receiving end comprises the following steps:
2-1: in the case of synchronization, the receiving end is in one bit period T b After demultiplexing the received N random sequences, dividing the N random sequences into 2 random sequences with the length of N/2, namely r = [ r ] 0 ,r 1 ](ii) a Then making a pair r 1 X (-1) processing such that the skewness sign is the same for the first and second half bit periods; then multiplexing, combining the 2 random sequences with the length of N/2 into a random sequence with the length of N, and recording the random sequence as a random sequence with the length of N
Under ideal channel, i.e. without attenuation, delay and noise, it is obvious that
2-2: from length N
In the random sequence, an estimate of the parameter skewness is estimated>
The estimated value of skewness is
2-3: obtaining estimates of concealed bits using hard decisions
The rules for hard decision are:
2. the covert communication method based on alpha steadily distributed random process skewness parameters of claim 1, wherein: skewness estimation
Has a probability density function of
/>
In the formula (I), the compound is shown in the specification,
on the basis, the estimator is an approximate unbiased estimation obtained by numerical integration through mathematic mathematical tool software, and when the characteristic index alpha tends to 1 or 2, the variance becomes large, and the performance of the estimator is deteriorated.
3. The covert communication method based on alpha-steadily distributed random process skewness parameters as claimed in claim 2, wherein: when the hidden bits are '0', '1', etc., the bit error rate ρ under the ideal channel is
The equation indicates the relationship between the bit error rate and the characteristic index α, the skew β and the number of samples N.
4. The covert communication method based on alpha steadily distributed random process skewness parameters of claim 3, wherein: under the additive white Gaussian noise channel, the divergence ratio is defined as
Wherein gamma is a stably distributed powder of alphaThe degree of the magnetic field is measured,
the bit error rate is reduced with the increase of the divergence ratio, but a bit error rate platform exists, and when the divergence ratio tends to be infinite, the value of the bit error rate platform is the bit error rate of an ideal channel. />
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2016129363A1 (en) * | 2015-02-12 | 2016-08-18 | 学校法人東京理科大学 | Calculating device relating to concealment computation system employing distribution of secrets |
| CN106714148A (en) * | 2016-12-09 | 2017-05-24 | 浙江警察学院 | Concealed communication method based on joint normal random process |
| CN107769862A (en) * | 2017-10-19 | 2018-03-06 | 厦门大学 | A kind of bionical low communication interception method |
| CN108882236A (en) * | 2017-05-17 | 2018-11-23 | 中国电子科技集团公司第三十研究所 | Physical layer signal watermark embedding method based on S-transformation |
Family Cites Families (1)
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2016129363A1 (en) * | 2015-02-12 | 2016-08-18 | 学校法人東京理科大学 | Calculating device relating to concealment computation system employing distribution of secrets |
| CN106714148A (en) * | 2016-12-09 | 2017-05-24 | 浙江警察学院 | Concealed communication method based on joint normal random process |
| CN108882236A (en) * | 2017-05-17 | 2018-11-23 | 中国电子科技集团公司第三十研究所 | Physical layer signal watermark embedding method based on S-transformation |
| CN107769862A (en) * | 2017-10-19 | 2018-03-06 | 厦门大学 | A kind of bionical low communication interception method |
Non-Patent Citations (1)
| Title |
|---|
| 王亢 等.基于对称α稳定分布的隐蔽通信系统.《中国科学》.2017,全文. * |
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