CN110677236A - OFDM encryption method based on composite chaotic system and XOR operation - Google Patents
OFDM encryption method based on composite chaotic system and XOR operation Download PDFInfo
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Abstract
The invention discloses an OFDM encryption method based on a composite chaotic system and XOR operation. A new composite discrete chaotic system is constructed by combining Logistic mapping, Sine mapping and tent mapping, and a chaotic sequence generated by the new system is used for carrying out double encryption on complex symbols after QAM mapping of an OFDM communication system, firstly bitwise XOR operation is adopted, secondly scrambling is carried out by adopting a scrambling matrix, after the first encryption, a constellation diagram after QAM mapping is changed from 16 original points into 49 constellation points, and an obvious confusion effect is achieved; after the second encryption, the constellation points after the first encryption are further scrambled, and decryption is performed at a receiving end according to the same chaotic sequence by inverse operation, and the error rate after decryption is within an acceptable range. The encryption scheme can dynamically adjust the size of the disturbing matrix according to the size of the transmitted data, has high flexibility, and can effectively prevent violent attack.
Description
Technical Field
The invention relates to the field of secret communication, in particular to an OFDM encryption method based on a composite chaotic system and XOR operation.
Background
Orthogonal Frequency Division Multiplexing (OFDM) has been widely used in modern wireless communication networks, traditional OFDM signals are susceptible to malicious eavesdropping due to their unique time and Frequency characteristics, chaotic systems have been successfully applied to wireless systems, multimedia and other aspects to improve the security of systems, such as chaotic scrambling, chaotic constellation operation, chaotic IQ encryption technology and the like, chaotic-based communication systems are concerned about their robustness and security, and the research of chaotic systems has promoted the development of secure communication.
Existing chaotic maps can be divided into two categories: the method comprises the steps of one-dimensional (1D) chaotic mapping and high-dimensional (HD) chaotic mapping, wherein examples of the one-dimensional chaotic mapping comprise Logistic, Sine and Chebyshev mapping, generally, a high-dimensional chaotic structure is more complicated than a one-dimensional structure and is more difficult to realize, and a chaotic system can be uniformly distributed in a limited area by improving the simple one-dimensional chaotic mapping, so that the encryption performance can be improved. For another example, by utilizing the characteristics of reciprocity, position correlation and time variation of wireless channels, a novel anti-eavesdropping OFDM system by dynamic subcarrier coordinate interleaving is provided, in addition, the transmission beam forming, artificial noise and cooperative transmission can be adopted to improve the safety based on OFDM transmission, but the encryption technologies may also need additional resources, such as cooperative terminals, channel resources and a plurality of antennas, and due to the obvious pseudo-random characteristic of the methods based on the digital chaotic system, chaotic sequence tracks generated under the initial condition with small difference are quickly diverged and never repeated.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an OFDM encryption method based on a composite chaotic system and XOR operation, wherein the composite chaotic system is used for generating a pseudo-random chaotic sequence, a real part and an imaginary part are extracted from a complex matrix after QAM mapping in the OFDM system, the complex matrix and the chaotic sequence are respectively subjected to XOR operation to realize first encryption, and different chaotic sequences are used for generating a scrambling matrix to perform secondary encryption. The invention provides an OFDM encryption method based on a composite chaotic system and XOR operation, which has the technical scheme that:
an OFDM encryption method based on a composite chaotic system and XOR operation comprises the following steps:
the method comprises the following steps: constructing a composite chaotic system used in an encryption process of an OFDM communication system, combining Logistic mapping, Tent mapping and Sine mapping to obtain a mapping equation of the composite chaotic system, inputting different parameters to generate different chaotic sequences X1～X8Carrying out nonlinear operation processing on the chaotic sequence to finally obtain a key required in the encryption process;
step two: encrypting QAM symbols in the OFDM communication system by using a chaotic exclusive or method;
step three: the inverse of the encryption is used to decrypt QAM symbols in an OFDM communication system.
The step one is specifically expressed as:
1.1) combining Logistic mapping, Tent mapping and Sine mapping to obtain a mapping equation of the composite chaotic system as shown in a formula (1),
in the formula, xn+1Chaotic sequence representing the (n + 1) th iteration, xnRepresents the chaos sequence of the nth iteration, mu represents the control parameter, mu belongs to [0,2 ]]；
1.2) inputting different initial values and control parameters mu into a mapping equation obtained by the formula (1) to generate different chaotic sequences, carrying out nonlinear operation on the chaotic sequences by using the formula (2) to obtain a key required in an encryption process,
Xq'＝(Xq*106)mod 4 (2)
in the formula, XqRepresenting a chaotic sequence, Xq' denotes an encryption key used in the encryption process, mod4 denotes a remainder for 4, and q is 1,2, …, 6.
The second step is specifically expressed as follows:
2.1) reading complex symbols of original data after QAM mapping of an OFDM communication system, respectively extracting a real part and an imaginary part, respectively storing the complex symbols and the imaginary part in a matrix mode, encrypting the matrix where the real part is located by using a formula (3), encrypting the matrix where the imaginary part is located by using a formula (4), then converting the encrypted data into a complex form, completing a first encryption operation, and generating a first encrypted complex matrix C;
wherein I 'represents the encrypted real matrix, Q' represents the encrypted imaginary matrix, I (I) represents the ith value in the real matrix before encryption, and Q (I) represents the ith value, X 'in the imaginary matrix before encryption'1(i) Is X'1Of (i) number, X'2(i) Is X'2Of (i) number, X'3(i) Represents X3'the i-th number, X'4(i) Represents X4The i-th numerical value, X in5' (i) denotes X5'the i-th number, X'6(i) Represents X6' i-th numerical value, i represents coordinate value of matrix;
2.2) carrying out second encryption on the complex matrix C after the first encryption, and utilizing a formula (5) to carry out second encryption on the chaotic sequence X7Is processed into [1, M]Number X 'within interval'7Using the formula (6) to convert the chaotic sequence X8Is processed into [1, N]Number X in interval8', where M represents the row values of the scrambling matrix and N represents the column values of the scrambling matrix, and X is cyclically traversed7、X8Each number in the sequenceAnd (3) calculating the values through the formula (5) and the formula (6), and if the value generated by the (n + 1) th iteration is different from the value generated by the previous n iterations, keeping the values until the size of the row matrix is [1, M ]]The size of the column matrix is [1, N]Until now, and the chaotic sequence X is processed7Corresponding to [1, M]The values in the interval are stored in a matrix P, and the chaotic sequence X is stored8Corresponding to [1, N]The numerical values in the interval are stored in a matrix S, the matrix P represents a row matrix, the matrix S represents a column matrix, the product of the transposition of the row matrix P and the column matrix S forms a disturbing matrix, and the size of the disturbing matrix is M rows and N columns;
X'7＝(X7*1015)mod M (5)
X8'＝(X8*1015)mod N (6)
2.3) disturbing the once-encrypted complex matrix C generated in the step 2.1) according to the row-column index corresponding to the disturbing matrix, converting the first-encrypted complex matrix C into M rows and N columns of matrices, if the complex point in the first-encrypted complex matrix C is greater than M x N, dividing the first-encrypted complex matrix C into k M x N matrices, k being selected according to the actual situation, generating k different disturbing matrices according to the step 2.2) by using 2k chaotic sequences, and then disturbing the k M x N matrices after conversion according to a formula (7) respectively,
Dk(u,v)＝Ck(Pk(u),Sk(v))u＝1,2,3,…,M；v＝1,2,3,…,N (7)
in the formula, Dk(u, v) complex points, C, representing the kth scrambled u row v columnkRepresenting the k M matrix, P in the once encrypted complex matrix Ck(u) denotes the u-th value in the row matrix P in the generated k-th scrambling matrix, Sk(v) Represents the v-th value in the column matrix S in the k-th scrambling matrix;
2.4) converting the k M x N matrixes after encryption processing in the step 2.3) into matrixes with row values of 1 to obtain a complex matrix F after secondary encryption.
The third step is specifically expressed as follows:
3.1) reducing the complex matrix F after the second encryption in the OFDM communication system into a complex matrix C after the first encryption according to the coordinate position of the element in the disturbing matrix;
3.2) obtaining a real part matrix I of the original data according to a formula (8), and obtaining an imaginary part matrix Q of the original data according to a formula (9);
wherein, I '(I) represents the ith value in the real part matrix after encryption, and Q' (I) represents the ith value in the imaginary part matrix after encryption;
3.3) converting the real part matrix I and the imaginary part matrix Q into complex numbers to obtain a complex matrix of the original data.
The invention has the beneficial effects that:
the double encryption scheme provided by the invention can ensure the safe communication between the sender and the legal receiver, improves the safety of the OFDM communication system, does not need to insert artificial noise, can effectively prevent the waste of channel resources, and cannot obtain correct sending data if an eavesdropper does not have a correct key.
Drawings
Fig. 1 is a flowchart of an OFDM encryption method based on a complex chaotic system and an exclusive or operation in an embodiment of the present invention.
Fig. 2 is a diagram of a complex chaotic system bifurcation in the embodiment of the present invention.
Fig. 3 is an original constellation diagram of the OFOM system in the embodiment of the present invention.
Fig. 4 is a constellation diagram of the OFDM system after the first encryption in the embodiment of the present invention.
Fig. 5 is a constellation diagram of the OFDM system after the second encryption in the embodiment of the present invention.
Fig. 6 is a diagram of the relationship between the snr of the OFDM encryption and decryption and the ber in the embodiment of the present invention.
Detailed Description
The following is a detailed description of the technical solution of the present invention with reference to the accompanying drawings.
As shown in fig. 1, which is a flow chart of an OFDM encryption method based on a composite chaotic system and an exclusive or operation in an embodiment of the present invention, an OFDM encryption method based on a composite chaotic system and an exclusive or operation combines existing Logistic mapping, Sine mapping, and Tent mapping to obtain a composite chaotic system, and uses the composite chaotic system to generate a chaotic sequence to perform a first encryption on a complex matrix mapped by QAM in the OFDM system; different chaotic sequences are used for generating a scrambling matrix, and the matrix after the first encryption is scrambled to finish the second encryption, which comprises the following steps:
the method comprises the following steps: constructing a composite chaotic system used in an encryption process of an OFDM communication system, combining Logistic mapping, Tent mapping and Sine mapping to obtain a mapping equation of the composite chaotic system, inputting different parameters to generate different chaotic sequences X1～X8And carrying out nonlinear operation processing on the chaotic sequence to finally obtain a key required in the encryption process, wherein the specific expression is as follows:
1.1) combining Logistic mapping, Tent mapping and Sine mapping to obtain a mapping equation of the composite chaotic system as shown in a formula (1),
in the formula, xn+1Chaotic sequence representing the (n + 1) th iteration, xnRepresents the chaos sequence of the nth iteration, mu represents the control parameter, mu belongs to [0,2 ]]The bifurcation diagram of the composite chaotic system is shown in FIG. 2;
1.2) inputting different initial values and control parameters mu into the mapping equation obtained by the formula (1) to generate different chaotic sequences, wherein the chaotic sequence X is required in the whole encryption process1-X6The chaotic sequences are respectively 1 × 11400 (row × column), wherein X1-X6Respectively of 0.5 and 0.55. 0.65, 0.7, 0.75, 0.8, the control parameters are respectively 0.5, 0.7, 0.9, 1.3, 1.5, 1.8, the initial value can be [0,1]The arbitrary value of the interval and the control parameter can be [0,2 ]]The random value of the interval utilizes the formula (2) to carry out nonlinear operation on the chaotic sequence to obtain a key required in the encryption process,
Xq'＝(Xq*106)mod 4 (2)
in the formula, XqRepresenting a chaotic sequence, Xq' denotes an encryption key used in the encryption process, mod4 denotes a remainder for 4, and q is 1,2, …, 6.
Step two: a chaos exclusive-or method is adopted to encrypt QAM symbols in an OFDM communication system, which is specifically expressed as follows:
2.1) reading complex symbols of original data after QAM mapping of an OFDM communication system, respectively extracting a real part and an imaginary part, respectively storing the real part and the imaginary part in a matrix mode, wherein the size of a real part matrix is 1 x 11400, the size of an imaginary part matrix is 1 x 11400, encrypting the matrix where the real part is positioned by using a formula (3), encrypting the matrix where the imaginary part is positioned by using a formula (4), then converting the encrypted data into a complex form, completing a first encryption operation, generating a first encrypted complex matrix C, and the size of the matrix C is 1 x 11400;
wherein I 'represents the real matrix after encryption, Q' represents the imaginary matrix after encryption, I (I) represents the ith value in the real matrix before encryption, Q (I) represents the ith value in the imaginary matrix before encryption, and X1' (i) denotes X1' the i-th number value, mod4, in this case indicates the remainder, X ', obtained for 4 '2(i) Represents X2The i-th numerical value, X in3' (i) denotes X3'the i-th number, X'4(i) Represents X4The ith ofNumber, X5' (i) denotes X5'the i-th number, X'6(i) Represents X6' i represents the coordinate value of the matrix, wherein the values of i are respectively [1,11400 ]]；
2.2) carrying out second encryption on the complex matrix C after the first encryption, and utilizing a formula (5) to carry out second encryption on the chaotic sequence X7Is processed into [1, M]The value in the interval is represented by the formula (6) to obtain the chaos sequence X8Is processed into [1, N]The values in the interval, wherein M represents the row value of the disturbance matrix, the value of M is 114, N represents the column value of the disturbance matrix, the value of N is 100, and X is traversed circularly7、X8Each value in the sequence is subjected to the operations of formula (5) and formula (6), and if the value generated in the (n + 1) th iteration is different from the value generated in the previous n iterations, the value is kept until the size of the row matrix is [1, M ]]The size of the column matrix is [1, N]So far, where n has a value of 10000, the program is terminated when the number of cycles is less than 10000, and a scramble matrix of a desired size is generated, so that the number of cycles may be set slightly larger when the number of cycles is set, and the chaotic sequence X may be set7Corresponds to [1,114 ]]The values in the interval are stored in a matrix P, and the chaotic sequence X is stored8Corresponds to [1,100 ]]The numerical values in the interval are stored in a matrix S, the matrix P represents a row matrix, the matrix S represents a column matrix, the product of the transposition of the row matrix P and the column matrix S forms a scrambling matrix, and the size of the scrambling matrix is 114 rows and 100 columns;
X'7＝(X7*1015)mod M (5)
X8'＝(X8*1015)mod N (6)
2.3) disturbing the once-encrypted complex matrix C generated in the step 2.1) according to the row-column index corresponding to the disturbed matrix, converting the once-encrypted complex matrix C into an M-row N-column matrix, if the complex point in the once-encrypted complex matrix C is larger than M multiplied by N, dividing the once-encrypted complex matrix C into k M multiplied by N matrices, selecting k according to the actual situation, generating k different disturbed matrices according to the step 2.2) by using 2k chaotic sequences, and disturbing the converted k M multiplied by N matrices according to a formula (7) respectively, wherein the value of k is 1,
Dk(u,v)＝Ck(Pk(u),Sk(v))u＝1,2,3,…,M；v＝1,2,3,…,N (7)
in the formula, Dk(u, v) complex points, C, representing the kth scrambled u row v columnkRepresenting the k M matrix, P in the once encrypted complex matrix Ck(u) denotes the u-th value in the row matrix P in the generated k-th scrambling matrix, Sk(v) Represents the v-th value in the column matrix S in the k-th scrambling matrix;
2.4) converting the k M multiplied by N matrixes after encryption processing in the step 2.3) into matrixes with row values of 1 to obtain a complex matrix F after second encryption, wherein the size of the matrix F is 1 multiplied by 11400.
Step three: the method for decrypting QAM symbols in an OFDM communication system by adopting encrypted inverse operation specifically comprises the following steps:
3.1) reducing the complex matrix F after the second encryption in the OFDM communication system into a complex matrix C after the first encryption according to the coordinate position of the element in the disturbing matrix;
3.2) obtaining a real part matrix I of the original data according to a formula (8), and obtaining an imaginary part matrix Q of the original data according to a formula (9);
wherein, I '(I) represents the ith value in the real part matrix after encryption, and Q' (I) represents the ith value in the imaginary part matrix after encryption;
3.3) converting the real part matrix I and the imaginary part matrix Q into complex numbers to obtain a complex matrix of the original data.
The experimental environment and the configuration MATLABR2017b, the 64-bit Windows7 flagship edition operating system, the Intel i5-3230M dual-core processor 2.6GHz and 12GB memory realize the data transmission and reception of the chaotic system and the OFDM system through simulation.
The OFDM system parameters adopted in this embodiment are shown in table 1, the length of the chaotic sequence used in the first encryption process is 11400, and the size of the scrambling matrix generated in the second encryption process is [114,100 ].
TABLE 1 OFDM System parameters
The original 16QAM modulated constellation diagram at the transmitting end is shown in fig. 3, and the xor-operated constellation diagram is shown in fig. 4, as can be seen from fig. 4, the original 16QAM symbols totally have 16 data points, the xor-operated encrypted data point symbols are changed into 49 data point symbols, the number of the original data points is increased, the 49 symbols are scrambled again by the second scrambling encryption, so that the security can be strengthened, and the second scrambling encrypted constellation diagram is shown in fig. 5.
The relationship between the signal-to-noise ratio and the error rate of the conventional OFDM system and the encryption algorithm proposed by the present invention is shown in FIG. 6, when the error rate of an eavesdropper is 0.5, which indicates that the eavesdropper cannot recover the useful data of a legal receiver, as shown by the graph of FIG. 6, the error rate of the unencrypted OFDM system is 1 × 10 when the signal-to-noise ratio is 13-6The bit error rate of the encryption method provided by the invention is 0.0031, which is higher than the bit error rate of the traditional OFDM system without encryption, but the bit error rate standard can be reached when the signal-to-noise ratio is 20, so that the requirement of the encryption algorithm on the signal-to-noise ratio is higher than that of the OFDM system without encryption.
Claims (4)
1. An OFDM encryption method based on a composite chaotic system and XOR operation is characterized by comprising the following steps:
the method comprises the following steps: constructing a composite chaotic system used in an encryption process of an OFDM communication system, combining Logistic mapping, Tent mapping and Sine mapping to obtain a mapping equation of the composite chaotic system, and inputting different parametersNumber generation of different chaotic sequences X1～X8Carrying out nonlinear operation processing on the chaotic sequence to finally obtain a key required in the encryption process;
step two: encrypting QAM symbols in the OFDM communication system by using a chaotic exclusive or method;
step three: the inverse of the encryption is used to decrypt QAM symbols in an OFDM communication system.
2. The OFDM encryption method based on the complex chaotic system and the XOR operation as claimed in claim 1, wherein the step one is specifically expressed as:
1.1) combining Logistic mapping, Tent mapping and Sine mapping to obtain a mapping equation of the composite chaotic system as shown in a formula (1),
in the formula, xn+1Chaotic sequence representing the (n + 1) th iteration, xnRepresents the chaos sequence of the nth iteration, mu represents the control parameter, mu belongs to [0,2 ]]；
1.2) inputting different initial values and control parameters mu into a mapping equation obtained by the formula (1) to generate different chaotic sequences, carrying out nonlinear operation on the chaotic sequences by using the formula (2) to obtain a key required in an encryption process,
Xq'＝(Xq*106)mod4 (2)
in the formula, XqRepresenting a chaotic sequence, Xq' denotes an encryption key used in the encryption process, and mod4 denotes a remainder for 4, q is 1,2, …, 6.
3. The OFDM encryption method based on the complex chaotic system and the XOR operation as claimed in claim 1, wherein the second step is specifically expressed as:
2.1) reading complex symbols of original data after QAM mapping of an OFDM communication system, respectively extracting a real part and an imaginary part, respectively storing the complex symbols and the imaginary part in a matrix mode, encrypting the matrix where the real part is located by using a formula (3), encrypting the matrix where the imaginary part is located by using a formula (4), then converting the encrypted data into a complex form, completing a first encryption operation, and generating a first encrypted complex matrix C;
wherein I 'represents the encrypted real matrix, Q' represents the encrypted imaginary matrix, I (I) represents the ith value in the real matrix before encryption, and Q (I) represents the ith value, X 'in the imaginary matrix before encryption'1(i) Represents X1'the i-th number, X'2(i) Represents X2'the i-th number, X'3(i) Represents X3'the i-th number, X'4(i) Represents X4'the i-th number, X'5(i) Represents X5'the i-th number, X'6(i) Represents X6' i-th numerical value, i represents coordinate value of matrix;
2.2) carrying out second encryption on the complex matrix C after the first encryption, and utilizing a formula (5) to carry out second encryption on the chaotic sequence X7Is processed into [1, M]Number X 'within interval'7Using the formula (6) to convert the chaotic sequence X8Is processed into [1, N]Number X 'within interval'8Where M represents the row values of the scrambling matrix and N represents the column values of the scrambling matrix, and X is cyclically traversed7、X8Each value in the sequence is subjected to the operations of formula (5) and formula (6), and if the value generated in the (n + 1) th iteration is different from the value generated in the previous n iterations, the value is kept until the size of the row matrix is [1, M ]]The size of the column matrix is [1, N]Until now, and the chaotic sequence X is processed7Corresponding to [1, M]The values in the interval are stored in a matrix P, and the chaotic sequence X is stored8Corresponding to [1, N]The values within the interval are stored in a matrix S, saidThe matrix P represents a row matrix, the matrix S represents a column matrix, the product of the transposition of the row matrix P and the column matrix S forms a disturbing matrix, and the size of the disturbing matrix is M rows and N columns;
X'7＝(X7*1015)modM (5)
X′8＝(X8*1015)modN (6)
2.3) disturbing the once-encrypted complex matrix C generated in the step 2.1) according to the row-column index corresponding to the disturbing matrix, converting the first-encrypted complex matrix C into M rows and N columns of matrices, if the complex point in the first-encrypted complex matrix C is greater than M x N, dividing the first-encrypted complex matrix C into k M x N matrices, k being selected according to the actual situation, generating k different disturbing matrices according to the step 2.2) by using 2k chaotic sequences, and then disturbing the k M x N matrices after conversion according to a formula (7) respectively,
Dk(u,v)＝Ck(Pk(u),Sk(v)) u＝1,2,3,…,M；v＝1,2,3,…,N (7)
in the formula, Dk(u, v) complex points, C, representing the kth scrambled u row v columnkRepresenting the k M matrix, P in the once encrypted complex matrix Ck(u) denotes the u-th value in the row matrix P in the generated k-th scrambling matrix, Sk(v) Represents the v-th value in the column matrix S in the k-th scrambling matrix;
2.4) converting the k M x N matrixes after encryption processing in the step 2.3) into matrixes with row values of 1 to obtain a complex matrix F after secondary encryption.
4. The OFDM encryption method based on the complex chaotic system and the XOR operation as claimed in claim 1, wherein the step three is specifically expressed as:
3.1) reducing the complex matrix F after the second encryption in the OFDM communication system into a complex matrix C after the first encryption according to the coordinate position of the element in the disturbing matrix;
3.2) obtaining a real part matrix I of the original data according to a formula (8), and obtaining an imaginary part matrix Q of the original data according to a formula (9);
wherein, I '(I) represents the ith value in the real part matrix after encryption, and Q' (I) represents the ith value in the imaginary part matrix after encryption;
3.3) converting the real part matrix I and the imaginary part matrix Q into complex numbers to obtain a complex matrix of the original data.
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| CN113434892A (en) * | 2021-06-01 | 2021-09-24 | 北京理工大学 | Probability shaping method based on chaotic encryption |
| CN114142987A (en) * | 2021-11-25 | 2022-03-04 | 南京信息工程大学 | OCDM system based on novel Logistic chaotic encryption mode |
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| CN115766964A (en) * | 2022-11-14 | 2023-03-07 | 长安大学 | Image encryption method and system based on compressed sensing and variable filter diffusion |
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