CN108400865B - Chaotic encryption method based on DCSK - Google Patents

Abstract

The invention discloses a chaos encryption method based on DCSK, which comprises the following steps: 1) randomly generating a bipolar signal at a transmitting end; 2) inputting the bipolar signal in the step 1) into a second-order reverse time chaotic system to generate a chaotic signal; 3) multiplying the bipolar signal in the step 1) with the chaotic signal in the step 2) to obtain a multiplied signal; 4) changing the binary signal of the transmitting end into a bipolar signal; 5) multiplying the bipolar signal in the step 4) and the multiplied signal in the step 3) again to be used as a sending signal; 6) receiving signals, integrating in a neighborhood of a median at each integral point moment of each received signal, and binarizing to obtain a bipolar signal of a receiving end; 7) the bipolar signal of the receiving end is changed into a binary signal, and the binary signal of the transmitting end can be recovered. The invention utilizes the second-order reverse time chaotic system to generate chaotic signals to carry out keying encryption on binary signals to be transmitted.

Description

Chaotic encryption method based on DCSK

Technical Field

The invention belongs to the field of secret communication, and particularly relates to a chaotic encryption method based on DCSK.

Background

Although the chaotic signal structure is relatively complex, the chaotic system is relatively simple in composition. The research phase of chaotic communication mainly comprises the following aspects: carrying out encryption processing by using a chaos technology; the chaos is utilized to carry out spread spectrum communication and chaos modulation technology. The current chaotic modulation method (DCSK) encryption scheme mainly comprises two schemes. One approach is to use coherent demodulation, which requires the receiver to know the information of the transmitter to recover the transmitted signal, and thus relies heavily on chaotic synchronization and is sensitive to noise. The noncoherent demodulation mode does not need to adopt chaotic synchronization, and has stronger noise interference resistance, so the application is very wide.

Disclosure of Invention

The invention aims to provide a DCSK chaotic encryption method, which utilizes a second-order reverse time chaotic system to generate chaotic signals to carry out keying encryption on binary signals to be transmitted.

The invention is realized by adopting the following technical scheme:

a chaos encryption method based on DCSK comprises the following steps:

1) randomly generating a series of bipolar signals;

2) the bipolar signal in the step 1) is used as the input of a second-order reverse time chaotic system to generate a chaotic signal;

3) multiplying the bipolar sequence in the step 1) and the chaotic signal in the step 2) in each corresponding code element period to obtain a multiplied chaotic signal so as to ensure that the value of the chaotic signal is greater than 0 in a neighborhood of a median at each integer moment;

4) converting a binary signal to be transmitted into a bipolar signal;

5) multiplying the bipolar signal in the step 5) and the multiplied chaotic signal in the step 4) again to be used as a sending signal;

6) receiving a signal from a channel, then integrating the received signal in a neighborhood of a median at each integral point moment, and then binarizing the integrated signal to obtain a bipolar signal of a receiving end;

7) the bipolar signal of the receiving end is changed into a binary signal, and then the binary signal of the transmitting end can be obtained.

The further improvement of the invention is that in the step 3), the second-order inverse time chaotic system has the mathematical expression:

wherein u is the reverse time chaotic signal to be generated,

is the second order differential of u,

is the first differential of u, β and ω are the control parameters of the system, ω is the angular frequency;

the excitation function s (t) is described as:

s(t)＝s_n,n＜t≤n+1 (2)

wherein s is_nIs a bipolar sequence.

The further improvement of the present invention is that, in step 4), the bipolar signal s (t) and the inverse time chaotic signal u (t) are multiplied to obtain a multiplied chaotic signal y (t), that is:

y(t)＝u(t)×s(t) (3)。

the further improvement of the present invention is that, in step 6), the multiplied chaotic signal is multiplied by the binary signal m (t) to be transmitted to obtain a transmission signal r (t), that is:

r(t)＝m(t)×y(t) (4)

adding noise w (t) to the transmitted signal to obtain a received signal R (t), namely:

R(t)＝r(t)+w(t) (5)。

a further development of the invention consists in that, in step 7), the received signal is integrated in a neighborhood of its median point in time at integer points:

where l is the length of the neighborhood of the integral, then for st_nBinarizing to obtain k_nNamely:

the further improvement of the present invention is that, in step 8), the integrated bipolar sequence is changed into a binary signal to obtain a binary signal at the transmitting end:

the invention has the following beneficial technical benefits:

1) the encryption effect is good

The bipolar signal generating the chaotic signal is randomly generated and is not related to the binary signal to be transmitted at all.

2) Low error rate

The receiving end adopts integral to restore the binary signal of the transmitting end, and the bit error rate of the scheme is close to zero theoretically

3) High transmission efficiency

Conventional DCSK modulates a binary signal in two symbol periods, and the scheme proposed herein modulates a binary signal in one symbol period.

Drawings

FIG. 1 is a diagram of randomly generated bipolar signals;

FIG. 2 is a diagram of a reverse-time chaotic signal generated with a randomly generated bipolar signal;

FIG. 3 is a diagram of a chaotic signal after multiplication of a reverse-time chaotic signal by a bipolar sequence;

FIG. 4 is a diagram of a binary signal to be transmitted;

FIG. 5 is a diagram of a chaotic signal after multiplication of a transmitted binary signal and chaos;

FIG. 6 is a transmitted signal superimposed noise plot;

FIG. 7 is a diagram of the signal integrated by the receiving end in the neighborhood of the integer time of the output signal;

fig. 8 is a diagram of a binary signal at the transmitting end obtained by binarizing the integrated signal.

Detailed Description

The present invention will be described in detail with reference to the accompanying drawings and examples.

The invention utilizes a second-order reverse time chaotic system, and the expression is as follows:

wherein u isA reverse-time chaotic signal needs to be generated,

is the second order differential of u,

is the first differential of u, β and ω are the control parameters of the system, ω is the angular frequency;

the excitation function s (t) is described as:

s(t)＝s_n,n＜t≤n+1 (2)

wherein s is_nIs a bipolar signal.

Randomly generating a series of bipolar signals is shown in fig. 1: s_n＝[-1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1-1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1]；

Generating s as described above_nThe chaotic signal u (t) generated by substituting the chaotic signal into the formula (1) is shown in fig. 2;

the modulated chaotic signal y (t) at the transmitting end obtained by multiplying s (t) by u (t) is shown in fig. 3, namely:

y(t)＝s(t)×u(t) (3)

the binary signal m (t) to be transmitted is multiplied by the modulated chaotic signal y (t) as shown in fig. 4 to obtain a transmission signal as shown in fig. 5:

r(t)＝m(t)×y(t) (4)

adding noise w (t) to the transmitted signal to obtain a received signal r (t) as shown in fig. 6, that is:

R(t)＝r(t)+w(t) (5)

integrating the received signal in a neighborhood of the median of its integral point time to obtain st_nAs shown in fig. 7, l ═ 0.25:

where l is the half length of the neighborhood of the integral, then st_nBinarizing to obtain k_nNamely:

the integrated bipolar sequence is converted into a binary signal as shown in fig. 8, and the binary signal of the transmitting end can be obtained.

Examples

The invention is verified with a specific signal as an example, where fig. 6 is a transmitted signal, fig. 7 is a signal actually transmitted in a channel, fig. 8 is a finally recovered binary signal, the simulated noise in the channel is white gaussian noise, and the SNR is 0dB, and the feasibility of the method can be seen from the transmitted binary signal and the recovered binary signal.

Claims (2)

1. A chaos encryption method based on DCSK is characterized by comprising the following steps:

1) randomly generating a series of bipolar signals;

2) the bipolar signal in the step 1) is used as the input of a second-order reverse time chaotic system to generate a chaotic signal; the second-order reverse time chaotic system has the mathematical expression as follows:

wherein u is the reverse time chaotic signal to be generated,

is the second order differential of u,

is a first order micro of uBeta and omega are control parameters of the system, and omega is angular frequency;

the excitation function s (t) is described as:

s(t)＝s_n,n＜t≤n+1 (2)

wherein s is_nIs a bipolar sequence;

3) multiplying the bipolar sequence in the step 1) and the chaotic signal in the step 2) in each corresponding code element period to obtain a multiplied chaotic signal so as to ensure that the value of the chaotic signal is greater than 0 in a neighborhood of a median at each integer moment; multiplying the bipolar signal s (t) and the reverse time chaotic signal u (t) to obtain a multiplied chaotic signal y (t), namely:

y(t)＝u(t)×s(t) (3)

4) converting a binary signal to be transmitted into a bipolar signal;

5) multiplying the bipolar signal in the step 4) and the chaos signal multiplied in the step 3) again to be used as a sending signal; multiplying the multiplied chaotic signal with a binary signal m (t) to be transmitted to obtain a transmission signal r (t), namely:

r(t)＝m(t)×y(t) (4)

adding noise w (t) to the transmitted signal to obtain a received signal R (t), namely:

R(t)＝r(t)+w(t) (5)

6) receiving a signal from a channel, then integrating the received signal in a neighborhood of a median at each integral point moment, and then binarizing the integrated signal to obtain a bipolar signal of a receiving end; integrating the received signal in a neighborhood of its median at times of integer points:

where l is the length of the neighborhood of the integral, then for st_nBinarizing to obtain k_nNamely:

7) the bipolar signal of the receiving end is changed into a binary signal, and then the binary signal of the transmitting end can be obtained.

2. The DCSK chaos encryption method according to claim 1, wherein in step 7), the integrated bipolar sequence is changed into a binary signal to obtain the binary signal at the transmitting end:

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