A symmetric encryption method based on F-norm matrix multiplication

Abstract

The present invention discloses a symmetric encryption method based on F-norm matrix multiplication. By calculating the F-norm of the row vector of the cipher matrix and the column vector of the decoding matrix, the multiplication of the encryption-related matrices is realized, thereby shortening the calculation time spent on the matrix multiplication operation in the encryption process, improving the efficiency of the symmetric encryption method, and also providing a new idea and a new way for faster matrix multiplication.

Description

Technical Field

[0001] The invention belongs to the technical field of computer encryption calculation, and in particular relates to a symmetric encryption method based on F-norm matrix multiplication. Background Art

[0002] In the process of data transmission, if plain text is used for transmission, it is easy to cause data leakage, which gives hackers an opportunity to take advantage. With the development of cryptography, encryption methods such as symmetric encryption have gradually emerged. Among them, symmetric encryption is based on matrix multiplication. In the process of data encryption transmission, both the data sender and the data receiver hold a password matrix. The data sender first encodes the data to be sent into a message matrix, and encrypts the message by performing matrix multiplication between the password matrix and the message matrix to obtain an encrypted message matrix, and then sends the encrypted message matrix to the receiver. After receiving the encrypted message matrix, the receiver uses the inverse matrix of the password matrix to perform matrix multiplication with the encrypted message matrix to decrypt the encrypted message to obtain the decrypted message matrix, and finally decodes the message matrix into data, thereby completing the data encryption transmission process, which avoids the risk of data transmission in plain text. However, the traditional matrix multiplication is to multiply the corresponding elements of the corresponding row vector and column vector of the matrix and then add them. With the increase of the matrix dimension, the calculation time will increase significantly. Therefore, it is of great significance to shorten the calculation time while ensuring the accuracy of the calculation. Summary of the invention

[0003] In view of this, the present invention provides a symmetric encryption method based on F-norm matrix multiplication, which effectively speeds up the symmetric encryption process by shortening the calculation time of matrix multiplication.

[0004] The present invention provides a symmetric encryption method based on F-norm matrix multiplication, including an encryption process and a decryption process, which specifically includes the following steps:

[0005] During the encryption process, the message matrix after plaintext encoding is And the password matrix is Calculate the password matrix The row vector and message matrix The F norm of the column vector of , which realizes the matrix multiplication of the password matrix and the message matrix to obtain the encrypted message matrix C m×m ; During the decryption process, let the decoding matrix be Password Matrix The inverse matrix of the decrypted message matrix is ​​V m ×n , calculate the encrypted message matrix C m×m The row vector and decoding matrix The F norm of the column vector of , which realizes the matrix multiplication of the encrypted message matrix and the decoding matrix to obtain the decrypted message matrix V m×n .

[0006] Furthermore, during the encryption process, the password matrix is ​​calculated The row vector and message matrix The F norm of the column vector of , which realizes the matrix multiplication of the password matrix and the message matrix to obtain the encrypted message matrix C m×m The process includes the following steps:

[0007] Step 1.1: Calculate the message matrix using formula (2) The square value of the F norm of the k-th row vector in :

[0008]

[0009] in, Message Matrix The element in row k and column n, The message matrix A vector consisting of the square values ​​of the F norm of all row vectors in ;

[0010] Step 1.2: Use formula (3) to calculate the password matrix The square value of the F norm of the k-th column vector in:

[0011]

[0012] in, Password Matrix The element at row n and column k of The password matrix The vector formed by the square values ​​of the F norm of all column vectors in ; let l = 1 and t = 1;

[0013] Step 1.3: Calculate the message matrix using formula (4) The lth row vector and the password matrix The square value of the F-norm of the difference between the t-th column vectors in :

[0014]

[0015] Where T is the transpose of the vector;

[0016] Step 1.4, let t and l increase by 1, if t≤m and l≤m, execute step 1.3, otherwise execute step 1.5;

[0017] Step 1.5: Output the encrypted message matrix C m×m , C m×m It is expressed as shown in formula (5):

[0018]

[0019] Furthermore, during the decryption process, the encrypted message matrix C is calculated. m×m The row vector and decoding matrix The F norm of the column vector of , which realizes the matrix multiplication of the encrypted message matrix and the decoding matrix to obtain the decrypted message matrix V m×n The process includes the following steps:

[0020] Step 2.1: Use formula (7) to calculate the encrypted matrix C m×m The square value of the F norm of the k-th row vector in :

[0021]

[0022] Among them, c k×m is the encrypted matrix C m×m The k-th row and m-th column element in is the encrypted matrix C m×m A vector consisting of the square values ​​of the F norm of all row vectors in ;

[0023] Step 2.2: Use formula (8) to calculate the decoding matrix: The square value of the F norm of the k-th column vector in:

[0024]

[0025] in, is the decoding matrix The element in the mth row and kth column of

[0026] The decoding matrix The vector formed by the square values ​​of the F norm of all column vectors in; let ll=1 and tt=1;

[0027] Step 2.3: Use formula (9) to calculate the encrypted matrix C m×m The llth row vector and the decoding matrix are The square value of the F norm of the difference between the ttth column vectors in :

[0028]

[0029] Where T is the transpose of the vector;

[0030] Step 2.4, let tt increment by 1, let ll increment by 1, if tt≤n and ll≤m, execute step 2.3, otherwise execute step 2.5;

[0031] Step 2.5: Output the decrypted message matrix Vm×n , V m×n is the encrypted message matrix C m×m And the decoding matrix is The product of is expressed as shown in formula (10):

[0032]

[0033] Beneficial effects:

[0034] The present invention realizes the multiplication of encryption-related matrices by calculating the F-norm of the row vectors of the cipher matrix and the column vectors of the decoding matrix, thereby shortening the calculation time spent on matrix multiplication operations during the encryption process, improving the efficiency of the symmetric encryption method, and also providing new ideas and new ways for faster matrix multiplication. DETAILED DESCRIPTION

[0035] The present invention is described in detail with reference to the following embodiments.

[0036] The present invention provides a symmetric encryption method based on F-norm matrix multiplication, the basic idea of ​​which is: by calculating the F-norm of the row vector of the cipher matrix and the column vector of the message matrix, the matrix multiplication of the cipher matrix and the message matrix is ​​realized to obtain the encrypted message matrix; by calculating the F-norm of the row vector of the encrypted message matrix and the column vector of the decoding matrix, the matrix multiplication of the encrypted message matrix and the decoding matrix is ​​realized to obtain the decrypted message matrix.

[0037] The F-norm of the column vector of the decoding matrix realizes the multiplication of the encryption correlation matrix.

[0038] The present invention provides a symmetric encryption method based on F-norm matrix multiplication, including an encryption process and a decryption process, which specifically includes the following steps:

[0039] (a) Encryption process

[0040] Let the message matrix after plaintext encoding be And the password matrix is Encrypted message matrix C m×m Message Matrix With Password Matrix The product of is shown in formula (1):

[0041]

[0042] Step 1.1: Calculate the message matrix using formula (2) The square value of the F norm of the k-th row vector in :

[0043]

[0044] in, Message Matrix The element in row k and column n, The message matrix A vector consisting of the squared values ​​of the F norm of all row vectors in .

[0045] Step 1.2: Use formula (3) to calculate the password matrix The square value of the F norm of the k-th column vector in:

[0046]

[0047] in, Password Matrix The nth row and kth column element of The password matrix The vector consisting of the square values ​​of the F norm of all column vectors in . Let l=1 and t=1.

[0048] Step 1.3: Calculate the message matrix using formula (4) The lth row vector and the password matrix The square value of the F-norm of the difference between the t-th column vectors in :

[0049]

[0050] Where T is the transpose of the vector.

[0051] Step 1.4: Let t increment by 1, let l increment by 1. If t≤m and l≤m, execute step 1.3; otherwise, execute step 1.5.

[0052] Step 1.5: Output the encrypted message matrix C m×m , C m×m For the message matrix With Password Matrix The product of is expressed as shown in formula (5):

[0053]

[0054] (2) Decryption process

[0055] Let the decoding matrix be Password Matrix The inverse matrix of the decrypted message matrix V m×n is the encrypted message matrix C m×m And the decoding matrix is The product of is shown in formula (6):

[0056]

[0057] Step 2.1: Use formula (7) to calculate the encrypted matrix C m×m The square value of the F norm of the k-th row vector in :

[0058]

[0059] Among them, c k×m is the encrypted matrix C m×m The k-th row and m-th column element in is the encrypted matrix C m×m A vector consisting of the squared values ​​of the F norm of all row vectors in .

[0060] Step 2.2: Use formula (8) to calculate the decoding matrix: The square value of the F norm of the k-th column vector in:

[0061]

[0062] in, is the decoding matrix The element in the mth row and kth column of

[0063] The decoding matrix The vector consisting of the square values ​​of the F norm of all column vectors in . Let ll=1 and tt=1.

[0064] Step 2.3: Use formula (9) to calculate the encrypted matrix C m×m The llth row vector and the decoding matrix are The square value of the F norm of the difference between the ttth column vectors in :

[0065]

[0066] Where T is the transpose of the vector.

[0067] Step 2.4: Let tt increment by 1, let ll increment by 1. If tt≤n and ll≤m, execute step 2.3; otherwise, execute step 2.5.

[0068] Step 2.5: Output the decrypted message matrix V m×n , V m×n is the encrypted message matrix C m×m And the decoding matrix is The product of is shown in formula (10):

[0069]

[0070] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A symmetric encryption method based on F-norm matrix multiplication, characterized in that: Including encryption process and decryption process, specifically including the following steps: During the encryption process, let the message matrix after plaintext encoding be And the password matrix is Calculate the password matrix The row vector and message matrix The F norm of the column vector of , which realizes the matrix multiplication of the password matrix and the message matrix to obtain the encrypted message matrix C m×m ; During the decryption process, let the decoding matrix be Password Matrix The inverse matrix of the decrypted message matrix is ​​V m×n , calculate the encrypted message matrix C m×m The row vector and decoding matrix The F norm of the column vector of , which realizes the matrix multiplication of the encrypted message matrix and the decoding matrix to obtain the decrypted message matrix V m×n ; During the encryption process, the calculation password matrix The row vector and message matrix The F norm of the column vector of , which realizes the matrix multiplication of the password matrix and the message matrix to obtain the encrypted message matrix C m×m The process includes the following steps: Step 1.1: Calculate the message matrix using formula (2) The square value of the F norm of the k-th row vector in : in, Message Matrix The element in row k and column n, The message matrix A vector consisting of the square values ​​of the F norm of all row vectors in ; Step 1.2: Use formula (3) to calculate the password matrix The square value of the F norm of the k-th column vector in: in, Password Matrix The nth row and kth column element of The password matrix The vector formed by the square values ​​of the F norm of all column vectors in ; let l = 1 and t = 1; Step 1.3: Calculate the message matrix using formula (4) The lth row vector and the password matrix The square value of the F-norm of the difference between the t-th column vectors in : Where T is the transpose of the vector; Step 1.4, let t and l increase by 1, if t≤m and l≤m, execute step 1.3, otherwise execute step 1.5; Step 1.5: Output the encrypted message matrix C m×m , C m×m It is expressed as shown in formula (5): In the decryption process, the encrypted message matrix C is calculated. m×m The row vector and decoding matrix The F norm of the column vector of , which realizes the matrix multiplication of the encrypted message matrix and the decoding matrix to obtain the decrypted message matrix V m×n The process includes the following steps: Step 2.1: Use formula (7) to calculate the encrypted matrix C m×m The square value of the F norm of the k-th row vector in : Among them, c k×m is the encrypted matrix C m×m The k-th row and m-th column element in is the encrypted matrix C m×m A vector consisting of the square values ​​of the F norm of all row vectors in ; Step 2.2: Use formula (8) to calculate the decoding matrix: The square value of the F norm of the k-th column vector in: in, is the decoding matrix The element in the mth row and kth column of The decoding matrix The vector formed by the square values ​​of the F norm of all column vectors in; let ll=1 and tt=1; Step 2.3: Use formula (9) to calculate the encrypted matrix C m×m The llth row vector and the decoding matrix are The square value of the F norm of the difference between the ttth column vectors in : Where T is the transpose of the vector; Step 2.4, let tt increment by 1, let ll increment by 1, if tt≤n and ll≤m, execute step 2.3, otherwise execute step 2.5; Step 2.5: Output the decrypted message matrix V m×n , V m×n is the encrypted message matrix C m×m And the decoding matrix is The product of is expressed as shown in formula (10):

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