CN114337730A - Frequency hopping sequence generation method based on random sequencing - Google Patents
Frequency hopping sequence generation method based on random sequencing Download PDFInfo
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Abstract
The invention discloses a frequency hopping sequence generation method based on random sequencing, which comprises the following steps: step 1, discretizing an initial base value of a frequency hopping sequence, and generating and outputting a random base value adopted by the frequency hopping sequence; step 2, randomly ordering the random base values, and generating a random ordering array through an iteration process, wherein the random ordering array has the characteristic of uniform distribution in the iteration process; and 3, mapping the random sequencing array by adopting an encryption base sequence according to a sequence mapping relation, and outputting a random sequencing frequency hopping sequence. The embodiment of the invention solves the problem that the existing frequency hopping sequence has poor uniformity and orthogonality under the condition of small sample number.
Description
Technical Field
The present invention relates to, but not limited to, the field of airborne wireless communication technologies, and in particular, to a frequency hopping sequence generation method based on random sequencing.
Background
The frequency hopping communication is a spectrum spreading communication mode which satisfies a certain constraint relation and controls the frequency hopping of radio frequency carrier frequency by random sequence, and has good anti-interference capability and multiple access networking performance.
The existing frequency hopping sequence research mainly comprises the following steps: the research method is developed from an m sequence, a Bent function, a GMW sequence and an L-G (Lempel-Greenberger) sequence to a chaotic frequency hopping sequence based on Logistic mapping, a frequency hopping sequence based on coupling mapping lattice mapping, a frequency hopping sequence generated based on cascading chaotic mapping and the like, and the frequency hopping sequence generation algorithm based on cryptography and the combination of various technical schemes appear after twenty-one century, so that the anti-attack and anti-decoding capabilities of the frequency hopping sequence are improved to a great extent, and the anti-interference capability of frequency hopping communication in a complex electromagnetic environment is ensured.
In the future, a frequency hopping system faces changeable electromagnetic environments, complex interference strategies and high-speed broadband communication requirements, so that the high-reliability information transmission of the frequency hopping system requires that a frequency hopping sequence has excellent comprehensive performance including good uniformity, independence, complexity, relevance, large-scale networking characteristics and the like. However, several conventional frequency hopping sequences in the prior art are usually good only in one or more performance test indexes, and have the problems of poor uniformity and poor orthogonality under the condition of small sample number.
Disclosure of Invention
The purpose of the invention is as follows: the embodiment of the invention provides a frequency hopping sequence generation method based on random sequencing, which aims to solve the problem that the existing frequency hopping sequence has poor uniformity and orthogonality under the condition of small sample number.
The technical scheme of the invention is as follows: the embodiment of the invention provides a frequency hopping sequence generation method based on random sequencing, which comprises the following steps:
step 1, discretizing an initial base value of a frequency hopping sequence, and generating and outputting a random base value adopted by the frequency hopping sequence;
step 2, randomly ordering the random base values, and generating a random ordering array through an iteration process, wherein the random ordering array has the characteristic of uniform distribution in the iteration process;
and 3, mapping the random sequencing array by adopting an encryption base sequence according to a sequence mapping relation, and outputting a random sequencing frequency hopping sequence.
Optionally, in the method for generating a hopping sequence based on random ordering as described above, in step 1, discretizing an initial base value of the hopping sequence includes:
and sequentially carrying out amplification and modulus processing, byte decomposition processing, S box transformation processing, byte combination processing and value domain expansion processing on the initial base value to generate a random base value adopted by the frequency hopping sequence.
Optionally, in the method for generating a hopping sequence based on random ordering as described above, the initial base value is data [ N-1, …,0], N is 4 × i, and i ≧ 8;
the mode of amplification and modulus processing is as follows: data1[ N-1, …,0]＝mod(data[N-1,…,0]×G，2N) Wherein G is a prime number;
the byte decomposition processing mode is as follows: carrying out bitwise extraction on the data1[ N-1, …,0] to obtain dataparatj [ i-1, …,0 ];
the S box conversion processing mode is as follows: performing an S-box aliasing operation on dataparatj [ i-1, …,0] to output spartj [ i-1, …,0] ═ Sbox (dataparatj [ i-1, …,0]), where Sbox represents the S-box operation;
the byte merging processing mode is as follows: merging spartj [ i-1, …,0] byte by byte, outputting cdata [ N-1, …,0] ═ (spart1[ i-1, …,0], spart2[ i-1, …,0], spart3[ i-1, …,0], spart4[ i-1, …,0 ]);
the value range expansion processing mode is as follows: for cdata [ N-1, …,0]Performing high byte truncation to output random base value of rdata [ M, …,0]]Wherein, M takes the value of ceil (log)2(H!)) -1, where H is the number of available frequency points for the frequency hopping system.
Optionally, in the method for generating a hopping sequence based on random ordering as described above, the manner of performing bit-wise extraction on data1[ N-1, …,0] in the byte decomposition processing is as follows:
datapartj [ i-1, …,0] ═ data1(j-1+4 × (0,1,2, …, i-1)), where j is 1 or 3;
datapartj [ i-1, …,0] ═ data1(j-1+4 × (i-1, i-2, …,0)), where j takes 2 or 4.
Optionally, in the method for generating a hopping sequence based on random ordering as described above, the step 2 includes:
and (2) performing polynomial iterative decomposition on the random base value generated in the step (1), caching the remainder obtained by each decomposition, performing S-box transformation on the quotient obtained by each decomposition, performing next-order polynomial decomposition, and performing H-order polynomial iterative decomposition to obtain a random sequencing array.
Optionally, in the method for generating a hopping sequence based on random ordering as described above, the step 2 specifically includes:
step 21, carrying out polynomial decomposition processing on the random base value rdata [ M, …,0] according to H, and extracting a remainder as an element of a random sequencing array;
step 22, after performing S-box transformation on the quotient obtained by the previous stage polynomial decomposition, outputting quo (k) as an input value of the next stage polynomial decomposition, sequentially performing polynomial decomposition on the quo (k) obtained by each stage of processing according to H-1, H-2, … and 1, and extracting a remainder obtained by each decomposition as an element of the random order array; wherein k is 1,2, … or H-1.
Optionally, in the hopping sequence generation method based on random ordering described above, the expression manner of the polynomial iterative decomposition in step 2 is:
Quo(0)＝rdata[M,…,0]；
Rem(0)＝mod(Quo(0),H)；
Quo(k)＝sbox(floor(Quo(k-1)/(H-k)))；
rem (k) mod (quo (k), H-k); k is 1,2,3 … H-1.
Optionally, in the method for generating a hopping sequence based on random ordering as described above, the step 3 includes:
step 31, performing basic sequence mapping on the random ordering array, and outputting a random full-ordering array as Z ═ Z (0), Z (1), …, Z (H-1) ], where a mapping relationship of the basic sequence mapping is: z (k) ═ R [ rem (k) ], wherein R is the sequential sequence of 0,1,2, …, H-1;
and step 32, reading the random full-permutation group Z by adopting an encryption base sequence to obtain a random permutation frequency hopping sequence, wherein the encryption base sequence is generated by the equipment ID number and the secret key which use the frequency hopping sequence.
The invention has the beneficial effects that: in order to overcome the problem that the uniformity and orthogonality of the existing sequence are poor under the condition of small sample number, the embodiment of the invention provides a frequency hopping sequence generation method based on random sequencing.
Specifically, an initial base value discretization mode is adopted, and the random base value adopted by the generated frequency hopping sequence is output by carrying out operations such as amplification and modulus taking, byte decomposition, S box transformation, byte combination, value domain expansion and the like on the initial base value, so that the anti-decoding capacity of the initial base value is improved, and the safety and the randomness of the frequency hopping sequence are enhanced from the source. And randomly sequencing the random base values, and outputting a random sequencing array for sequence mapping, wherein the random sequencing array has uniform distribution characteristics in an iteration process, so that the short-time uniformity of the generated frequency hopping sequence is ensured. The random sequencing array is mapped by adopting the encryption base sequence according to the sequence mapping relation, the frequency hopping sequence is output, the nonlinearity degree generated by the frequency hopping sequence is enhanced, and the anti-decoding capability of the frequency hopping sequence is improved.
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The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the example serve to explain the principles of the invention and not to limit the invention.
Fig. 1 is a flowchart of a frequency hopping sequence generation method based on random ordering according to an embodiment of the present invention;
FIG. 2 is a flow chart of the discretization process of the initial basis values in an embodiment of the present invention;
FIG. 3 is a flow chart of random ordering in an embodiment of the present invention;
FIG. 4 is a flow chart of sequence mapping in an embodiment of the present invention;
fig. 5 is a schematic diagram of a comparison between a frequency hopping sequence obtained by using the frequency hopping sequence generation method based on random sequencing according to the embodiment of the present invention and a theoretical random sequencing sequence.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that the embodiments and features of the embodiments in the present application may be arbitrarily combined with each other without conflict.
The steps illustrated in the flow charts of the figures may be performed in a computer system such as a set of computer-executable instructions. Also, while a logical order is shown in the flow diagrams, in some cases, the steps shown or described may be performed in an order different than here.
It has been demonstrated in the above background that several conventional hopping sequences tend to perform well only in one or several performance metrics, and suffer from poor uniformity and orthogonality in the case of a small number of samples.
For example, the frequency hopping sequence based on the finite field theory has the problems of short period and low complexity, and the chaos frequency hopping sequence has the finite word length effect, so that the problems of short period and poor uniformity can be caused when the chaos frequency hopping sequence is applied to an actual system; and the sequence with better comprehensive performance is achieved by means of an optimization algorithm, and the precondition is longer time statistics. Particularly, in the context of large-scale networking application, frequency hopping networking uses a short-time burst message form for data transmission, and users in a local area network need to meet short-time small collision to ensure communication quality, namely, under the condition of small sample number, the uniformity and orthogonality of a frequency hopping sequence need to meet requirements.
In order to overcome the problem that the existing sequence has poor uniformity and orthogonality under the condition of small sample number, the embodiment of the invention aims to solve the technical problems that: the frequency hopping sequence generation method based on random sequencing is characterized in that a mode of combining initial basis value discretization, random sequencing and sequence mapping is adopted, through nonlinear operation, on the premise of ensuring safety, the designed frequency hopping sequence has good short-time uniformity and orthogonality, the short-time collision probability of simultaneous access of users in a frequency hopping networking can be effectively reduced, and the capacity of multi-address communication, comb interference resistance and tracking interference resistance is improved.
In the method provided by the embodiment of the invention, the initial base value discretization mode is adopted, and the random base value adopted for generating the frequency hopping sequence is output by carrying out operations such as amplification and modulus taking, byte decomposition, S box transformation, byte combination, value domain expansion and the like on the initial base value, so that the anti-decoding capability of the initial base value is improved, and the safety and the randomness of the frequency hopping sequence are enhanced from the source.
And randomly sequencing the random base values, and outputting a random sequencing array for sequence mapping, wherein the random sequencing array has uniform distribution characteristics in an iteration process, so that the short-time uniformity of the generated frequency hopping sequence is ensured.
The random sequencing array is mapped by adopting the encryption base sequence according to the sequence mapping relation, the frequency hopping sequence is output, the nonlinearity degree generated by the frequency hopping sequence is enhanced, and the anti-decoding capability of the frequency hopping sequence is improved.
The following specific embodiments of the present invention may be combined, and the same or similar concepts or processes may not be described in detail in some embodiments.
Fig. 1 is a flowchart of a frequency hopping sequence generation method based on random ordering according to an embodiment of the present invention. The frequency hopping sequence generation method based on random sequencing provided by the embodiment of the invention mainly comprises the following steps: the method comprises the steps of initial basis value discretization, random sequencing, sequence mapping and the like, and specifically comprises the following steps:
step 1, discretizing an initial base value of a frequency hopping sequence, and generating and outputting a random base value adopted by the frequency hopping sequence;
step 2, randomly ordering the random base values, and generating a random ordering array through an iteration process, wherein the random ordering array has the characteristic of uniform distribution in the iteration process;
and 3, mapping the random sequencing array by adopting an encryption base sequence according to a sequence mapping relation, and outputting a random sequencing frequency hopping sequence.
Fig. 2 is a flowchart of discretization processing of initial base values according to an embodiment of the present invention. In the embodiment of the present invention, the discretizing of the initial basis value in step 1 includes:
and sequentially carrying out amplification and modulus processing, byte decomposition processing, S box transformation processing, byte combination processing and value domain expansion processing on the initial base value to generate a random base value adopted by the frequency hopping sequence.
The initial base value is subjected to discretization, a random base value is generated by performing mathematical operation on the initial base value, the discretization of the initial base value is realized, the anti-decoding capacity of the initial base value is improved, and the safety and randomness of a frequency hopping sequence are enhanced from the source.
In the embodiment of the present invention, the initial base values in step 1 are: data [ N-1, …,0], N is 4 × i and i is greater than or equal to 8. The following explains the processing method of each step in step 1:
the specific processing mode of the amplification and modulus extraction processing in step 1 may be as follows: data1[ N-1, …,0]＝mod(data[N-1,…,0]×G，2N) Wherein G is a prime number.
The byte decomposition processing mode is as follows: and carrying out bitwise extraction on the data1[ N-1, …,0] to obtain dataparatj [ i-1, …,0 ].
The manner of the S-box transform process in this step 1 may be: s-box aliasing operation is performed on dataparatj [ i-1, …,0], and spartj [ i-1, …,0] ═ Sbox (dataparatj [ i-1, …,0]), where Sbox represents the S-box operation.
The byte merging processing in step 1 may be as follows: merging spartj [ i-1, …,0] byte by byte, outputting cdata [ N-1, …,0] ═ (spart1[ i-1, …,0], spart2[ i-1, …,0], spart3[ i-1, …,0], spart4[ i-1, …,0 ]);
the value domain expansion processing mode in step 1 may be as follows: for cdata [ N-1, …,0]Performing high byte truncation to output random base value of rdata [ M, …,0]]Wherein, M takes the value of ceil (log)2(H!)) -1, where H is the number of available frequency points for the frequency hopping system.
Fig. 3 is a flow chart of random ordering according to an embodiment of the present invention. The specific implementation process of the random ordering in step 2 in the embodiment of the present invention may include the following steps:
step 21, carrying out polynomial decomposition processing on the random base value rdata [ M, …,0] according to H, and extracting a remainder as an element of a random sequencing array;
step 22, after performing S-box transformation on the quotient obtained by the previous stage polynomial decomposition, outputting quo (k) as an input value of the next stage polynomial decomposition, sequentially performing polynomial decomposition on the quo (k) obtained by each stage of processing according to H-1, H-2, … and 1, and extracting a remainder obtained by each decomposition as an element of the random order array; wherein k is 1,2, … or H-1.
In the random ordering processing in step 2, the random base value is subjected to polynomial iterative decomposition, and the rest numbers are subjected to cache processing to generate a random ordering array, which has a uniform distribution characteristic in the iterative process, so as to ensure the short-term uniformity of the generated frequency hopping sequence, as shown in fig. 3.
In an implementation manner of the embodiment of the present invention, the expression manner of the polynomial iterative decomposition in step 2 is:
Quo(0)＝rata[M..0]；
Rem(0)＝mod(Quo(0),H)；
Quo(k)＝sbox(floor(Quo(k-1)/(H-k)))；
rem (k) mod (quo (k), H-k); k is 1,2,3 … H-1.
Fig. 4 is a flowchart of sequence mapping according to an embodiment of the present invention. The specific implementation process of the sequence mapping in step 3 in the embodiment of the present invention may include the following steps:
step 31, performing basic sequence mapping on the random ordering array, and outputting a random full-ordering array as Z ═ Z (0), Z (1), …, Z (H-1) ], where a mapping relationship of the basic sequence mapping is: z (k) ═ R [ rem (k) ], wherein R is the sequential sequence of 0,1,2, …, H-1;
and step 32, reading the random full-permutation group Z by adopting an encryption base sequence to obtain a random permutation frequency hopping sequence, wherein the encryption base sequence is generated by the equipment ID number and the secret key which use the frequency hopping sequence.
In the sequence mapping processing in step 3, the randomly ordered array is mapped according to the sequence mapping relationship by using the encryption base sequence, the randomly ordered hopping sequence is output, the nonlinearity of sequence generation is further increased, and the anti-decoding capability of the hopping sequence is improved, as shown in fig. 4.
In order to overcome the problem that the uniformity and orthogonality of the existing sequence are poor under the condition of small sample number, the embodiment of the invention provides a frequency hopping sequence generation method based on random sequencing. Specifically, through discretization of the initial base value, the anti-decoding capacity of the initial base value can be improved, and the safety and randomness of the frequency hopping sequence are enhanced from the source; the random ordering treatment has uniform distribution characteristics in the iteration process, so that the short-time uniformity of the generated frequency hopping sequence is ensured; the nonlinearity generated by the frequency hopping sequence can be enhanced through sequence mapping, and the anti-decoding capability of the frequency hopping sequence is improved.
The following describes in detail embodiments of a frequency hopping sequence generation method based on random ordering according to some specific embodiments.
As shown in fig. 1, the frequency hopping sequence generation method based on random ordering provided by this embodiment includes the steps of initial basis discretization, random ordering, and vector mapping.
In the design of this model, the following are claimed in this particular embodiment:
1. discretizing the initial base value to discretize the initial base value to generate a random base value, wherein the initial base value is represented by data [ N-1, …,0], N is 4 × i, and i is more than or equal to 8;
2. the initial discretization process comprises the following steps: amplifying and modulus taking, byte decomposition, S box transformation, byte combination, value domain expansion and the like;
3. the processing mode of the amplification and modulus operation processing is as follows:
data1[N-1,…,0]＝mod(data[N-1,…,0]×G，2N) Wherein G is a prime number;
4. the byte decomposition processing mode is as follows: bit-wise extraction is performed on data1[ N-1, …,0], i.e.,
datapartj [ i-1, …,0] ═ data1(j-1+4 × (0,1,2, …, i-1)), where j is 1 or 3;
datapartj [ i-1, …,0] ═ data1(j-1+4 × (i-1, i-2, …,0)), where j takes 2 or 4.
5. The way of the S box conversion processing is as follows: performing S-box obfuscation operation on dataparatj [ i-1, …,0] to output spartj [ i-1, …,0], namely:
spartj [ i-1, …,0] ═ Sbox (dataparatj [ i-1, …,0]), where Sbox is the S-box operation.
6. The byte merging processing mode is as follows: the spartj [ i-1, …,0] are combined byte by byte, and cdata [ N-1, …,0] is output, namely:
cdata[N-1,…,0]＝(spart1[i-1,…,0],spart2[i-1,…,0],spart3[i-1,…,0],spart4[i-1,…,0])。
7. the value range expansion processing mode is as follows: for cdata [ N-1, …,0]Performing high byte truncation to output random base value of rdata [ M, …,0]]Wherein M is ceil (log)2(H!)) -1, where H is the number of available frequency points for the frequency hopping system.
(2) Random ordering
The random sequencing mode is as follows: and carrying out polynomial iterative decomposition on the random base value rdata [ M, …,0], caching remainder, and generating a random sequencing array Rem.
In the design of this model, this particular embodiment claims the following:
1. the processing mode of random sequencing is as follows: and (4) performing polynomial iterative decomposition on the random base value rdata [ M, …,0], caching remainder, and generating a random sequencing array.
2. The random ordering includes polynomial iterative decomposition and S-box transformation.
2. The initial input value for the polynomial iterative decomposition is rdata [ M, …,0 ].
3. The polynomial iterative decomposition mode is step-by-step decomposition.
4. And decomposing the rdata [ M, …,0] step by step according to H-1, H-2, … and 1 to extract remainder Rem (k), and performing S-box transformation on the current quotient to output Quo (k), wherein the Quo (k) is an input value of the next division operation. The polynomial operation is summarized as follows:
Quo(0)＝rdata[M,…,0]；
Rem(0)＝mod(Quo(0),H)；
Quo(1)＝sbox(floor(Quo(0)/H))；
Rem(1)＝mod(Quo(1),H-1)；
by analogy, the following results are obtained:
Quo(k)＝sbox(floor(Quo(k-1)/(H-k)))；
rem (k) mod (quo (k), H-k); k is 1,2,3, …, H-1.
5. The randomly ordered array Rem is [ Rem (0), Rem (10), Rem (2), …, Rem (H-1) ].
(3) Sequence mapping
The sequence mapping specifically comprises the steps of mapping the random sequencing array Rem by adopting an encryption base sequence according to a sequence mapping relation, and outputting a random sequencing frequency hopping sequence.
In the design of this model, this particular embodiment claims the following:
1. and the sequence mapping is to map the random sequencing array Rem by adopting an encryption base sequence according to a sequence mapping relation and output a random full-sequencing array Z.
2. The random full rank set of the sequence map output is Z, and Z ═ Z (0), Z (1), …, Z (H-1) ].
3. The sequence mapping relation is as follows: z (k) ═ R [ rem (k) ], R is 0,1,2, …, H-1 in this order.
4. The randomly ordering hopping sequence is that the hopping sequence can be obtained by reading the random full-ordering group Z by using an encryption base sequence, wherein the encryption base sequence is generated by a user ID number and a secret key.
In the method for generating a frequency hopping sequence based on random ordering according to this embodiment, the number H of available frequency points is 16, the analysis length of the frequency hopping sequence is 256, and the average chi-square test value is used as a comparison basis. Fig. 5 is a schematic diagram illustrating a comparison between a frequency hopping sequence obtained by using the frequency hopping sequence generation method based on random ordering according to the embodiment of the present invention and a theoretical random ordering sequence. It can be seen that under the condition of small sample number, the frequency hopping sequence constructed by the method is equivalent to a theoretical random sequencing sequence and is superior to the traditional block cipher frequency hopping sequence.
Although the embodiments of the present invention have been described above, the above description is only for the convenience of understanding the present invention, and is not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A frequency hopping sequence generation method based on random sequencing is characterized by comprising the following steps:
step 1, discretizing an initial base value of a frequency hopping sequence, and generating and outputting a random base value adopted by the frequency hopping sequence;
step 2, randomly ordering the random base values, and generating a random ordering array through an iteration process, wherein the random ordering array has the characteristic of uniform distribution in the iteration process;
and 3, mapping the random sequencing array by adopting an encryption base sequence according to a sequence mapping relation, and outputting a random sequencing frequency hopping sequence.
2. The method according to claim 1, wherein the discretizing the initial base value of the hopping sequence in step 1 comprises:
and sequentially carrying out amplification and modulus processing, byte decomposition processing, S box transformation processing, byte combination processing and value domain expansion processing on the initial base value to generate a random base value adopted by the frequency hopping sequence.
3. The method according to claim 2, wherein the initial base value is data [ N-1, …,0], N is 4 x i, and i ≧ 8;
the mode of amplification and modulus processing is as follows: data1[ N-1, …,0]＝mod(data[N-1,…,0]×G，2N) Wherein G is a prime number;
the byte decomposition processing mode is as follows: carrying out bitwise extraction on the data1[ N-1, …,0] to obtain dataparatj [ i-1, …,0 ];
the S box conversion processing mode is as follows: performing an S-box aliasing operation on dataparatj [ i-1, …,0] to output spartj [ i-1, …,0] ═ Sbox (dataparatj [ i-1, …,0]), where Sbox represents the S-box operation;
the byte merging processing mode is as follows: merging spartj [ i-1, …,0] byte by byte, outputting cdata [ N-1, …,0] ═ (spart1[ i-1, …,0], spart2[ i-1, …,0], spart3[ i-1, …,0], spart4[ i-1, …,0 ]);
the value range expansion processing mode is as follows: for cdata [ N-1, …,0]Performing high byte truncation to output random base value of rdata [ M, …,0]]Wherein, M takes the value of ceil (log)2(H!)) -1, where H is the number of available frequency points for the frequency hopping system.
4. The method of claim 3, wherein the data1[ N-1, …,0] is extracted by bits in the byte decomposition process according to the following steps:
datapartj [ i-1, …,0] ═ data1(j-1+4 × (0,1,2, …, i-1)), where j is 1 or 3;
datapartj [ i-1, …,0] ═ data1(j-1+4 × (i-1, i-2, …,0)), where j takes 2 or 4.
5. The method according to claim 3, wherein the step 2 comprises:
and (2) performing polynomial iterative decomposition on the random base value generated in the step (1), caching the remainder obtained by each decomposition, performing S-box transformation on the quotient obtained by each decomposition, performing next-order polynomial decomposition, and performing H-order polynomial iterative decomposition to obtain a random sequencing array.
6. The method according to claim 5, wherein the step 2 specifically includes:
step 21, carrying out polynomial decomposition processing on the random base value rdata [ M, …,0] according to H, and extracting a remainder as an element of a random sequencing array;
step 22, after performing S-box transformation on the quotient obtained by the previous stage polynomial decomposition, outputting quo (k) as an input value of the next stage polynomial decomposition, sequentially performing polynomial decomposition on the quo (k) obtained by each stage of processing according to H-1, H-2, … and 1, and extracting a remainder obtained by each decomposition as an element of the random order array; wherein k is 1,2, … or H-1.
7. The method according to claim 6, wherein the polynomial iterative decomposition in step 2 is expressed as:
Quo(0)＝rdata[M,…,0]；
Rem(0)＝mod(Quo(0),H)；
Quo(k)＝sbox(floor(Quo(k-1)/(H-k)))；
rem (k) mod (quo (k), H-k); k is 1,2,3 … H-1.
8. The method according to claim 6, wherein the step 3 comprises:
step 31, performing basic sequence mapping on the random ordering array, and outputting a random full-ordering array as Z ═ Z (0), Z (1), …, Z (H-1) ], where a mapping relationship of the basic sequence mapping is: z (k) ═ R [ rem (k) ], wherein R is the sequential sequence of 0,1,2, …, H-1;
and step 32, reading the random full-permutation group Z by adopting an encryption base sequence to obtain a random permutation frequency hopping sequence, wherein the encryption base sequence is generated by the equipment ID number and the secret key which use the frequency hopping sequence.
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