Dynamic coding construction of error correction encryption fusion and low complexity coding method and device

Abstract

A dynamic coding construction and low-complexity coding method and apparatus for error correction and encryption fusion, the method comprising: continuously receiving a sequence of plaintext information sent by a source, and constructing a corresponding dynamic sparse random parity check matrix H for each plaintext information. i For each H i Perform matrix block processing to obtain the H i The corresponding multiple submatrices and a double diagonal matrix T i According to T i Calculate the intermediate matrix φ from the inverse matrix and submatrix i For every K intermediate matrices φ obtained i Then, the grouping inverse algorithm is used to calculate each φ. i The corresponding inverse matrix K≥2, for each plaintext m i Based on the corresponding dynamic matrix encoding, m is obtained. i The corresponding ciphertext P is sent. i The encoding matrix is ​​constructed by combining a double diagonal matrix structure and a dynamic sparse random parity check matrix block processing method. The encoding process uses a group inversion algorithm, which reduces the complexity of obtaining the encoding matrix and the computational complexity of encoding, thus greatly improving the encoding efficiency.

Description

Technical Field

[0001] This article relates to the field of communication and information security, and in particular to a dynamic coding structure and low-complexity coding method and apparatus that integrates error correction and encryption. Background Technology

[0002] With the development of wireless communication technology, error correction and encryption fusion coding technology has made some progress in modern communication technology in order to ensure both the reliability and security of data transmission. This technology combines encryption and error correction at the physical layer. In the communication system, a dynamically changing channel coding matrix is ​​used, and the parity check matrices of the sender and receiver are updated synchronously and dynamically. Eavesdroppers can only passively track these changes, and once a decoding error occurs, they will be unable to continue tracking, thus ensuring the security of communication. At the same time, error correction codes with efficient error correction performance are used to further ensure the reliability of information transmission. However, the existing error correction and encryption fusion channel coding method generates a massive amount of dynamic parity check matrices under the scheme of dynamically changing coding matrices. Each encoding requires the inversion of the new dynamic parity check matrix to obtain the coding matrix. In the encoding process, the traditional Gaussian elimination method is used for matrix inversion. The matrix inversion operation is huge, the encoding time is long, and the computational complexity is high, which limits the efficiency of encoding and has become a bottleneck in the development of dynamic matrix coding for error correction and encryption fusion. Summary of the Invention

[0003] This application provides a dynamic encoding construction and low-complexity encoding method and apparatus that integrates error correction and encryption. When constructing the encoding matrix, it combines a double diagonal matrix structure and a dynamic sparse random parity check matrix block processing method. During encoding, a group inversion algorithm is used, which reduces the complexity of obtaining the encoding matrix and the computational complexity of encoding using the encoding matrix, thereby greatly improving the encoding efficiency.

[0004] On the one hand, embodiments of this application provide a dynamic encoding construction and low-complexity encoding method for error correction and encryption fusion, including:

[0005] Continuously receive the plaintext sequence {m0, m1, m2, ...} sent by the source, and process each plaintext m i Construct the corresponding dynamic sparse random check matrix H i , where i = 0, 1, 2, ...;

[0006] For each H i Perform matrix block processing to obtain the H i The corresponding multiple submatrices and a double diagonal matrix T i According to T i The inverse matrix and the submatrix are used to calculate the intermediate matrix φ. i ;

[0007] For every K intermediate matrices φ obtained i Then, the grouping inverse algorithm is used to calculate each φ. i The corresponding inverse matrix Where K≥2;

[0008] For each of the aforementioned plaintext m i Based on the corresponding Perform dynamic matrix encoding to obtain m i The corresponding ciphertext P is sent. i .

[0009] On the other hand, embodiments of this application also provide a dynamic coding structure and a low-complexity coding device for error correction and encryption fusion, including a memory and a processor;

[0010] The memory is used to store the dynamic encoding structure and low-complexity encoding program of error correction and encryption fusion.

[0011] The processor is used to read the dynamic encoding structure and low-complexity encoding program of the error correction and encryption fusion, and to perform the dynamic encoding structure and low-complexity encoding method of the error correction and encryption fusion as described in the above embodiments.

[0012] Compared with related technologies, the error correction and encryption fusion dynamic coding matrix construction and low-complexity coding method and apparatus of this application combine a double diagonal matrix structure and a dynamic sparse random parity check matrix block processing method when constructing the coding matrix. The group inversion algorithm is used during coding, which reduces the complexity of obtaining the coding matrix and reduces the computational complexity of coding with the coding matrix, thus greatly improving the coding efficiency.

[0013] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the application. Other advantages of this application can be realized and obtained by means of the solutions described in the description and the accompanying drawings. Attached Figure Description

[0014] The accompanying drawings are used to provide an understanding of the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application and do not constitute a limitation on the technical solutions of this application.

[0015] Figure 1 This is a flowchart illustrating a dynamic encoding construction and low-complexity encoding method for error correction and encryption fusion according to an embodiment of this application.

[0016] Figure 2 The diagram illustrates the effect and variation of reducing computational complexity of the grouping inversion algorithm in Example 2 of this application;

[0017] Figure 3 This is a schematic diagram of a dynamic coding structure and low-complexity coding device for error correction and encryption fusion according to an embodiment of this application. Detailed Implementation

[0018] This application describes several embodiments, but these descriptions are exemplary and not restrictive, and it will be apparent to those skilled in the art that many more embodiments and implementations are possible within the scope of the embodiments described herein. Although many possible combinations of features are shown in the drawings and discussed in the detailed description, many other combinations of the disclosed features are also possible. Unless specifically limited, any feature or element of any embodiment may be used in combination with, or may replace, any feature or element of any other embodiment.

[0019] This application includes and contemplates combinations of features and elements known to those skilled in the art. The embodiments, features, and elements disclosed in this application can also be combined with any conventional features or elements to form unique inventive solutions. Any feature or element of any embodiment can also be combined with features or elements from other inventive solutions to form another unique inventive solution. Therefore, it should be understood that any feature shown and / or discussed in this application can be implemented individually or in any suitable combination. Therefore, the embodiments are not limited except by the limitations imposed by the appended claims and their equivalents. Furthermore, various modifications and changes can be made within the scope of the appended claims.

[0020] Furthermore, in describing representative embodiments, the specification may have presented methods and / or processes as a specific sequence of steps. However, the method or process should not be limited to the specific order of steps described herein, to the extent that it does not depend on such a specific order. As will be understood by those skilled in the art, other sequences of steps are also possible. Therefore, the specific order of steps set forth in the specification should not be construed as a limitation of the claims. Moreover, the claims concerning the method and / or process should not be limited to the steps performed in the written order, and those skilled in the art will readily understand that these orders can be varied and still remain within the spirit and scope of the embodiments of this application.

[0021] This application provides a dynamic encoding construction and low-complexity encoding method for error correction and encryption fusion, including steps S100-S400, such as... Figure 1 As shown:

[0022] S100: Continuously receive the plaintext sequence {m0,m1,m2,……} sent by the source, and process each plaintext mi Construct the corresponding dynamic sparse random check matrix H i , where i = 0, 1, 2, ...;

[0023] S200: For each H i Perform matrix block processing to obtain the H i The corresponding multiple submatrices and a double diagonal matrix T i According to T i The inverse matrix and the submatrix are used to calculate the intermediate matrix φ. i ;

[0024] S300: For every K intermediate matrices φ obtained i Then, the grouping inverse algorithm is used to calculate each φ. i The corresponding inverse matrix Where K≥2;

[0025] S400: For each of the aforementioned plaintext messages m i Based on the corresponding Perform dynamic matrix encoding to obtain m i The corresponding ciphertext P is sent. i .

[0026] In this embodiment, each plaintext m is processed separately. i Execute the corresponding steps S100, S200, and S400. Step S300 corresponds to the K plaintext messages m. i The overall steps.

[0027] In this embodiment, in step S200, for each H i Perform matrix block processing, that is, for each H i Divide into multiple corresponding submatrices and a double diagonal matrix T. i For each bidiagonal matrix T i Find the inverse to obtain the corresponding T. i -1 And according to T i -1 and H i Calculate the intermediate matrix φ from the corresponding multiple submatrices i Because of T i T is a double diagonal matrix. i The inversion calculation is simple and has low time complexity, which greatly shortens the calculation time of execution step S200, simplifies dynamic matrix encoding, and shortens the encoding time.

[0028] In this embodiment, after performing steps S100 and S200 on the plaintext information respectively, each plaintext m is obtained. i The corresponding dynamic sparse random parity check matrices Hi Multiple submatrices, T i T i -1 and intermediate matrix φ i ; For each K intermediate matrices φ obtained i Then, based on the K plaintext messages m i One-to-one corresponding intermediate matrix φ i Execute step S300, which involves sending K plaintext messages m. i As a plaintext group, its corresponding intermediate matrix set {φ0,φ1,…,φ} K-1}Execute step S300.

[0029] In this embodiment, the grouping inversion algorithm in step S300 is a low-complexity algorithm for solving inverse matrices. By constructing a matrix set, the high-complexity matrix inversion calculation is transformed into a low-complexity matrix multiplication, which combines K φ... i The corresponding K inversion calculations are transformed into single matrix inversions and a series of matrix multiplications, reducing the average complexity of the K inversion calculations. That is, step S300 further reduces the complexity of dynamic matrix encoding and shortens the encoding time. After executing step S300, the set of inverse matrices is obtained. That is, the K m elements in the plaintext group were obtained. i One-to-one corresponding inverse matrix For each plaintext message m i Based on its corresponding inverse matrix Execute step S400 to perform dynamic matrix encoding and obtain the corresponding ciphertext P to be sent. i Send encrypted P i With plaintext m i One-to-one correspondence.

[0030] The error correction and encryption fusion dynamic coding construction and low-complexity coding method in this embodiment introduces a double diagonal structure matrix into the dynamic parity check matrix, and adopts a dynamic sparse random parity check matrix block processing method and a group inversion algorithm, which reduces the complexity of inverting the dynamic parity check matrix, that is, reduces the complexity of obtaining the coding matrix and significantly improves coding efficiency.

[0031] In one exemplary embodiment, in step S100, "for each plaintext message m" i Construct the corresponding dynamic sparse random check matrix H i Previously, a basis matrix H could be constructed based on a multidimensional external information transfer graph. B,0 Each of the stated information plaintext m i Corresponding to the basis matrix H B,0 All are the same, construct the basis matrix H B,0 This may include steps S110-S140:

[0032] S110: Construct M B Line M B B, a double diagonal matrix of columns C Among them, B C The elements on the main diagonal and the diagonals above the main diagonal are all 1, and the other elements are 0;

[0033] S120: B C Located in the Mth B The element in row 1 and column 1 and the element in column 1 Setting the elements of each row to 1 yields a partial bidiagonal matrix B. P ,in, Represents M B The result obtained by rounding down / 2;

[0034] S130: Based on the obtained B P Based on the multidimensional external information transfer graph, the basis matrix H B,0 The minimum iterative decoding threshold is searched to obtain B. I ;

[0035] S140: According to B I and B P Obtain the basis matrix H B,0 =[B I B P ], where H B,0 For M B Line N B A matrix of columns.

[0036] In this embodiment, all information is in plaintext m i The corresponding basis matrix H B,0 All are the same, the basis matrix H B,0 It has a partially partitioned double diagonal structure, and the basis matrix H B,0 Includes two matrices B I and B P To reduce coding complexity, B P M with a partially double diagonal structure B Line M B A square matrix of columns, B I For M B Line N B -M B A matrix of columns.

[0037] In this embodiment, B can be obtained based on the multidimensional external information transfer graph (EXIT). IMultidimensional EXIT is a method for analyzing the convergence of iterative decoding algorithms. In step S130, it is used to analyze the basis matrix H. B,0 The performance can be obtained based on the multidimensional EXIT to make the basis matrix H B,0 The matrix B with the minimum iterative decoding threshold I .

[0038] In this embodiment, the double diagonal matrix B C For M B Line M B A square array of columns, That is, B C There is 2M B -1 element is 1, and all other elements are 0.

[0039] In this embodiment, when executing step S120, B is... C The Mth B Set the element in row 1 and column 1 to 1, and set B... C Located in the first column Set the element of the row to 1. Represents M B / 2 performs a floor operation, for example, when M B =8 o'clock When M B =7 o'clock After executing step S120, a partial diagonal matrix B is obtained. P , That is, in B C The first column has been increased by two elements, 1 and B. P The first column has 3 elements: 1, B P China has 2M B +1 element is 1, and all other elements are 0.

[0040] In this embodiment, after obtaining B P Subsequently, the multidimensional EXIT method was used for analysis on the basis matrix H. B,0 The minimum iterative decoding threshold is searched to obtain B. I Based on B P and B I Obtain the basis matrix

[0041] In one exemplary embodiment, step S100 involves "for each plaintext message m" i Construct the corresponding dynamic sparse random check matrix H i "This can include each plaintext m" i Execution steps S150-S160:

[0042] S150: For the basis matrix H B,0Perform L-1 structuring extensions to obtain the extended matrix H. B,L-1 Where L≥2;

[0043] S160: For the extended matrix H B,L-1 Perform a random expansion to obtain the plaintext m of the information. i The corresponding dynamic sparse random check matrix H i .

[0044] In this embodiment, for each plaintext m i Perform steps S150 and S160 to process the basis matrix H. B,0 L expansions were performed, where the first L-1 expansions were structured expansions and the last expansion was a random expansion, where L≥2, i.e., for the basis matrix H B,0 Perform at least one structured expansion and one random expansion to obtain the dynamic sparse random parity-check matrix H. i .

[0045] In this embodiment, a dynamic sparse random parity check matrix H corresponding to each piece of plaintext is obtained by structurally expanding and randomly expanding the basis matrix with a partially block-based double diagonal structure. i The double diagonal structure is integrated into the dynamic sparse random parity check matrix H. i The design achieves low coding complexity for the dynamic sparse random parity check matrix, reducing the size of the matrix that needs to be inverted and thus lowering the coding complexity.

[0046] In one exemplary embodiment, step S150 may include:

[0047] The structure expansion is performed L-1 times in a loop. The l-th structure expansion includes steps S151-S152, where l = 1, 2, ..., L-1:

[0048] S151: For the extended matrix H B,l-1 Each non-zero element E in n The structured cyclic permutation matrix CPM corresponding to this structured extension is obtained using a predetermined optimization algorithm. ln Among them, CPM ln For F l Line F l A square matrix of columns, F l The pre-set structure extension factor for this structure extension, n = 0, 1, 2, ... w l -1, w l For H B,l-1 The number of non-zero elements;

[0049] S152: H B,l-1 Each non-zero element E nReplace with the corresponding CPM ln , will H B,l-1 Replace each element 0 with F l Line F l The zero matrix of the column is used to obtain the extended matrix H corresponding to this structured extension. B,l ;

[0050] In this embodiment, the matrix before the first structured expansion is the base matrix H. B,0 The matrix before the l-th structured expansion is the expanded matrix H obtained from the (l-1)-th structured expansion. B,l-1 The extended matrix obtained by the (L-1)th structured expansion is the extended matrix H. B,L-1 .

[0051] In this embodiment, L-1 structure expansions are performed sequentially; in two adjacent structure expansions (the (l-1)th and the lth structure expansion), the (l-1)th structure expansion yields the expanded matrix H. B,l-1 As the matrix before the l-th structured expansion, in step S151, to avoid small trap sets and ensure the performance of the expanded matrix, a predetermined optimization algorithm is used to obtain the structured cyclic permutation matrix CPM. ln ; Structured extension and structured extension factor F l One-to-one correspondence, F used in any two structured extensions l They can be the same or different.

[0052] In this embodiment, the predetermined optimization algorithm includes the progressive edge growth algorithm, etc. The examples of the above optimization algorithms are exemplary descriptions and are not intended to limit this application, and will not be described in detail.

[0053] In one exemplary embodiment, step S160 may include steps S161-S162:

[0054] S161: Get H B,L-1 Each non-zero element E j The corresponding random cyclic permutation matrix CPM Lj Among them, CPM Lj For F L Line F L A square matrix of columns, F L The pre-set random expansion factor, j = 0, 1, 2, ... w L -1, w L For H B,L-1 The number of non-zero elements;

[0055] S162: H B,L-1 Each non-zero element E jReplace with the corresponding CPM Lj , will H B,L-1 Replace each element 0 in the formula with F. L Line F L The zero matrix of the columns is used to obtain the dynamic sparse random parity check matrix H. i .

[0056] In this embodiment, after performing the random expansion, the dynamic sparse random parity-check matrix H is obtained. i Its row number M is M B F (L) The number of columns N is N B F (L) , of which F (L) For L-1 structured expansion factors F l and a random expansion factor F L The product of

[0057] In one exemplary embodiment, step S161 may include steps S1611-S1614:

[0058] S1611: Use a pseudo-random number generator to generate numbers including w L binary vectors r i,j pseudo-random vector r i ,in, Each r i,j The length is log2F L r i The length is w L log2 F L r i,j With non-zero element E j One-to-one correspondence;

[0059] For each E j Execution steps S1612-S1614:

[0060] S1612: E j The corresponding binary vector r i,j Convert to decimal value D i,j ;

[0061] S1613: CPM Lj The first line, D i,j Set the elements of the column to 1, and set the other elements of the first row to 0;

[0062] S1614: Execute F L -1 step to obtain CPM Lj Line 2 to line F L Line: CPM LjThe CPM is obtained by shifting the f-th row one position to the right. Lj The (f+1)th row, 1 ≤ f ≤ F L -1.

[0063] In this embodiment, the pseudo-random vector r i With the dynamic sparse random parity check matrix H i In a one-to-one correspondence, a pseudo-random vector r is generated using a pseudo-random number generator in step S1611. i CPM (Cyclic Permutation Matrix) Lj The number of rows and columns F L From pseudo-random vector r i Control can guarantee the acquisition of the dynamic sparse random parity-check matrix H i The confidentiality and independence.

[0064] In this embodiment, the pseudo-random vector r i binary vector r i,j The number of H B,L-1 Central African zero element E j The number of them is equal, which is H. B,L-1 Each non-zero element E j Calculate the random cyclic permutation matrix CPM Lj During step S1612, E j The corresponding r i,j Convert to decimal value D i,j For example, r i,j = (0,1,0), then D i,j =1*2 1 =2, for example r i,j = (1,0,1,0), then D i,j =1*2 1 +1*2 3 =10.

[0065] In this embodiment, for example r i,j = (0,1,0), then D i,j =1*2 1 =2, assume F L =5, then after executing step S1613, we obtain CPM. Lj The first line is [0 1 0 0 0]. By executing step S1614 4 times, the CPM is obtained. Lj The second line is [0 01 0 0], the third line is [0 0 0 1 0], the fourth line is [0 0 0 0 1], and the fifth line is [1 0 0 0 0], that is...

[0066] In one exemplary embodiment, step S200 may include steps S210-S230:

[0067] S210: This H i Divided into H iI and H iP , where H i =[H iI H iP ], H iP It is a square array;

[0068] S220: H iI Divided into submatrix A i and C i , will H iP Divided into submatrix B i D i E i and the double diagonal matrix T i ,in,

[0069] S230: Calculate T i inverse matrix And according to the formula Calculate the intermediate matrix φ i .

[0070] In this embodiment, step S210 is executed to process H, which has M rows and N columns. i Divide into H i Divided into H iI and H iP H iP Let M be a square matrix with M rows and M columns, and let B be the basis matrix. P H was obtained through L-1 structured expansions and one random expansion. iI For an M-row NM-column matrix, the base matrix is ​​B. I It is obtained after L-1 structured expansions and one random expansion, where the meanings of M and N are the same as in the above embodiment, and the number of rows M is M B F (L) The number of columns N is N B F (L) , of which F (L) For L-1 structured expansion factors F l and a random expansion factor F L The product of

[0071] In this embodiment, by executing step S220, H can be... i Divided into 5 submatrices A i B i C i D i E iand a double diagonal matrix T i , where A i It is of size (MF) (L) A matrix of size B × (NM) i It is of size (MF) (L) )×F (L) The matrix, T i It is of size (MF) (L) )×(MF (L) The matrix C i It is of size F (L) A matrix of size ×(NM), D i It is of size F (L) ×F (L) The matrix, E i It is of size F (L) ×(MF (L) A matrix of ).

[0072] In this embodiment, D i =[P D,0 ]; Among them, P B,0 P B,r P D,0 P E,0 and P Tm,z P Ts,z All are of size F L ×F L A matrix, z = 0, 1, ..., M B -2.

[0073] In this embodiment, T i Given a doubly diagonal matrix, in step S230, for T... i Obtain by performing inverse calculation The computational cost of inversion is small, which reduces the computational complexity of inversion and shortens the dynamic matrix encoding time.

[0074] In this embodiment, a matrix-based method is proposed for processing a dynamic sparse random parity check matrix H with a partially partitioned double diagonal structure. i Divide the data into blocks to obtain a double diagonal matrix T. i And for this bidiagonal matrix T i Performing the inversion operation effectively reduces the computational cost of the dynamic sparse random parity check matrix H. i The complexity of performing the inversion.

[0075] In this embodiment, by applying each dynamic sparse random check matrix H i After executing steps S210-S230, each plaintext message m is obtained. i Corresponding Ai B i C i D i E i T i , φ i .

[0076] In one exemplary embodiment, step S300 may include steps S310-S330:

[0077] S310: Transfer K φ i The corresponding plaintext m i Set as plaintext group {m0,m1,m2,……m K-1}, based on K φ i Construct the intermediate matrix set {φ0,φ1,…,φ K-1}, where φ k For the plaintext m of the information k The corresponding intermediate matrix, k = 0, 1, 2, ..., K-1;

[0078] S320: Construct the first set of matrices {W 0,0 W 0,1 ,…,W 0,K-1} and the second set of matrices {W 1,1 W 1,2 ,…,W 1,K-1};

[0079] S330: According to the formula K inverse matrices are obtained in, For the plaintext m of the information k The corresponding intermediate matrix φ k The inverse matrix;

[0080] In this embodiment,

[0081] In this embodiment, after obtaining the plaintext m of information K... i The corresponding intermediate matrices φ i Then, steps S310-S330 are executed using a grouping method to divide the plaintext m of the K information. i As a plaintext group {m0,m1,m2,……m K-1 In the operations of this group, based on K φ i The constructed intermediate matrix set {φ0,φ1,…,φ K-1} Execute steps S320-S330, φ0,φ1,…,φ K-1 Each is associated with a plaintext message m0, m1, ..., m K-1Correspondingly, performing the grouping inversion algorithm once yields K results. K Each is represented as a plaintext group {m0, m1, m2, ... m K-1 K m in} i The inverse matrix, the grouping inverse algorithm and the separate calculation of φ i Compared to the inverse matrix, this effectively reduces computational complexity.

[0082] In this embodiment, after executing steps S100-S300, each plaintext message m is obtained. i Corresponding A i B i C i D i E i T i , φ i ,

[0083] In one exemplary embodiment, step S400 may include steps S410-S460, that is, for each plaintext message m i Perform the following steps:

[0084] S410: Based on the plaintext m of this message i Corresponding to the submatrix A i calculate

[0085] S420: Based on the plaintext m of this message i Corresponding to the submatrix C i calculate

[0086] S430: Based on the plaintext m of this message i Corresponding to the submatrix A i E i The inverse matrix calculate

[0087] S440: According to the formula calculate

[0088] S450: According to the formula calculate

[0089] S460: Based on and Obtain the transmitted ciphertext P i , where P i =[p i,1 ,p i,2].

[0090] In this embodiment, after executing step S400, each plaintext message m is obtained. i The corresponding ciphertext P is sent. i , including P0, P1, ..., which correspond to the plaintext information m0, m1, ... respectively.

[0091] To illustrate the technical effects of the dynamic coding matrix construction and low-complexity coding method of error correction and encryption fusion in the embodiments of this application, a specific example is described in detail below.

[0092] This example demonstrates the generation of an inverse matrix. The complexity mainly lies in the computation. Calculate φ i and φ i Obtain by performing inverse calculation As shown in Table 1, the specific complexity analysis during the process is as follows:

[0093] In step S220, H i Blocks, in which T i It has a double diagonal matrix structure, for T i Obtained by inverse It can be represented as in, The calculation can be expressed using the following formula:

[0094] In the following descriptions, Representing L-1 structured expansion factors F l and 1 random expansion factor F L The product; Representing L-1 structured expansion factors F l The product of.

[0095] The error correction and encryption fusion dynamic coding matrix construction and low-complexity coding method in this application embodiment, for each P Ts,z and P Tm,z Each row and each column of the matrix has only one cyclic permutation matrix CPM; therefore, for each P Ts,z and P Tm,z In total, there are F (L-1) For each CPM, the operations on these matrices can be divided into multiplication and inversion of the CPMs. Multiplication of two CPMs has a complexity of O(1), and inversion of a single CPM also has a complexity of O(1). Here, O is an asymptotic upper bound on the computational complexity. Therefore, for the aforementioned P... B,0 P B,r P D,0 PE,0 P Ts,z P Tm,z Both have the following two properties: (1) The complexity of multiplying two matrices is O(F) (L-1) (2) The complexity of matrix inversion is O(F) (L-1) For property (1), since the multiplication of different matrices can be decomposed into the multiplication of different CPMs, a total of F is required. (L-1) Therefore, the complexity is O(F) multiplication operations. (L-1) Similarly, for the above property (2), since the matrix inversion operation can be decomposed into inversion operations of different CPMs in the matrix, a total of F is required. (L-1) Therefore, the time complexity is O(F)^2 inverse operations. (L-1) Therefore, in order to calculate Requires (M) B -3-z)+(M B -2-z)=(2M B The total complexity is (2^M) multiplications and one matrix inversion, requiring -2^z - 5 multiplications. B -2z-6)O(F (L-1) ).

[0096] In summary, the dynamic coding matrix construction and low-complexity coding method for error correction and encryption fusion in the embodiments of this application can be used to obtain... calculate The complexity is as follows:

[0097]

[0098] Similarly, it can be obtained Similarly, we can obtain the calculation of φ. i The complexity is (4M) B -1)O(F (L-1) ) = O(M B F (L-1) ).

[0099] For φ i Obtain by performing inverse calculation Because its size is F (L) ×F (L) The complexity of directly performing the inversion operation is . The grouping and inversion operations in steps S310-S330 of this application embodiment can further reduce the computational complexity of inversion. A total of (3K-3) matrix multiplication operations and one matrix inversion operation are required, where the complexity of one matrix inversion operation is O(n log n). One matrix multiplication operation requires approximately [calculation details needed] Submatrix multiplication and This is a matrix addition operation where the matrix size is F. L ×F L Therefore, the complexity of matrix multiplication is O(F). L log2 F L The complexity of matrix addition is O(F). L Therefore, calculate each The average complexity is: Obtained by directly performing inversion calculation Compared to the complexity of the previous method, the complexity of the group inversion operation in this application is 1 / K of the complexity of the direct inversion calculation, which effectively reduces the complexity of the inversion.

[0100] In summary, based on the error correction and encryption fusion dynamic coding matrix construction and low-complexity coding method of this application, the dynamic check matrix H... i Generate the inverse matrix The computational complexity includes the sum of the three terms in the "Generate Encoding Matrix" stage in Table 1. The computational complexity calculation formula is as follows: f g,m (K) is much smaller than the complexity of traditional algorithms in generating the encoding matrix. In the encoding stage, specifically the stage of generating the ciphertext for transmission based on the encoding matrix, the computational complexity of this application includes the sum of the seven terms in the "Generating and Transmitting Ciphertext" stage in Table 1. The computational complexity calculation formula is as follows: f c,m (K) is much smaller than the complexity of the coding stage in traditional algorithms. As can be seen from this example, the error correction and encryption fusion dynamic coding matrix construction and low-complexity coding method of this application reduces the computational complexity in both the coding matrix generation stage and the coding stage, and greatly improves the efficiency of dynamic matrix coding.

[0101] Table 1 Summary of Computational Complexity

[0102]

[0103]

[0104] To further illustrate the technical effects of the dynamic coding matrix construction and low-complexity coding method of error correction and encryption fusion in the embodiments of this application, a specific example 2 is used below for detailed description.

[0105] This example uses Monte Carlo simulation to evaluate the performance of the dynamic coding matrix construction and low-complexity coding method for error correction and encryption fusion in this application. Both the main communication channel and the eavesdropping channel are additive white Gaussian noise channels, and the basis matrix H... B,0 The size is M B ×N B=8×12, use multidimensional EXIT to obtain the basis matrix H B,0 The minimum iterative decoding threshold is 0.782 dB, and the basis matrix H B,0 The number of 1s in the middle is w(H) B,0 =31, in constructing the dynamic sparse random parity-check matrix H i When, for the basis matrix H B,0 The expansion was performed L=2 times, including one structured expansion and one random expansion. The structured expansion factor F1 was 8, and the random expansion factor F2 was 4, 8, 16 or 32. During transmission, in order to ensure information security, all information bits of the codeword were punched, and only the check bits of the codeword were transmitted.

[0106] In terms of computational complexity, such as Figure 2 As shown, with a structured expansion factor F1 of 8 and random expansion factors F2 of 4, 8, 16, or 32, the effect and variation law of reducing computational complexity using the grouping inversion algorithm are demonstrated. The computational complexity exhibits an inverse proportional function trend as K increases; simultaneously, as F2 increases, i.e., as F... (L) =F (2) As the value of F1×F2 increases, the reduction in computational complexity will also increase; that is, the more matrices K the grouped inversion algorithm has, the larger the structured expansion factor and the random expansion factor will be, and the more significant the reduction in computational complexity will be.

[0107] This application also provides a dynamic coding structure and a low-complexity coding device for error correction and encryption fusion, such as... Figure 3 As shown, it includes a processor and memory.

[0108] The memory is used to store the dynamic encoding structure and low-complexity encoding program of error correction and encryption fusion.

[0109] The processor is used to read the dynamic encoding structure and low-complexity encoding program of the error correction and encryption fusion, and to perform the dynamic encoding structure and low-complexity encoding method of the error correction and encryption fusion as described in the above embodiments.

[0110] It will be understood by those skilled in the art that all or some of the steps, systems, or apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all components may be implemented as software executed by a processor, such as a digital signal processor or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software may be distributed on a computer-readable medium, which may include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term "computer storage medium" includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

Claims

1. A dynamic coding construction and low complexity coding method of error correction encryption fusion, characterized in that, Comprising: Continuously receive the information plaintext sequence {m0, m1, m2, …} sent by the source end, and for each information plaintext m i A corresponding dynamic sparse random check matrix H is constructed i Wherein, i = 0, 1, 2, … for each H i performing matrix block processing to obtain the H i corresponding to a plurality of sub-matrices and a double diagonal matrix T i , calculating an intermediate matrix φ i according to the inverse matrix of T i and the sub-matrices, comprising: dividing the H i into H iI and H iP , wherein H i = [H iI H iP ], H iP is a square matrix; dividing H iI into sub-matrices A i and C i , dividing H iP into sub-matrices B i , D i , E i and the double diagonal matrix T i , wherein, calculating the inverse matrix of T i and calculating the intermediate matrix φ i according to the formula ;​ for each K-th obtained intermediate matrix φ i Then, each φ i corresponding inverse matrix where K≥2; For each of the information plaintexts m i , based on the corresponding dynamic matrix encoding, obtaining m i corresponding sending ciphertext P i , comprising: according to the sub-matrix A i corresponding to the information plaintext m i calculate According to the sub-matrix C i corresponding to the information plaintext m i calculate According to the sub-matrix A i corresponding to the information plaintext m i , E i , the inverse matrix calculate According to the formula calculate According to the formula calculate Based on and obtain the sending ciphertext P i , wherein P i =[p i,1 , p i,2 ].

2. The error correction encryption fusion dynamic encoding construction and low complexity encoding method of claim 1, wherein: The information plaintext m i Constructing a corresponding dynamic sparse random check matrix H i Previously, a base matrix H is constructed based on a multi-dimensional external information transfer graph B,0 Wherein, each of the information plaintext m i Corresponding to the base matrix H B,0 Are the same, including: Constructing M B Row M B Column pair diagonal matrix B C Wherein, B C The elements of the main diagonal and the diagonal above the main diagonal are 1, and other elements are 0; B C M B 1 1, obtaining a partial double-diagonal matrix B P wherein, M B / 2 According to the obtained B P , search the minimum iterative decoding threshold of the base matrix H B,0 based on the multi-dimensional external information transfer graph, and obtain B I ; According to B I and B P obtaining the base matrix H B,O = [B I B p ], wherein H B,O is a matrix of M B rows and N B columns.

3. The error correction encryption fusion dynamic encoding construction and low complexity encoding method of claim 2, wherein, The information plaintext m is i Constructing the corresponding dynamic sparse random check matrix H i , comprising: For each information plaintext m i The following operations are performed: performing L-1 structured expansions on the base matrix H B,0 to obtain an expanded matrix H B,L-1 where L≥2. to the expanded matrix H B,L-1 a random expansion is performed to obtain the information plaintext m i corresponding to the dynamic sparse random check matrix H i .

4. The error correction encryption fusion dynamic encoding construction and low complexity encoding method of claim 3, wherein, said base matrix H B,0 obtaining an extended matrix H B,L-1 , comprising: performing L-1 times cyclically structured extension, the lth structured extension comprising the following steps, wherein l = 1, 2, …, L-1: For the extended matrix H B,l-1 Each non-zero element E in n The structured cyclic permutation matrix CPM corresponding to this structured extension is obtained using a predetermined optimization algorithm. ln Among them, CPM ln For F l Line F l A square matrix of columns, F l The pre-set structure extension factor for this structure extension, n = 0, 1, 2, ... w l -1, w l For H B,l-1 The number of non-zero elements; Replace each non-zero element E B,l-1 of H n with the corresponding CPM ln , and replace each element 0 of H B,l-1 with F l , and replace the zero matrix of row F l and column F with the corresponding expanded matrix H B,l ; wherein the pre-expansion matrix for the first structured expansion is the base matrix H B,0 ; the pre-expansion matrix for the lth structured expansion is the post-expansion matrix H B,l-1 ; the post-expansion matrix obtained from the L-lth structured expansion is the post-expansion matrix H B,L-1 .

5. The error correction encryption fusion dynamic encoding construction and low complexity encoding method of claim 3, wherein, The pair of the expanded matrix H B,L-1 A random expansion is performed to obtain the information plaintext m i The corresponding dynamic sparse random check matrix H i , comprising: H B,L-1 each non-zero element E j corresponding random circulant permutation matrix CPM Lj where CPM Lj is F L a square matrix of F L rows and F L is a pre-set random spreading factor, j = 0, 1, 2,... w L - 1, w L is the number of non-zero elements in H B,L-1 ; H B,L-1 Each non-zero element E j Replace with the corresponding CPM Lj , will H B,L-1 Replace each element 0 in the formula with F. L Line F L The zero matrix of the columns is used to obtain the dynamic sparse random parity check matrix H. i .

6. The error correction encryption fusion dynamic encoding construction and low complexity encoding method of claim 5, wherein, The acquisition H B,L-1 Each non-zero element E j The corresponding random circulant permutation matrix CPM Lj , comprising: A pseudo-random vector r L comprising w i,j binary vectors r i is generated using a pseudo-random number generator, wherein Each r i,j has a length of log2F L , r i has a length of w L log2F L , and r i,j corresponds one-to-one to a non-zero element E j . For each E j The following steps are performed: E j corresponding said binary vector r i,j converted into a decimal number D i,j ; CPM Lj The element in the first row, D i,j column is set to 1 and the other elements in the first row are set to 0. Perform F L -1st step to obtain CPM Lj L Row 2 to F Lj th row of CPM Lj th row of CPM L -1.​ 7. The error correction encryption fusion dynamic encoding construction and low complexity encoding method of claim 1, wherein, said K intermediate matrices φ i Afterwards, each φ i corresponding inverse matrix comprises: K number of φ i The information plaintext m i Set to plaintext group {m0, m1, m2, … m K-1} based on K number of φ i Construct intermediate matrix set {φ0, φ1, …, φ K-1}, wherein φ k The information plaintext m k Corresponding to the intermediate matrix, k = 0, 1, 2, … K-1; constructing a first set of matrix collections {W 0,0 ,W 0,1 ,…,W 0,K-1} and a second set of matrix collections {W 1,1 ,W 1,2 ,…,W 1,K-1}; According to the formula K inverse matrices are obtained wherein is the information plaintext m k the corresponding intermediate matrix φ k the inverse matrix of φ wherein 8. An error correction encryption fusion dynamic coding construction and low complexity coding device, comprising a memory and a processor, characterized in that: the memory is used to save the error correction encryption fusion dynamic coding construction and low complexity coding program; the processor is used to read the error correction encryption fusion dynamic coding construction and low complexity coding program, and perform the error correction encryption fusion dynamic coding construction and low complexity coding method of any one of claims 1-7.

Images