CN115276992A - Domain arithmetic-based symmetric image password processing method - Google Patents

Domain arithmetic-based symmetric image password processing method Download PDF

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CN115276992A
CN115276992A CN202211210136.6A CN202211210136A CN115276992A CN 115276992 A CN115276992 A CN 115276992A CN 202211210136 A CN202211210136 A CN 202211210136A CN 115276992 A CN115276992 A CN 115276992A
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pseudo
random number
elements
number matrix
representing
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张勇
方玉明
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Jiangxi University of Finance and Economics
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Jiangxi University of Finance and Economics
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/065—Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3
    • H04L9/0656—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher
    • H04L9/0662—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher with particular pseudorandom sequence generator
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/002—Countermeasures against attacks on cryptographic mechanisms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0891—Revocation or update of secret information, e.g. encryption key update or rekeying
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • H04N1/32267—Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
    • H04N1/32272—Encryption or ciphering

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  • Computer Security & Cryptography (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
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  • Facsimile Transmission Control (AREA)

Abstract

The invention provides a domain arithmetic-based password processing method for symmetric images, wherein a pseudorandom matrix participates in encryption control, and different cipher text images are obtained by encrypting the same secret key and the same plaintext image at different moments on an encryption side; the cryptographic processing method of the symmetric image based on the domain arithmetic has the characteristic of one-time pad, and can resist various existing passive attacks; in addition, the cipher processing method is a symmetric cipher algorithm, a pseudo-random number matrix is not needed on a decryption side, and an original plaintext image can be restored from a ciphertext image.

Description

Domain arithmetic-based symmetric image password processing method
Technical Field
The invention relates to the technical field of image encryption, in particular to a cryptographic processing method of a symmetric image based on domain arithmetic.
Background
In the field of image encryption, a conventional image encryption scheme is shown in fig. 1, and comprises an equivalent key generator and a scrambling and diffusing module, and a chaotic system is generally selected as the key generator. Specifically, the image encryption scheme shown in fig. 1 is widely used, and in this encryption scheme, the image decryption algorithm is the reverse process of the image encryption algorithm. In fig. 1, the scrambling algorithm is used to scramble the positions of the pixels of the image without changing the values of the individual pixels; the diffusion algorithm is used for diffusing the information of any pixel point in the image into as many pixel points as possible, and the diffusion mainly changes the value of the pixel point without paying attention to the position of the pixel point. The scrambling and diffusion algorithms require a sequence of pseudo-random numbers generated by means of an equivalent key generator. In addition, the scrambling algorithm and the diffusion algorithm can be combined together for implementation, and a plaintext image is converted into a ciphertext image similar to a noise image by circularly executing the scrambling algorithm and the diffusion algorithm for multiple times, so that the aim of hiding image information is fulfilled.
However, the existing image encryption method has the following disadvantages:
(1) In the existing scheme, a plaintext image is encrypted into a unique ciphertext image by a key, and an enemy who steals the encryption equipment can use the equipment to generate a plurality of pairs of plaintext-ciphertext pairs, so that known plaintext attack or plaintext attack selection can be implemented to obtain an equivalent key of an encryption system;
(2) An adversary who steals the decryption device can use the device to generate a plurality of pairs of ciphertext-plaintext pairs, so that known ciphertext attacks or ciphertext attack selection can be effectively implemented to obtain an equivalent key of a decryption system;
(3) When an adversary has only obtained a pair of plaintext-ciphertext pairs, the adversary can take a ciphertext-only attack or an exhaustive key attack to obtain a key or an equivalent key of the encryption system.
Based on this, it is necessary to provide a symmetric image encryption method based on domain arithmetic to solve the above technical problems.
Disclosure of Invention
In view of the above situation, the main object of the present invention is to provide a symmetric image encryption method based on domain arithmetic to solve the above technical problems.
The embodiment of the invention provides a cryptographic processing method of a symmetric image based on domain arithmetic, wherein the method comprises the following steps:
step one, generating a pseudo-random number matrix by using an equivalent key generator:
step 1.1, from the first subkeykey 1 With a second subkeykey 2 Respectively calculating to obtain first state variablesx 0 And a second state changeQuantity ofy 0 ；
Step 1.2, setting circulation variableiIncrement from 0 to 1 stepd-3 at the firstiIn the secondary cycle, willx 0 Andy 0 the updating is carried out by substituting into a H non mapping equation, and the loop is carried outM×(N+ 4) times, the update is completed, and the updated first state variable is still recorded asx 0 The updated second state variable is still recorded asy 0 (ii) a Wherein,drepresenting the number of subkeys;
step 1.3, the extraction length isM×(N+ 4) state variablex i }, i=1,2,…, M×(N+ 4) and converted to a size ofM×(N+ 4) first pseudo-random number matrixSWherein, in the process,Mrepresenting the number of rows of a pseudo-random number matrix,Nrepresenting the number of columns of the pseudo random number matrix;
step two, an image encryption method;
step 2.1, the computer-based pseudo-random number generator generates a pseudo-random number of sizeMSecond pseudo-random number matrix of x 4R；
Step 2.2, based on the second pseudo-random number matrixRAnd elements of columns 1 and 3, and a first pseudo-random number matrixSTo middleN+3 columns andN+4 columns of elements, calculated to have a size ofMX 2 third pseudo-random number matrixY；
Step 2.3, based on the third pseudo-random number matrixYMiddle 2 nd column element, first pseudo random number matrixSElement of middle 2 nd column and second pseudo random number matrixRThe elements in column 2 scramble the elements of the plaintext image and are calculated to have a size ofM×NFourth pseudo random number matrix ofZ；
Step 2.4, based on the third pseudo-random number matrixYElement of middle 4 th column, first pseudo random number matrixSMiddle 4 th column of elements and a second pseudo-random number matrixRThe 4 th column element scrambles the fourth pseudo random number matrixZAnd calculating a size ofM×NOf the fifth pseudo-random number matrixW；
Step 2.5, use the first pseudo randomMachine number matrixSTo (1) aN+1 columns andN+2 columns of elements, for the sixth pseudo-random number matrixGScrambling is carried out, and the matrix after scrambling is marked as a seventh pseudo-random number matrixH；
Step 2.6, apply the fifth pseudo-random number matrixWAnd a seventh pseudo-random number matrixHAre combined into a size ofM×(N+ 2) eighth pseudo random number matrixC；
Step 2.7, based on the first pseudo-random number matrixSAnd ninth pseudo random number matrixQIs scrambled by a value ofCTo calculate a new position coordinate;
step three, an image decryption method;
step 3.1, apply the first pseudo-random number matrixS1 toMAnd lines 1 to 1NThe upper 4 bits and the lower 4 bits of each element in the region surrounded by +2 columns are interchanged to obtain a ninth pseudo-random number matrixQ；
Step 3.2, based on the first pseudo-random number matrixSAnd ninth pseudo random number matrixQA value of (b), restoring the eighth pseudo random number matrix before scramblingCThe element position of (a);
step 3.3, decompose the eighth pseudo-random number matrixCIs a fifth pseudo-random number matrixWAnd a seventh pseudo random number matrixH；
Step 3.4, based on the first pseudo-random number matrixSTo (1)N+1 columns andN+2 columns the seventh pseudo-random number matrixHReverting to a sixth pseudo-random number matrixG；
Step 3.5, based on the ninth pseudo-random number matrixQFirst pseudo random number matrixSAnd a sixth pseudo-random number matrixGA fifth pseudo random number matrixWInto a fourth pseudo-random number matrixZ；
Step 3.6, based on the first pseudo-random number matrixSAnd a sixth pseudo-random number matrixGApplying a fourth pseudo-random number matrixZConversion to a tenth pseudo-random number matrixPTenth pseudorandom number matrixPIs a restored plaintext image.
The invention has the following advantages:
(1) By introducing a sequence of pseudo-random numbers, a set of pseudo-random numbers generated randomly by the computer as part of the key participates in the encryption algorithm during encryption, the set of computer-generated pseudo-random numbers being time-dependent on the computer. Therefore, each time an image is encrypted, a different pseudo-random number is introduced, so that equivalent keys participating in operation in the encryption process are different, and the process is not reproducible; even if the same plaintext image is encrypted, ciphertext images obtained by encrypting at different moments are completely different.
(2) Because the encryption process uses the pseudo-random number generated by the computer, the relation between the plaintext image and the ciphertext image is not in one-to-one correspondence, and a plaintext image can be encrypted into different ciphertext images at different moments. Therefore, an adversary who steals the encryption device or the decryption device cannot implement various passive attacks.
(3) The whole image cryptosystem is a symmetric cryptosystem, and a legal decryption party can complete decryption only by owning a legal decryption key (the same as an encryption key) and a ciphertext image to obtain an original plaintext image. The encryptor uses a discrete exponent (or discrete logarithm) method to convert the introduced pseudo random number into a discrete exponent value and hide the discrete exponent value in the ciphertext information.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
FIG. 1 is a block diagram of a prior art image encryption algorithm;
FIG. 2 is a schematic block diagram of an encryption algorithm proposed by the present invention;
fig. 3 is a schematic block diagram of a decryption algorithm proposed by the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
These and other aspects of embodiments of the invention will be apparent with reference to the following description and attached drawings. In the description and drawings, particular embodiments of the invention have been disclosed in detail as being indicative of some of the ways in which the principles of the embodiments of the invention may be practiced, but it is understood that the scope of the embodiments of the invention is not limited correspondingly. On the contrary, the embodiments of the invention include all changes, modifications and equivalents coming within the spirit and terms of the claims appended hereto.
The symmetric image encryption algorithm provided by the invention comprises three parts: namely an equivalent cipher generator, an image encryption algorithm and an image decryption algorithm, and each algorithm module is described in detail as follows:
the invention provides a cryptographic processing method of a symmetric image based on domain arithmetic, wherein the method comprises the following steps:
step one, generating a pseudo-random number matrix by using an equivalent key generator:
noting the key of an image encryption system asKLength of 24dA bit. For example, taked=20, the key length is 480 bits. Let the plain text image be a 8-bit grayscale image with a size ofM×N。
In the invention, a H non mapping equation is used as the core of a key expansion algorithm. Specifically, the hnon mapping equation is expressed as:
Figure 268245DEST_PATH_IMAGE001
（1）
wherein,
Figure 600000DEST_PATH_IMAGE002
are all represented as state variables, and are,
Figure 355467DEST_PATH_IMAGE003
，
Figure 823488DEST_PATH_IMAGE004
，
Figure 373418DEST_PATH_IMAGE005
are all constants.
Secret keyKIs divided intodSecondary keykey 1 , key 2 ,…,key d Each subkey is 24 bits long, and is composed of keysKGenerating a size ofM×(N+4) First pseudo random number matrix ofS. As a supplement, whena=1.4，bWhen =0.3, the hnon map has a chaotic attractor with a maximum Lyapunov exponent of 0.654.
Step 1.1, from the first subkeykey 1 With a second subkeykey 2 Respectively calculating to obtain first state variablesx 0 And a second state variabley 0 。
In step 1.1, the following formula exists:
Figure 192470DEST_PATH_IMAGE006
（2）
the first state variablex 0 And a second state variabley 0 After iteration is carried out for 20 times in the formula (1), a group of chaotic states are obtained and still recorded asx 0 And withy 0 。
Step 1.2, setting circulation variableiIncrement from 0 to 1 stepd-3 in the first placeiIn the second cycle, willx 0 Andy 0 the updating is carried out by substituting into a H non mapping equation, and the loop is carried outM×(N+ 4) times, the update is completed, and the updated first state variable is still recorded asx 0 The updated second state variable is still recordedy 0 (ii) a Wherein,dindicating the number of subkeys.
In step 1.2, the following formula exists:
Figure 486048DEST_PATH_IMAGE007
（3）
wherein,
Figure 198789DEST_PATH_IMAGE008
denotes the first
Figure 559101DEST_PATH_IMAGE009
A sub-key.
Will be provided withx 0 A second expression substituted in formula (1) yields a state, denoted asy 0 . Then will bex 1 Andy 1 in formula (1), after 20 iterations, a new set of states is obtained, which are still recorded asx 0 Andy 0 and adding a new state variable to realize the transition of the chaotic orbit.
Step 1.3, the extraction length isM×(N+ 4) state variablex i }, i=1,2,…, M×(N+ 4) and converted to a size ofM×(N+ 4) first pseudo-random number matrixSWherein, in the process,Mrepresenting the number of rows of the pseudo-random number matrix,Nrepresenting the number of columns of the pseudo random number matrix.
In step 1.3, the following formula exists:
Figure 724503DEST_PATH_IMAGE010
（4）
wherein,
Figure 431559DEST_PATH_IMAGE011
representing a first pseudo-random number matrixSTo (1)iGo to the firstjThe elements of the column are,
Figure 264386DEST_PATH_IMAGE012
is shown as
Figure 297064DEST_PATH_IMAGE013
The state variable of the state machine is changed into a state variable,
Figure 949762DEST_PATH_IMAGE014
，
Figure 585143DEST_PATH_IMAGE015
，
Figure 147842DEST_PATH_IMAGE016
representing a modulo operation.
Step two, an image encryption method;
the image encryption algorithm uses a Galois field GF (257) (Galois denotes a Galois field), and a set of all elements thereof is denoted byZ 257 ={0, 1, 2, …, 256}，Z 257 The remaining classes of the module 257. Three parameter vectors are definedT 1 、T 2 AndT 3 as follows:
T 1 ={3, 5, 6, 7, 10, 12, 14, 19, 20, 24, 27, 28, 33, 37, 38, 39, 40, 41, 43, 45, 47, 48, 51, 53, 54, 55, 56, 63, 65, 66, 69, 71, 74, 75, 76, 77, 78, 80, 82, 83, 85, 86, 87, 90, 91, 93, 94, 96, 97, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 115, 119, 125, 126, 127, 130, 131, 132, 138, 142, 145, 147, 148, 149, 150, 151, 152, 154, 155, 156, 160, 161, 163, 164, 166, 167, 170, 171, 172, 174, 175, 177, 179, 180, 181, 182, 183, 186, 188, 191, 192, 194, 201, 202, 203, 204, 206, 209, 210, 212, 214, 216, 217, 218, 219, 220, 224, 229, 230, 233, 237, 238, 243, 245, 247, 250, 251, 252, 254}。
T 2 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255}。
T 3 ={1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251, 253, 255}。
the image encryption algorithm provided by the invention is shown in fig. 2:
step 2.1, the computer-based pseudo-random number generator generates a pseudo-random number of sizeMSecond pseudo random number matrix of x 4R。
In step 2.1, the following formula exists:
Figure 476056DEST_PATH_IMAGE017
（5）
wherein,
Figure 727302DEST_PATH_IMAGE018
representing a sixth pseudo-random number matrixGTo (1) aiGo to the firstjThe elements of the column are,
Figure 166373DEST_PATH_IMAGE019
representing a second pseudo-random number matrixRTo (1) aiLine 2j-1 column of elements,
Figure 442634DEST_PATH_IMAGE020
representing a second pseudo-random number matrixRTo (1) aiLine 2jThe elements of the column are,
Figure 817114DEST_PATH_IMAGE021
representing a vectorT 1 To (1) a
Figure 444405DEST_PATH_IMAGE022
The elements at the location of the position,
Figure 296954DEST_PATH_IMAGE023
representing a vectorT 3 To (1)
Figure 693301DEST_PATH_IMAGE024
The elements at the location of the position(s),
Figure 238683DEST_PATH_IMAGE014
，
Figure 353269DEST_PATH_IMAGE025
。
step 2.2, based on the second pseudo-random number matrixRAnd elements of columns 1 and 3, and a first pseudo-random number matrixSTo middleN+3 columns andN+4 columns of elements, calculated to have a size ofMX 2 third pseudo-random number matrixY。
In step 2.2, the following formula exists:
Figure 773624DEST_PATH_IMAGE026
（6）
wherein,
Figure 758897DEST_PATH_IMAGE027
representing a third pseudo-random number matrixYTo (1)iGo to the firstjThe elements of the column are,
Figure 599815DEST_PATH_IMAGE028
representing a first pseudo-random number matrixSTo (1)iGo to the firstN+2+jThe elements of the column are,
Figure 811484DEST_PATH_IMAGE029
representing a vectorT 2 To (1)
Figure 396049DEST_PATH_IMAGE028
The elements at the location of the position,
Figure 642354DEST_PATH_IMAGE014
，
Figure 388593DEST_PATH_IMAGE025
。
step 2.3, based on the third pseudo-random number matrixYElement of middle 2 nd column, first pseudo random number matrixSElement of middle 2 nd column and second pseudo random number matrixRThe elements in column 2 scramble the elements of the plaintext image and are calculated to have a size ofM×NFourth pseudo random number matrix ofZ。
Step 2.3 corresponds to a forward scrambling procedure, which corresponds to the following formula:
(1) For a pixel point
Figure 477772DEST_PATH_IMAGE030
；
Figure 475815DEST_PATH_IMAGE031
(7)
Wherein,
Figure 435681DEST_PATH_IMAGE032
representing an eleventh pseudo-random number matrixURow 1 and column 1 elements of (a),
Figure 618400DEST_PATH_IMAGE030
representing a tenth pseudorandom number matrixPRow 1 and column 1 elements of (a),
Figure 306127DEST_PATH_IMAGE033
representing a third pseudo-random number matrixYRow 1 and column 1 elements of,
Figure 232495DEST_PATH_IMAGE034
representing a second pseudo-random number matrixRRow 1 and column 2 elements of (a),
Figure 453391DEST_PATH_IMAGE035
representing a vectorT 3 To (1) a
Figure 541433DEST_PATH_IMAGE034
The elements at the location of the position,
Figure 214991DEST_PATH_IMAGE036
representing a fourth pseudo-random number matrixZRow 1 and column 1 elements of,
Figure 679471DEST_PATH_IMAGE037
representing a first pseudo-random number matrixSRow 1, column 1 elements;
(2) For the tenth pseudo random number matrixPDivision of line 1
Figure 879508DEST_PATH_IMAGE030
The element (b);
Figure 279396DEST_PATH_IMAGE038
(8)
wherein,
Figure 564884DEST_PATH_IMAGE039
representing an eleventh pseudo-random number matrixULine 1 tojThe elements of the column(s) are,
Figure 941376DEST_PATH_IMAGE040
representing a fourth pseudo-random number matrixZLine 1 toj-1 column of elements of a group,
Figure 995920DEST_PATH_IMAGE041
representing a tenth pseudorandom number matrixPLine 1 tojThe elements of the column are,
Figure 832289DEST_PATH_IMAGE042
representing a fourth pseudo-random number matrixZLine 1 tojThe elements of the column are,
Figure 339494DEST_PATH_IMAGE043
representing a first pseudo-random number matrixSLine 1 tojElements of a column;
(3) For the tenth pseudo random number matrixPOther than line 1;
(i) For the firstiRow column 1 elements:
Figure 145776DEST_PATH_IMAGE044
(9)
wherein,
Figure 930192DEST_PATH_IMAGE045
representing an eleventh pseudo-random number matrixUTo (1)iThe elements of row column 1 are shown,
Figure 796517DEST_PATH_IMAGE046
representing a fourth pseudo-random number matrixZTo (1) ai-1 line 1NThe elements of the column are,
Figure 791018DEST_PATH_IMAGE047
representing a tenth pseudorandom number matrixPTo (1) aiThe elements of row column 1 are,
Figure 276357DEST_PATH_IMAGE048
representing a third pseudo-random number matrixYTo (1) aiThe elements of row column 1 are shown,
Figure 39914DEST_PATH_IMAGE049
representing a second pseudo-random numberMatrix arrayRTo (1) aiThe elements of row and column 2 are,
Figure 731269DEST_PATH_IMAGE050
representing a vectorT 3 To (1) a
Figure 213066DEST_PATH_IMAGE049
The elements at the location of the position,
Figure 502096DEST_PATH_IMAGE051
representing a fourth pseudo-random number matrixZTo (1) aiThe elements of row column 1 are,
Figure 120159DEST_PATH_IMAGE052
representing a first pseudo-random number matrixSTo (1) aiRow column 1 element;
(ii) For the firstiGo to the firstjElements of the column:
Figure 593866DEST_PATH_IMAGE053
(10)
wherein,
Figure 438325DEST_PATH_IMAGE054
representing an eleventh pseudo-random number matrixUTo (1)iGo to the firstjThe elements of the column(s) are,
Figure 124521DEST_PATH_IMAGE055
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstj-1 column of elements,
Figure 3615DEST_PATH_IMAGE056
representing a tenth pseudorandom number matrixPTo (1)iGo to the firstjThe elements of the column are,
Figure 648223DEST_PATH_IMAGE057
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstjThe elements of the column are,
Figure 839033DEST_PATH_IMAGE058
representing a first pseudo-random number matrixSTo (1)iGo to the firstjThe elements of the column.
Step 2.3 of converting the plaintext image into a fourth pseudo-random number matrixZ。
Step 2.4, based on the third pseudo-random number matrixYColumn 4 element, first pseudo random number matrixSMiddle 4 th column of elements and a second pseudo-random number matrixRThe 4 th column element scrambles the fourth pseudo random number matrixZAnd calculating a size ofM×NOf the fifth pseudo-random number matrixW。
In step 2.4, the following formula exists:
(1) The first pseudo random number matrixS1 toMAnd lines 1 to 1NInterchanging the upper 4 bits and the lower 4 bits of each element in the area surrounded by the +2 columns to obtain a ninth pseudo-random number matrixQ；
(2) For elements
Figure 968401DEST_PATH_IMAGE059
：
Figure 295477DEST_PATH_IMAGE060
(11)
Wherein,
Figure 986353DEST_PATH_IMAGE061
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstNThe elements of the column are,
Figure 930038DEST_PATH_IMAGE059
representing a fourth pseudo-random number matrixZTo (1) aMGo to the firstNThe elements of the column(s) are,
Figure 364561DEST_PATH_IMAGE062
representing a third pseudo-random number matrixYTo (1) aMThe elements of row and column 2 are,
Figure 77302DEST_PATH_IMAGE063
representing a second pseudo-random number matrixRTo (1) aMThe elements of row and column 4,
Figure 532555DEST_PATH_IMAGE064
representing a vectorT 3 To (1) a
Figure 838902DEST_PATH_IMAGE065
The elements at the location of the position,
Figure 936171DEST_PATH_IMAGE066
representing a fifth pseudo-random number matrixWTo (1) aMGo to the firstNThe elements of the column are,
Figure 880250DEST_PATH_IMAGE067
representing a ninth pseudorandom number matrixQTo (1)MGo to the firstNElements of a column;
(3) For the fourth pseudo random number matrixZFirst, theMRemoval of rows
Figure 771982DEST_PATH_IMAGE059
The elements (c):
Figure 565626DEST_PATH_IMAGE068
(12)
wherein,
Figure 201007DEST_PATH_IMAGE069
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstjThe elements of the column are,
Figure 622761DEST_PATH_IMAGE070
representing a fifth pseudo-random number matrixWTo (1) aMGo to the firstjThe elements of the +1 column are,
Figure 826340DEST_PATH_IMAGE071
representing a fourth pseudo-random number matrixZTo (1) aMGo to the firstjThe elements of the column are,
Figure 966334DEST_PATH_IMAGE072
representing a fifth pseudo-random number matrixWTo (1)MGo to the firstjThe elements of the column(s) are,
Figure 546351DEST_PATH_IMAGE073
representing a ninth pseudorandom number matrixQTo (1) aMGo to the firstjElements of a column;
(4) For the fourth pseudo-random number matrixZIs except forMElements of other rows outside the row:
(i) For the firstiGo to the firstNElements of a column
Figure 822612DEST_PATH_IMAGE074
；
Figure 695628DEST_PATH_IMAGE075
(13)
Wherein,
Figure 57339DEST_PATH_IMAGE076
twelfth pseudo random number matrixVTo (1) aiGo to the firstNThe elements of the column are,
Figure 300102DEST_PATH_IMAGE077
representing a fifth pseudo-random number matrixWTo (1) aiThe element of +1 row and column 1,
Figure 306235DEST_PATH_IMAGE074
representing a fourth pseudo-random number matrixZTo (1)iGo to the firstNThe elements of the column are,
Figure 976251DEST_PATH_IMAGE078
representing a third pseudo-random number matrixYTo (1) aiThe elements of row and column 2 are,
Figure 966203DEST_PATH_IMAGE079
representing a second pseudo-random number matrixRTo (1)iThe elements of row column 4 are shown,
Figure 481498DEST_PATH_IMAGE080
representing a vectorT 3 To (1) a
Figure 997930DEST_PATH_IMAGE081
The elements at the location of the position(s),
Figure 714213DEST_PATH_IMAGE082
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstNThe elements of the column(s) are,
Figure 316096DEST_PATH_IMAGE083
representing a ninth pseudo-random number matrixQTo (1)iRow, column N element;
(ii) For the firstiGo to the firstjThe elements of the column:
Figure 11913DEST_PATH_IMAGE084
(14)
wherein,
Figure 382852DEST_PATH_IMAGE085
representing a twelfth pseudo-random number matrixVTo (1) aiGo to the firstjThe elements of the column are,
Figure 270036DEST_PATH_IMAGE086
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstjThe elements of the +1 column are,
Figure 828056DEST_PATH_IMAGE087
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstjThe elements of the column are,
Figure 216312DEST_PATH_IMAGE088
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstjThe elements of the column are,
Figure 51544DEST_PATH_IMAGE089
representing a ninth pseudorandom number matrixQTo (1) aiGo to the firstjThe elements of the column.
Step 2.5, use the first pseudo-random number matrixSTo (1) aN+1 columns andN+2 columns of elements, for the sixth pseudo-random number matrixGScrambling is carried out, and the matrix after scrambling is recorded as a seventh pseudo-random number matrixH。
In step 2.5, the following formula exists:
Figure 234264DEST_PATH_IMAGE090
(15)
wherein,
Figure 686105DEST_PATH_IMAGE091
representing a seventh pseudo-random number matrixHRow 1 and column 1 elements of,
Figure 612473DEST_PATH_IMAGE092
representing a sixth pseudo-random number matrixGRow 1 and column 1 elements of (a),
Figure 66326DEST_PATH_IMAGE093
representing a first pseudo-random number matrixSLine 1 toNThe elements of the +1 column are,
Figure 419947DEST_PATH_IMAGE094
representing a seventh pseudo-random number matrixHTo (1) aiThe elements of row column 1 are shown,
Figure 952559DEST_PATH_IMAGE095
representing a seventh pseudo-random number matrixHTo (1) ai-1 row and column 1 elements,
Figure 557984DEST_PATH_IMAGE096
representing a sixth pseudo-random number matrixGTo (1)iThe elements of row column 1 are shown,
Figure 492442DEST_PATH_IMAGE097
representing a first pseudo-random number matrixSTo (1) aiGo to the firstNThe elements of the +1 column are,
Figure 16964DEST_PATH_IMAGE098
representing a seventh pseudo-random number matrixHRow 1 and column 2 elements of (a),
Figure 177818DEST_PATH_IMAGE099
representing a seventh pseudo-random number matrixHTo (1) aMThe elements of row column 1 are,
Figure 445988DEST_PATH_IMAGE100
representing a sixth pseudo-random number matrixGRow 1 and column 2 elements of (a),
Figure 375898DEST_PATH_IMAGE101
representing a first pseudo-random number matrixSLine 1 toNThe elements of column +2 are,
Figure 336901DEST_PATH_IMAGE102
representing a seventh pseudo-random number matrixHTo (1)iThe elements of row and column 2 are,
Figure 220937DEST_PATH_IMAGE103
representing a seventh pseudo-random number matrixHTo (1) ai-1 row and 2 column of elements,
Figure 27219DEST_PATH_IMAGE104
representing a sixth pseudo-random number matrixGTo (1) aiThe elements of row and column 2 are,
Figure 77214DEST_PATH_IMAGE105
representing a first pseudo-random number matrixSTo (1) aiGo to the firstN+2 columns of elements.
Step 2.6, apply the fifth pseudo-random number matrixWAnd a seventh pseudo-random number matrixHAre combined into a size ofM×(N+ 2) eighth pseudo random number matrixC。
In step 2.6, the following formula exists:
Figure 677960DEST_PATH_IMAGE106
(16)
Figure 938040DEST_PATH_IMAGE107
(17)
wherein,
Figure 157800DEST_PATH_IMAGE108
representing an eighth pseudo-random number matrixCTo (1) aiGo to the firstjThe elements of the column are,
Figure 921357DEST_PATH_IMAGE109
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstjThe elements of the column are,
Figure 958583DEST_PATH_IMAGE110
representing an eighth pseudo-random number matrixCTo (1)iGo to the firstN+jThe elements of the column are,
Figure 581325DEST_PATH_IMAGE111
representing a seventh pseudo-random number matrixHTo (1) aiGo to the firstjThe elements of the column.
Step 2.7, based on the first pseudo-random number matrixSAnd a ninth pseudo-random number matrixQValue of (a) disturbs the eighth pseudo-random number matrixCTo calculate a new position coordinate.
In step 2.7, the following formula exists:
Figure 994989DEST_PATH_IMAGE112
(18)
Figure 986953DEST_PATH_IMAGE113
(19)
wherein,ka row coordinate representing the new position coordinate,ta column coordinate representing the new position coordinate,
Figure 460660DEST_PATH_IMAGE114
representing an eighth pseudo-random number matrixCTo (1) auGo to the firstjThe elements of the column are,
Figure 164174DEST_PATH_IMAGE115
representing parametersuIncrement from 1 to 1 by step sizeMIn-process accumulation of
Figure 991316DEST_PATH_IMAGE114
，
Figure 995044DEST_PATH_IMAGE116
Representing a first pseudo-random number matrixSTo (1) aiGo to the firstjThe elements of the column are,
Figure 983859DEST_PATH_IMAGE117
representing an eighth pseudo-random number matrixCTo (1) aiGo to the firstvThe elements of the column are,
Figure 440249DEST_PATH_IMAGE118
representing parametersvIncrement from 1 to 1 by step sizeN+2 in-process accumulation
Figure 71081DEST_PATH_IMAGE117
。
Step three, an image decryption method;
in the present invention, the principle of the image decryption algorithm is shown in fig. 3:
step 3.1, apply the first pseudo-random number matrixS1 toMAnd lines 1 to 1NThe upper 4 bits and the lower 4 bits of each element in the region surrounded by +2 columns are interchanged to obtain a ninth pseudo random number matrixQ。
Step 3.2, based on the first pseudo-random number matrixSAnd a ninth pseudo-random number matrixQA value of (d), restoring the eighth pseudo random number matrix before scramblingCThe element position of (2).
Step 3.3, decompose the eighth pseudo-random number matrixCIs a fifth pseudo random number matrixWAnd a seventh pseudo-random number matrixH。
In step 3.3, the following formula exists:
Figure 663737DEST_PATH_IMAGE119
(20)
Figure 479246DEST_PATH_IMAGE120
(21)
wherein,
Figure 788043DEST_PATH_IMAGE109
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstjThe elements of the column are,
Figure 81621DEST_PATH_IMAGE108
representing an eighth pseudo-random number matrixCTo (1) aiGo to the firstjThe elements of the column.
Step 3.4, based on the first pseudo-random number matrixSTo (1)N+1 columns andN+2 columns the seventh pseudo-random number matrixHReverting to a sixth pseudo-random number matrixG。
In step 3.4, the following formula exists:
Figure 669729DEST_PATH_IMAGE121
(22)
wherein,
Figure 390560DEST_PATH_IMAGE092
representing a sixth pseudo-random number matrixGRow 1 and column 1 elements of (a),
Figure 696908DEST_PATH_IMAGE091
representing a seventh pseudo-random number matrixHRow 1 and column 1 elements of (a),
Figure 528597DEST_PATH_IMAGE122
representing a first pseudo-random number matrixSLine 1 toNThe elements in the +1 column are,
Figure 95845DEST_PATH_IMAGE096
sixth pseudo random number matrixGTo (1) aiRow column 1 element，
Figure 128523DEST_PATH_IMAGE094
Representing a seventh pseudo-random number matrixHTo (1)iThe elements of row column 1 are,
Figure 781221DEST_PATH_IMAGE095
representing a seventh pseudo-random number matrixHTo (1) ai-1 row and column 1 elements,
Figure 790503DEST_PATH_IMAGE123
representing a first pseudo-random number matrixSTo (1)iGo to the firstNThe elements of the +1 column are,
Figure 212257DEST_PATH_IMAGE100
representing a sixth pseudo-random number matrixGRow 1 and column 2 elements of (a),
Figure 540470DEST_PATH_IMAGE098
representing a seventh pseudo-random number matrixHRow 1 and column 2 elements of (a),
Figure 290252DEST_PATH_IMAGE099
representing a seventh pseudo-random number matrixHTo (1)MThe elements of row column 1 are,
Figure 994903DEST_PATH_IMAGE124
representing a first pseudo-random number matrixSLine 1 toNThe elements of column +2 are,
Figure 412109DEST_PATH_IMAGE104
representing a sixth pseudo-random number matrixGTo (1) aiThe elements of row and column 2 are,
Figure 645644DEST_PATH_IMAGE102
representing a seventh pseudo-random number matrixHTo (1)iThe elements of row and column 2 are,
Figure 272934DEST_PATH_IMAGE103
representing a seventh pseudo-random number matrixHTo (1) ai-1 row and 2 column of elements,
Figure 125484DEST_PATH_IMAGE125
representing a first pseudo-random number matrixSTo (1) aiGo to the firstN+2 columns of elements.
Step 3.5, based on the ninth pseudo-random number matrixQA first pseudo random number matrixSAnd a sixth pseudo-random number matrixGA fifth pseudo random number matrixWInto a fourth pseudo-random number matrixZ。
In step 3.5, the following formula exists:
for elements
Figure 521830DEST_PATH_IMAGE126
：
Figure 568677DEST_PATH_IMAGE127
(23)
Wherein,
Figure 417684DEST_PATH_IMAGE128
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstNThe elements of the column are,
Figure 198558DEST_PATH_IMAGE129
representing a fifth pseudo-random number matrixWTo (1) aMGo to the firstNThe elements of the column(s) are,
Figure 324777DEST_PATH_IMAGE130
representing a ninth pseudorandom number matrixQTo (1)MGo to the firstNThe elements of the column(s) are,
Figure 165694DEST_PATH_IMAGE131
representing a fourth pseudo-random number matrixZTo (1) aMGo to the firstNThe elements of the column are,
Figure 501998DEST_PATH_IMAGE132
representing a sixth pseudo-random number matrixGTo (1)MThe elements of row and column 2 are,
Figure 961929DEST_PATH_IMAGE133
representing a first pseudo-random number matrixSTo (1) aMGo to the firstNThe elements in the +4 column(s),
Figure 332868DEST_PATH_IMAGE134
representing a vectorT 2 To (1) a
Figure 220052DEST_PATH_IMAGE133
An element at a location;
for the fifth pseudo random number matrixWFirst, theMRemoval of rows
Figure 778072DEST_PATH_IMAGE129
The external elements are as follows:
Figure 540230DEST_PATH_IMAGE135
(24)
wherein,
Figure 500096DEST_PATH_IMAGE136
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstjThe elements of the column(s) are,
Figure 682815DEST_PATH_IMAGE137
representing a fifth pseudo-random number matrixWTo (1) aMGo to the firstjThe elements of the column are,
Figure 869077DEST_PATH_IMAGE138
representing a ninth pseudo-random number matrixQTo (1) aMGo to the firstjThe elements of the column are,
Figure 795445DEST_PATH_IMAGE139
representing a thirteenth pseudo-random number matrixETo (1)MGo to the firstjThe elements of the column(s) are,
Figure 750762DEST_PATH_IMAGE140
representing a fourth pseudo-random number matrixZLine M ofjThe elements of the column are,
Figure 104383DEST_PATH_IMAGE141
representing a fifth pseudo-random number matrixWTo (1) aMGo to the firstjAn element of column + 1;
for the fifth pseudo random number matrixWIs except forMElements of other rows outside the row:
for the firstiGo to the firstNElements of the column:
Figure 902575DEST_PATH_IMAGE142
(25)
wherein,
Figure 976841DEST_PATH_IMAGE143
representing a twelfth pseudo-random number matrixVTo (1) aiGo to the firstNThe elements of the column are,
Figure 176879DEST_PATH_IMAGE144
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstNThe elements of the column are,
Figure 343811DEST_PATH_IMAGE145
representing a ninth pseudo-random number matrixQTo (1) aiGo to the firstNThe elements of the column are,
Figure 98141DEST_PATH_IMAGE146
representing a thirteenth pseudo-random number matrixETo (1) aiGo to the firstNThe elements of the column are,
Figure 631890DEST_PATH_IMAGE147
representing a sixth pseudo-random number matrixGTo (1) aiThe elements of row and column 2 are,
Figure 296221DEST_PATH_IMAGE148
representing a first pseudo-random number matrixSTo (1) aiGo to the firstNThe elements of column +4 are,
Figure 991644DEST_PATH_IMAGE149
representing a vectorT 2 To (1) a
Figure 639794DEST_PATH_IMAGE148
The elements at the location of the position,
Figure 446076DEST_PATH_IMAGE150
representing a fourth pseudo-random number matrixZTo (1)iGo to the firstNThe elements of the column are,
Figure 355127DEST_PATH_IMAGE151
representing a fifth pseudo-random number matrixWTo (1)i+1 row, column 1 element;
for the firstiGo to the firstjElements of a column
Figure 96818DEST_PATH_IMAGE109
：
Figure 91318DEST_PATH_IMAGE152
(26)
Wherein,
Figure 340772DEST_PATH_IMAGE153
representing a twelfth pseudo-random number matrixVTo (1) aiGo to the firstjThe elements of the column(s) are,
Figure 104329DEST_PATH_IMAGE109
representing a fifth pseudo-random number matrixWTo (1) aiGo to the firstjThe elements of the column are,
Figure 141555DEST_PATH_IMAGE154
representing a ninth pseudorandom number matrixQTo (1) aiGo to the firstjThe elements of the column are,
Figure 498718DEST_PATH_IMAGE155
representing a thirteenth pseudo-random number matrixETo (1)iGo to the firstjThe elements of the column are,
Figure 912382DEST_PATH_IMAGE156
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstjThe elements of the column are,
Figure 671390DEST_PATH_IMAGE157
representing a fifth pseudo-random number matrixWTo (1) aiGo to the firstj+1 columns of elements.
Step 3.6, based on the first pseudo-random number matrixSAnd a sixth pseudo-random number matrixGApplying a fourth pseudo-random number matrixZConversion to a tenth pseudo-random number matrixPTenth pseudorandom number matrixPIs a restored plaintext image.
In step 3.6, the following formula exists:
(1) For a pixel point
Figure 613938DEST_PATH_IMAGE158
：
Figure 583031DEST_PATH_IMAGE159
(27)
Wherein,
Figure 410173DEST_PATH_IMAGE160
representing an eleventh pseudo-random number matrixURow 1 and column 1 elements of,
Figure 148322DEST_PATH_IMAGE158
representing a fourth pseudo-random number matrixZRow 1 and column 1 elements of,
Figure 169761DEST_PATH_IMAGE161
representing a first pseudo-random number matrixSRow 1 and column 1 elements of,
Figure 360571DEST_PATH_IMAGE030
representing a tenth pseudorandom number matrixPRow 1 and column 1 elements of,
Figure 116037DEST_PATH_IMAGE162
representing a sixth pseudo-random number matrixGTo (1) aThe elements of row 1 and column 1,
Figure 584059DEST_PATH_IMAGE163
representing a first pseudo-random number matrixSLine 1 toNThe elements of the +3 column are,
Figure 399568DEST_PATH_IMAGE164
representing a vectorT 2 To (1) a
Figure 953040DEST_PATH_IMAGE163
An element at a location;
(2) For the fourth pseudo-random number matrixZDivision of line 1
Figure 246619DEST_PATH_IMAGE158
The elements (c):
Figure 959360DEST_PATH_IMAGE165
(28)
wherein,
Figure 821136DEST_PATH_IMAGE166
representing an eleventh pseudo-random number matrixULine 1 tojThe elements of the column are,
Figure 986538DEST_PATH_IMAGE167
representing a fourth pseudo-random number matrixZLine 1 tojThe elements of the column(s) are,
Figure 818228DEST_PATH_IMAGE168
representing a first pseudo-random number matrixSLine 1 tojThe elements of the column are,
Figure 759377DEST_PATH_IMAGE169
representing a fourteenth pseudo-random number matrixFLine 1 tojThe elements of the column(s) are,
Figure 651110DEST_PATH_IMAGE041
representing a tenth pseudorandom number matrixPLine 1 tojThe elements of the column are,
Figure 179174DEST_PATH_IMAGE170
representing a fourth pseudo-random number matrixZLine 1 toj-1 column of elements;
(3) For the fourth pseudo random number matrixZOther rows than row 1 elements:
(i) For the firstiRow column 1 elements:
Figure 80134DEST_PATH_IMAGE171
(29)
wherein,
Figure 501888DEST_PATH_IMAGE172
representing an eleventh pseudo-random number matrixUTo (1) aiThe elements of row column 1 are shown,
Figure 705468DEST_PATH_IMAGE051
representing a fourth pseudo-random number matrixZTo (1)iThe elements of row column 1 are shown,
Figure 845462DEST_PATH_IMAGE052
representing a first pseudo-random number matrixSTo (1) aiThe elements of row column 1 are,
Figure 894320DEST_PATH_IMAGE173
representing a fourteenth pseudo-random number matrixFTo (1)iThe elements of row column 1 are shown,
Figure 436160DEST_PATH_IMAGE174
representing a sixth pseudo-random number matrixGTo (1)iThe elements of row column 1 are,
Figure 669695DEST_PATH_IMAGE047
representing a tenth pseudorandom number matrixPTo (1)iThe elements of row column 1 are,
Figure 685536DEST_PATH_IMAGE175
representing a fourth pseudo randomMachine number matrixZTo (1)i-1 line 1NElements of a column;
(ii) For the firstiGo to the firstjElements of the column:
Figure 928298DEST_PATH_IMAGE176
(30)
wherein,
Figure 200011DEST_PATH_IMAGE177
representing an eleventh pseudo-random number matrixUTo (1) aiGo to the firstjThe elements of the column are,
Figure 870026DEST_PATH_IMAGE156
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstjThe elements of the column are,
Figure 453455DEST_PATH_IMAGE116
representing a first pseudo-random number matrixSTo (1) aiGo to the firstjThe elements of the column are,
Figure 375274DEST_PATH_IMAGE178
representing a fourteenth pseudo-random number matrixFTo (1) aiGo to the firstjThe elements of the column are,
Figure 891706DEST_PATH_IMAGE056
representing a tenth pseudorandom number matrixPTo (1) aiGo to the firstjThe elements of the column are,
Figure 342410DEST_PATH_IMAGE179
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstj-1 column of elements;
finally, the tenth pseudo random number matrix is obtainedPIs a restored plaintext image.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following technologies, which are well known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is specific and detailed, but not to be understood as limiting the scope of the present invention. It should be noted that various changes and modifications can be made by those skilled in the art without departing from the spirit of the invention, and these changes and modifications are all within the scope of the invention. Therefore, the protection scope of the present patent should be subject to the appended claims.

Claims (10)

1. A cryptographic processing method of a symmetric image based on domain arithmetic, the method comprising the steps of:
step one, generating a pseudo-random number matrix by using an equivalent key generator:
step 1.1, from the first subkeykey 1 With a second subkeykey 2 Respectively calculating to obtain first state variablesx 0 And a second state variabley 0 ；
Step 1.2, setting circulation variableiStep 1 delivery from 0Is increased tod-3 in the first placeiIn the second cycle, willx 0 Andy 0 substituting into the H non mapping equation to update, and circulatingM×(N+ 4) time update is completed, and the updated first state variable is still recorded asx 0 The updated second state variable is still recorded asy 0 (ii) a Wherein,drepresenting the number of subkeys;
step 1.3, the extraction length isM×(N+ 4) state variable-x i }, i=1,2,…, M×(N+ 4) and converted to a size ofM×(N+ 4) first pseudo-random number matrixSWhereinMrepresenting the number of rows of the pseudo-random number matrix,Nrepresenting the number of columns of the pseudo random number matrix;
step two, an image encryption method;
step 2.1, the computer-based pseudo-random number generator generates a pseudo-random number of sizeMSecond pseudo-random number matrix of x 4R；
Step 2.2, based on the second pseudo-random number matrixRAnd elements of columns 1 and 3, and a first pseudo-random number matrixSTo middleN+3 columns andN+4 columns of elements, one size calculated asMX 2 third pseudo-random number matrixY；
Step 2.3, based on the third pseudo-random number matrixYMiddle 2 nd column element, first pseudo random number matrixSMiddle 2 nd column element and second pseudo-random number matrixRThe elements of column 2, perturbing the elements of the plaintext image, and calculating to obtain a size ofM×NOf the fourth pseudo-random number matrixZ；
Step 2.4, based on the third pseudo-random number matrixYColumn 4 element, first pseudo random number matrixSElement of middle 4 th column and second pseudo random number matrixRThe 4 th column element scrambles the fourth pseudo random number matrixZAnd calculating a size ofM×NOf the fifth pseudo-random number matrixW；
Step 2.5, use the first pseudo-random number matrixSTo (1)N+1 columns andN+2 columns of elements, for the sixth pseudo-random number matrixGScrambling is carried out, and the matrix after scrambling is marked as a seventh pseudo-random number matrixH；
Step 2.6, apply the fifth pseudo-random number matrixWAnd a seventh pseudo-random number matrixHAre combined into a size ofM×(N+ 2) eighth pseudo random number matrixC；
Step 2.7, based on the first pseudo-random number matrixSAnd a ninth pseudo-random number matrixQIs scrambled by a value ofCTo calculate a new position coordinate;
step three, an image decryption method;
step 3.1, apply the first pseudo-random number matrixS1 toMAnd row 1 toNThe upper 4 bits and the lower 4 bits of each element in the region surrounded by +2 columns are interchanged to obtain a ninth pseudo random number matrixQ；
Step 3.2, based on the first pseudo-random number matrixSAnd a ninth pseudo-random number matrixQA value of (b), restoring the eighth pseudo random number matrix before scramblingCThe element position of (a);
step 3.3, decompose the eighth pseudo-random number matrixCIs a fifth pseudo-random number matrixWAnd a seventh pseudo-random number matrixH；
Step 3.4, based on the first pseudo-random number matrixSTo (1)N+1 columns andN+2 columns the seventh pseudo random number matrixHReverting to a sixth pseudo-random number matrixG；
Step 3.5, based on the ninth pseudo-random number matrixQA first pseudo random number matrixSAnd a sixth pseudo-random number matrixGA fifth pseudo random number matrixWInto a fourth pseudo-random number matrixZ；
Step 3.6, based on the first pseudo-random number matrixSAnd a sixth pseudo-random number matrixGApplying a fourth pseudo-random number matrixZConversion to a tenth pseudo-random number matrixPTenth pseudorandom number matrixPIs a restored plaintext image.
2. The cryptographic processing method of a symmetric image based on domain arithmetic as claimed in claim 1, wherein in step one, the hnon mapping equation is expressed as:
Figure 209133DEST_PATH_IMAGE001
（1）
wherein,
Figure 595115DEST_PATH_IMAGE002
are all represented as state variables, and are,
Figure 109273DEST_PATH_IMAGE003
，
Figure 347225DEST_PATH_IMAGE004
，
Figure 630439DEST_PATH_IMAGE005
are all constants;
in step 1.1, the following formula exists:
Figure 311956DEST_PATH_IMAGE006
（2）
in step 1.2, the following formula exists:
Figure 47831DEST_PATH_IMAGE007
（3）
wherein,
Figure 590939DEST_PATH_IMAGE008
is shown as
Figure 994239DEST_PATH_IMAGE009
A sub-key;
in step 1.3, the following formula exists:
Figure 456444DEST_PATH_IMAGE010
（4）
wherein,
Figure 69828DEST_PATH_IMAGE011
representing a first pseudo-random number matrixSTo (1)iGo to the firstjThe elements of the column(s) are,
Figure 275681DEST_PATH_IMAGE012
is shown as
Figure 633020DEST_PATH_IMAGE013
The state variable of the state machine is changed into a state variable,
Figure 797285DEST_PATH_IMAGE014
，
Figure 507752DEST_PATH_IMAGE015
，
Figure 641931DEST_PATH_IMAGE016
representing a modulo operation.
3. A cryptographic processing method of symmetric images based on domain arithmetic as claimed in claim 2, characterized in that in said step 2.1, the following formula exists:
Figure 754243DEST_PATH_IMAGE017
（5）
wherein,
Figure 823830DEST_PATH_IMAGE018
representing a sixth pseudo-random number matrixGTo (1) aiGo to the firstjThe elements of the column(s) are,
Figure 896960DEST_PATH_IMAGE019
representing a second pseudo-random number matrixRTo (1)iLine 2j-1 column of elements of a group,
Figure 444616DEST_PATH_IMAGE020
representing a second pseudo-random number matrixRTo (1) aiLine 2jThe elements of the column(s) are,
Figure 801648DEST_PATH_IMAGE021
representing a vectorT 1 To (1)
Figure 42136DEST_PATH_IMAGE022
The elements at the location of the position,
Figure 569938DEST_PATH_IMAGE023
representing a vectorT 3 To (1) a
Figure 186864DEST_PATH_IMAGE024
The elements at the location of the position(s),
Figure 132824DEST_PATH_IMAGE014
，
Figure 544213DEST_PATH_IMAGE025
；
in said step 2.2, the following formula exists:
Figure 326356DEST_PATH_IMAGE026
（6）
wherein,
Figure 215814DEST_PATH_IMAGE027
representing a third pseudo-random number matrixYTo (1) aiGo to the firstjThe elements of the column(s) are,
Figure 422805DEST_PATH_IMAGE028
representing a first pseudo-random number matrixSTo (1) aiGo to the firstN+2+jThe elements of the column(s) are,
Figure 129730DEST_PATH_IMAGE029
representing a vectorT 2 To (1) a
Figure 789381DEST_PATH_IMAGE028
The elements at the location of the position(s),
Figure 859362DEST_PATH_IMAGE014
，
Figure 389700DEST_PATH_IMAGE025
。
4. a cryptographic processing method of a symmetric image based on domain arithmetic as claimed in claim 3, characterized in that in said step 2.3, the following formula exists:
for a pixel point
Figure 267526DEST_PATH_IMAGE030
；
Figure 414474DEST_PATH_IMAGE031
(7)
Wherein,
Figure 911314DEST_PATH_IMAGE032
representing the eleventh pseudo-random number matrixURow 1 and column 1 elements of (a),
Figure 702684DEST_PATH_IMAGE030
representing a tenth pseudorandom number matrixPRow 1 and column 1 elements of (a),
Figure 361198DEST_PATH_IMAGE033
representing a third pseudo-random number matrixYRow 1 and column 1 elements of,
Figure 854497DEST_PATH_IMAGE034
representing a second pseudo-random number matrixRRow 1 and column 2 elements of (a),
Figure 155028DEST_PATH_IMAGE035
representing a vectorT 3 To (1) a
Figure 925538DEST_PATH_IMAGE034
The elements at the location of the position(s),
Figure 394434DEST_PATH_IMAGE036
representing a fourth pseudo-random number matrixZRow 1 and column 1 elements of (a),
Figure 250395DEST_PATH_IMAGE037
representing a first pseudo-random number matrixSRow 1, column 1 elements of (a);
for the tenth pseudo random number matrixPDivision of line 1
Figure 354617DEST_PATH_IMAGE030
The element (b);
Figure 838688DEST_PATH_IMAGE038
(8)
wherein,
Figure 104584DEST_PATH_IMAGE039
representing an eleventh pseudo-random number matrixULine 1 tojThe elements of the column(s) are,
Figure 323207DEST_PATH_IMAGE040
representing a fourth pseudo-random number matrixZLine 1 toj-1 column of elements,
Figure 965541DEST_PATH_IMAGE041
representing a tenth pseudorandom number matrixPLine 1 tojThe elements of the column(s) are,
Figure 710643DEST_PATH_IMAGE042
representing a fourth pseudo-random number matrixZLine 1 tojThe elements of the column are,
Figure 272074DEST_PATH_IMAGE043
representing a first pseudo-random number matrixSLine 1 tojElements of a column;
for the tenth pseudo random number matrixPOther than line 1;
for the firstiRow column 1 elements:
Figure 102627DEST_PATH_IMAGE044
(9)
wherein,
Figure 659904DEST_PATH_IMAGE045
representing the eleventh pseudo-random number matrixUTo (1)iThe elements of row column 1 are,
Figure 993933DEST_PATH_IMAGE046
representing a fourth pseudo-random number matrixZTo (1)i-1 line 1NThe elements of the column(s) are,
Figure 867211DEST_PATH_IMAGE047
representing a tenth pseudorandom number matrixPTo (1) aiThe elements of row column 1 are,
Figure 44115DEST_PATH_IMAGE048
representing a third pseudo-random number matrixYTo (1)iThe elements of row column 1 are shown,
Figure 28251DEST_PATH_IMAGE049
representing a second pseudo-random number matrixRTo (1)iThe elements of row and column 2 are,
Figure 357732DEST_PATH_IMAGE050
representing a vectorT 3 To (1)
Figure 401912DEST_PATH_IMAGE049
The elements at the location of the position,
Figure 941478DEST_PATH_IMAGE051
representing a fourth pseudo-random number matrixZTo (1)iThe elements of row column 1 are,
Figure 588360DEST_PATH_IMAGE052
representing a first pseudo-random number matrixSTo (1) aiRow column 1 element;
for the firstiGo to the firstjElements of the column:
Figure 162560DEST_PATH_IMAGE053
(10)
wherein,
Figure 485963DEST_PATH_IMAGE054
representing the eleventh pseudo-random number matrixUTo (1) aiGo to the firstjThe elements of the column(s) are,
Figure 512825DEST_PATH_IMAGE055
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstj-1 column of elements of a group,
Figure 838764DEST_PATH_IMAGE056
representing a tenth pseudorandom number matrixPTo (1)iGo to the firstjThe elements of the column are,
Figure 126526DEST_PATH_IMAGE057
representing a fourth pseudo-random number matrixZTo (1)iGo to the firstjThe elements of the column(s) are,
Figure 246929DEST_PATH_IMAGE058
representing a first pseudo-random number matrixSTo (1)iGo to the firstjThe elements of the column.
5. A cryptographic processing method of symmetric images based on domain arithmetic as claimed in claim 4, characterized in that in step 2.4, the following formula exists:
applying a first pseudo-random number matrixS1 toMAnd lines 1 to 1NInterchanging the upper 4 bits and the lower 4 bits of each element in the area surrounded by +2 columns to obtain a ninth pseudo random number matrixQ；
For elements
Figure 902032DEST_PATH_IMAGE059
：
Figure 766083DEST_PATH_IMAGE060
(11)
Wherein,
Figure 49297DEST_PATH_IMAGE061
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstNThe elements of the column are,
Figure 730814DEST_PATH_IMAGE059
representing a fourth pseudo-random number matrixZTo (1) aMGo to the firstNThe elements of the column(s) are,
Figure 466689DEST_PATH_IMAGE062
representing a third pseudo-random number matrixYTo (1) aMThe elements of row and column 2 are,
Figure 511261DEST_PATH_IMAGE063
representing a second pseudo-random number matrixRTo (1)MThe elements of row and column 4,
Figure 648982DEST_PATH_IMAGE064
representing a vectorT 3 To (1)
Figure 501400DEST_PATH_IMAGE065
The elements at the location of the position,
Figure 990150DEST_PATH_IMAGE066
representing a fifth pseudo-random number matrixWTo (1)MGo to the firstNThe elements of the column(s) are,
Figure 196004DEST_PATH_IMAGE067
representing a ninth pseudorandom number matrixQTo (1)MGo to the firstNElements of a column;
for the fourth pseudo random number matrixZFirst, theMRemoval of rows
Figure 63597DEST_PATH_IMAGE059
The elements (c):
Figure 227862DEST_PATH_IMAGE068
(12)
wherein,
Figure 797383DEST_PATH_IMAGE069
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstjThe elements of the column are,
Figure 806928DEST_PATH_IMAGE070
representing a fifth pseudo-random number matrixWTo (1)MGo to the firstjThe elements of the +1 column are,
Figure 184819DEST_PATH_IMAGE071
representing a fourth pseudo-random number matrixZTo (1)MGo to the firstjThe elements of the column are,
Figure 362729DEST_PATH_IMAGE072
represents a fifth dummyRandom number matrixWTo (1) aMGo to the firstjThe elements of the column are,
Figure 826071DEST_PATH_IMAGE073
representing a ninth pseudorandom number matrixQTo (1) aMGo to the firstjElements of a column;
for the fourth pseudo random number matrixZIs except forMElements of other rows outside the row:
for the firstiGo to the firstNElements of a column
Figure 498361DEST_PATH_IMAGE074
；
Figure 730759DEST_PATH_IMAGE075
(13)
Wherein,
Figure 705668DEST_PATH_IMAGE076
twelfth pseudo random number matrixVTo (1) aiGo to the firstNThe elements of the column(s) are,
Figure 266094DEST_PATH_IMAGE077
representing a fifth pseudo-random number matrixWTo (1) aiThe element of +1 row and column 1,
Figure 883020DEST_PATH_IMAGE074
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstNThe elements of the column are,
Figure 828979DEST_PATH_IMAGE078
representing a third pseudo-random number matrixYTo (1) aiThe elements of row and column 2 are,
Figure 505948DEST_PATH_IMAGE079
representing a second pseudo-random number matrixRTo (1) aiThe elements of row column 4 are shown,
Figure 412724DEST_PATH_IMAGE080
representing a vectorT 3 To (1) a
Figure 690733DEST_PATH_IMAGE081
The elements at the location of the position,
Figure 897723DEST_PATH_IMAGE082
representing a fifth pseudo-random number matrixWTo (1) aiGo to the firstNThe elements of the column are,
Figure 339069DEST_PATH_IMAGE083
representing a ninth pseudorandom number matrixQTo (1) aiRow, column N element;
for the firstiGo to the firstjElements of the column:
Figure 998720DEST_PATH_IMAGE084
(14)
wherein,
Figure 691870DEST_PATH_IMAGE085
representing a twelfth pseudo-random number matrixVTo (1) aiGo to the firstjThe elements of the column(s) are,
Figure 363154DEST_PATH_IMAGE086
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstjThe elements of the +1 column are,
Figure 381925DEST_PATH_IMAGE087
representing a fourth pseudo-random number matrixZTo (1)iGo to the firstjThe elements of the column(s) are,
Figure 387927DEST_PATH_IMAGE088
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstjThe elements of the column(s) are,
Figure 619189DEST_PATH_IMAGE089
representing a ninth pseudo-random number matrixQTo (1)iGo to the firstjThe elements of the column.
6. A cryptographic processing method of symmetric images based on domain arithmetic as claimed in claim 5, characterized in that in step 2.5, the following formula exists:
Figure 535192DEST_PATH_IMAGE090
(15)
wherein,
Figure 833187DEST_PATH_IMAGE091
representing a seventh pseudo-random number matrixHRow 1 and column 1 elements of,
Figure 201851DEST_PATH_IMAGE092
representing a sixth pseudo-random number matrixGRow 1 and column 1 elements of (a),
Figure 627017DEST_PATH_IMAGE093
representing a first pseudo-random number matrixSLine 1 toNThe elements in the +1 column are,
Figure 131947DEST_PATH_IMAGE094
representing a seventh pseudo-random number matrixHTo (1) aiThe elements of row column 1 are shown,
Figure 102308DEST_PATH_IMAGE095
representing a seventh pseudo-random number matrixHTo (1) ai-1 row and 1 column of elements,
Figure 223848DEST_PATH_IMAGE096
representing a sixth pseudo-random number matrixGTo (1)iThe elements of row column 1 are,
Figure 796912DEST_PATH_IMAGE097
representing a first pseudo-random number matrixSTo (1)iGo to the firstNThe elements of the +1 column are,
Figure 546562DEST_PATH_IMAGE098
representing a seventh pseudo-random number matrixHRow 1 and column 2 elements of (a),
Figure 78038DEST_PATH_IMAGE099
representing a seventh pseudo-random number matrixHTo (1)MThe elements of row column 1 are,
Figure 532546DEST_PATH_IMAGE100
representing a sixth pseudo-random number matrixGRow 1 and column 2 elements of (a),
Figure 440459DEST_PATH_IMAGE101
representing a first pseudo-random number matrixSLine 1 toNThe elements in the +2 column(s),
Figure 919982DEST_PATH_IMAGE102
representing a seventh pseudo-random number matrixHTo (1)iThe elements of row and column 2 are,
Figure 481413DEST_PATH_IMAGE103
representing a seventh pseudo-random number matrixHTo (1)i-1 row and 2 column of elements,
Figure 311966DEST_PATH_IMAGE104
representing a sixth pseudo-random number matrixGTo (1)iThe elements of row and column 2 are,
Figure 102199DEST_PATH_IMAGE105
representing a first pseudo-random number matrixSTo (1)iGo to the firstN+2 columns of elements.
7. A cryptographic processing method of a symmetric image based on domain arithmetic as claimed in claim 6, characterized in that in step 2.6 the following formula exists:
Figure 967387DEST_PATH_IMAGE106
(16)
Figure 575086DEST_PATH_IMAGE107
(17)
wherein,
Figure 751989DEST_PATH_IMAGE108
representing an eighth pseudo-random number matrixCTo (1)iGo to the firstjThe elements of the column are,
Figure 736125DEST_PATH_IMAGE109
representing a fifth pseudo-random number matrixWTo (1) aiGo to the firstjThe elements of the column(s) are,
Figure 564142DEST_PATH_IMAGE110
representing an eighth pseudo-random number matrixCTo (1) aiGo to the firstN+jThe elements of the column are,
Figure 608321DEST_PATH_IMAGE111
representing a seventh pseudo-random number matrixHTo (1)iGo to the firstjElements of a column;
in step 2.7, the following formula exists:
Figure 147887DEST_PATH_IMAGE112
(18)
Figure 794769DEST_PATH_IMAGE113
(19)
wherein,ka row coordinate representing the coordinates of the new position,ta column coordinate representing the new position coordinate,
Figure 368970DEST_PATH_IMAGE114
representing an eighth pseudo-random number matrixCTo (1)uGo to the firstjThe elements of the column are,
Figure 193838DEST_PATH_IMAGE115
representing parametersuIncrement from 1 to 1 by step sizeMIn-process accumulation of
Figure 955120DEST_PATH_IMAGE114
，
Figure 546638DEST_PATH_IMAGE116
Representing a first pseudo-random number matrixSTo (1)iGo to the firstjThe elements of the column are,
Figure 834400DEST_PATH_IMAGE117
representing an eighth pseudo-random number matrixCTo (1) aiGo to the firstvThe elements of the column are,
Figure 220382DEST_PATH_IMAGE118
representing parametersvIncrement from 1 to 1 by step sizeN+2 in-process accumulation
Figure 111371DEST_PATH_IMAGE117
。
8. A cryptographic processing method of a symmetric image based on domain arithmetic as claimed in claim 7, characterized in that in step 3.3 the following formula exists:
Figure 241001DEST_PATH_IMAGE119
(20)
Figure 258636DEST_PATH_IMAGE120
(21)
wherein,
Figure 205732DEST_PATH_IMAGE109
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstjThe elements of the column are,
Figure 941607DEST_PATH_IMAGE108
representing an eighth pseudo-random number matrixCTo (1)iGo to the firstjElements of a column;
in step 3.4, the following formula exists:
Figure 219136DEST_PATH_IMAGE121
(22)
wherein,
Figure 622435DEST_PATH_IMAGE092
representing a sixth pseudo-random number matrixGRow 1 and column 1 elements of (a),
Figure 350220DEST_PATH_IMAGE091
representing a seventh pseudo-random number matrixHRow 1 and column 1 elements of (a),
Figure 432445DEST_PATH_IMAGE122
representing a first pseudo-random number matrixSLine 1 toNThe elements in the +1 column are,
Figure 169457DEST_PATH_IMAGE096
sixth pseudo random number matrixGTo (1)iThe elements of row column 1 are,
Figure 535585DEST_PATH_IMAGE094
representing a seventh pseudo-random number matrixHTo (1)iThe elements of row column 1 are shown,
Figure 434271DEST_PATH_IMAGE095
representing a seventh pseudo-random number matrixHTo (1)i-1 row and column 1 elements,
Figure 144738DEST_PATH_IMAGE123
representing a first pseudo-random number matrixSTo (1)iGo to the firstNThe elements in the +1 column are,
Figure 278916DEST_PATH_IMAGE100
representing a sixth pseudo-random number matrixGRow 1 and column 2 elements of (a),
Figure 391229DEST_PATH_IMAGE098
representing a seventh pseudo-random number matrixHRow 1 and column 2 elements of (a),
Figure 336182DEST_PATH_IMAGE099
representing a seventh pseudo-random number matrixHTo (1)MThe elements of row column 1 are shown,
Figure 268366DEST_PATH_IMAGE124
representing a first pseudo-random number matrixSLine 1 toNThe elements of column +2 are,
Figure 347181DEST_PATH_IMAGE104
representing a sixth pseudo-random number matrixGTo (1)iThe elements of row and column 2 are,
Figure 438633DEST_PATH_IMAGE102
representing a seventh pseudo-random number matrixHTo (1)iThe elements of row and column 2 are,
Figure 679122DEST_PATH_IMAGE103
representing a seventh pseudo-random number matrixHTo (1) ai-1 row and 2 column of elements,
Figure 741012DEST_PATH_IMAGE125
representing a first pseudo-random number matrixSTo (1) aiGo to the firstN+2 columns of elements.
9. A cryptographic processing method of a symmetric image based on domain arithmetic as claimed in claim 8, characterized in that in step 3.5 the following formula exists:
for elements
Figure 92359DEST_PATH_IMAGE126
：
Figure 179264DEST_PATH_IMAGE127
(23)
Wherein,
Figure 449708DEST_PATH_IMAGE128
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstNThe elements of the column(s) are,
Figure 622063DEST_PATH_IMAGE129
representing a fifth pseudo-random number matrixWTo (1) aMGo to the firstNThe elements of the column(s) are,
Figure 652467DEST_PATH_IMAGE130
representing a ninth pseudo-random number matrixQTo (1) aMGo to the firstNThe elements of the column(s) are,
Figure 328299DEST_PATH_IMAGE131
representing a fourth pseudo-random number matrixZTo (1)MGo to the firstNThe elements of the column(s) are,
Figure 176170DEST_PATH_IMAGE132
representing a sixth pseudo-random number matrixGTo (1) aMThe elements of row and column 2 are,
Figure 694876DEST_PATH_IMAGE133
representing a first pseudo-random number matrixSTo (1) aMGo to the firstNThe elements in the +4 column(s),
Figure 388025DEST_PATH_IMAGE134
representing a vectorT 2 To (1) a
Figure 823424DEST_PATH_IMAGE133
An element at a location;
for the fifth pseudo random number matrixWFirst, theMRemoval of rows
Figure 842195DEST_PATH_IMAGE129
The external elements are as follows:
Figure 457984DEST_PATH_IMAGE135
(24)
wherein,
Figure 345038DEST_PATH_IMAGE136
representing a twelfth pseudo-random number matrixVTo (1) aMGo to the firstjThe elements of the column are,
Figure 995462DEST_PATH_IMAGE137
representing a fifth pseudo-random number matrixWTo (1)MGo to the firstjThe elements of the column are,
Figure 794922DEST_PATH_IMAGE138
representing a ninth pseudo-random number matrixQTo (1) aMGo to the firstjThe elements of the column(s) are,
Figure 163586DEST_PATH_IMAGE139
representing a thirteenth pseudo-random number matrixETo (1) aMGo to the firstjThe elements of the column(s) are,
Figure 464118DEST_PATH_IMAGE140
representing a fourth pseudo-random number matrixZLine M ofjThe elements of the column are,
Figure 93682DEST_PATH_IMAGE141
representing a fifth pseudo-random number matrixWTo (1) aMGo to the firstjAn element of column + 1;
for the fifth pseudo random number matrixWIs except forMElements of other rows outside the row:
for the firstiGo to the firstNElements of the column:
Figure 454256DEST_PATH_IMAGE142
(25)
wherein,
Figure 409750DEST_PATH_IMAGE143
representing a twelfth pseudo-random number matrixVTo (1) aiGo to the firstNThe elements of the column are,
Figure 513972DEST_PATH_IMAGE144
representing a fifth pseudo-random number matrixWTo (1) aiGo to the firstNThe elements of the column are,
Figure 138988DEST_PATH_IMAGE145
representing a ninth pseudorandom number matrixQTo (1) aiGo to the firstNThe elements of the column(s) are,
Figure 529518DEST_PATH_IMAGE146
representing a thirteenth pseudo-random number matrixETo (1) aiGo to the firstNThe elements of the column are,
Figure 872775DEST_PATH_IMAGE147
representing a sixth pseudo-random number matrixGTo (1) aiThe elements of row and column 2 are,
Figure 124896DEST_PATH_IMAGE148
representing a first pseudo-random number matrixSTo (1) aiGo to the firstNThe elements of column +4 are,
Figure 604419DEST_PATH_IMAGE149
representing a vectorT 2 To (1) a
Figure 306796DEST_PATH_IMAGE148
The elements at the location of the position,
Figure 996403DEST_PATH_IMAGE150
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstNThe elements of the column(s) are,
Figure 176849DEST_PATH_IMAGE151
representing a fifth pseudo-random number matrixWTo (1)i+1 row, column 1 element;
for the firstiGo to the firstjElements of a column
Figure 415938DEST_PATH_IMAGE109
：
Figure 23637DEST_PATH_IMAGE152
(26)
Wherein,
Figure 934961DEST_PATH_IMAGE153
representing a twelfth pseudo-random number matrixVTo (1) aiGo to the firstjThe elements of the column are,
Figure 184677DEST_PATH_IMAGE109
representing a fifth pseudo-random number matrixWTo (1) aiGo to the firstjThe elements of the column are,
Figure 638792DEST_PATH_IMAGE154
representing a ninth pseudo-random number matrixQTo (1) aiGo to the firstjThe elements of the column are,
Figure 292758DEST_PATH_IMAGE155
representing a thirteenth pseudo random number matrixETo (1)iGo to the firstjThe elements of the column are,
Figure 832324DEST_PATH_IMAGE156
representing a fourth pseudo-random number matrixZTo (1)iGo to the firstjThe elements of the column are,
Figure 479206DEST_PATH_IMAGE157
representing a fifth pseudo-random number matrixWTo (1)iGo to the firstj+1 columns of elements.
10. A method of cryptographic processing of symmetric images based on domain arithmetic according to claim 9, characterized in that in step 3.6 the following formula exists:
for a pixel point
Figure 53407DEST_PATH_IMAGE158
：
Figure 2908DEST_PATH_IMAGE159
(27)
Wherein,
Figure 406601DEST_PATH_IMAGE160
representing an eleventh pseudo-random number matrixURow 1 and column 1 elements of (a),
Figure 732540DEST_PATH_IMAGE158
representing a fourth pseudo-random number matrixZRow 1 and column 1 elements of (a),
Figure 285881DEST_PATH_IMAGE161
representing a first pseudo-random number matrixSRow 1 and column 1 elements of,
Figure 406284DEST_PATH_IMAGE030
representing a tenth pseudorandom number matrixPRow 1 and column 1 elements of,
Figure 920442DEST_PATH_IMAGE162
representing a sixth pseudo-random number matrixGRow 1 and column 1 elements of (a),
Figure 659859DEST_PATH_IMAGE163
representing a first pseudo-random number matrixSLine 1 toNThe elements in the +3 column(s),
Figure 208652DEST_PATH_IMAGE164
representing a vectorT 2 To (1)
Figure 624590DEST_PATH_IMAGE163
An element at a location;
for the fourth pseudo random number matrixZDivision of line 1
Figure 360465DEST_PATH_IMAGE158
The elements (c):
Figure 402108DEST_PATH_IMAGE165
(28)
wherein,
Figure 539828DEST_PATH_IMAGE166
representing an eleventh pseudo-random number matrixULine 1 tojThe elements of the column(s) are,
Figure 267613DEST_PATH_IMAGE167
representing a fourth pseudo-random number matrixZLine 1 tojThe elements of the column(s) are,
Figure 615417DEST_PATH_IMAGE168
representing a first pseudo-random number matrixSLine 1 tojThe elements of the column are,
Figure 86850DEST_PATH_IMAGE169
representing a fourteenth pseudo-random number matrixFLine 1 tojThe elements of the column(s) are,
Figure 220022DEST_PATH_IMAGE041
representing a tenth pseudorandom number matrixPLine 1 tojThe elements of the column are,
Figure 853129DEST_PATH_IMAGE170
representing a fourth pseudo-random number matrixZLine 1 toj-1 column of elements;
for the fourth pseudo random number matrixZOther rows than row 1 elements:
for the firstiRow column 1 elements:
Figure 829175DEST_PATH_IMAGE171
(29)
wherein,
Figure 963353DEST_PATH_IMAGE172
representing an eleventh pseudo-random number matrixUTo (1) aiThe elements of row column 1 are shown,
Figure 75666DEST_PATH_IMAGE051
representing a fourth pseudo-random number matrixZTo (1)iThe elements of row column 1 are shown,
Figure 522084DEST_PATH_IMAGE052
representing a first pseudo-random number matrixSTo (1)iThe elements of row column 1 are,
Figure 454268DEST_PATH_IMAGE173
representing a fourteenth pseudo-random number matrixFTo (1) aiThe elements of row column 1 are shown,
Figure 533082DEST_PATH_IMAGE174
representing a sixth pseudo-random number matrixGTo (1) aiThe elements of row column 1 are shown,
Figure 358956DEST_PATH_IMAGE047
representing a tenth pseudorandom number matrixPTo (1)iThe elements of row column 1 are,
Figure 865023DEST_PATH_IMAGE175
representing a fourth pseudo-random number matrixZTo (1) ai-1 line 1NElements of a column;
for the firstiGo to the firstjElements of the column:
Figure 159870DEST_PATH_IMAGE176
(30)
wherein,
Figure 511217DEST_PATH_IMAGE177
representing an eleventh pseudo-random number matrixUTo (1) aiGo to the firstjThe elements of the column(s) are,
Figure 598121DEST_PATH_IMAGE156
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstjThe elements of the column are,
Figure 134145DEST_PATH_IMAGE116
representing a first pseudo-random number matrixSTo (1) aiGo to the firstjThe elements of the column are,
Figure 40921DEST_PATH_IMAGE178
representing a fourteenth pseudo-random number matrixFTo (1) aiGo to the firstjThe elements of the column are,
Figure 835439DEST_PATH_IMAGE056
representing a tenth pseudorandom number matrixPTo (1) aiGo to the firstjThe elements of the column are,
Figure 511271DEST_PATH_IMAGE179
representing a fourth pseudo-random number matrixZTo (1) aiGo to the firstj-1 column of elements.
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CN108234813A (en) * 2018-01-11 2018-06-29 重庆邮电大学 Plaintext associated images Encryption Algorithm based on Hyperchaotic Chen System

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CN108234813A (en) * 2018-01-11 2018-06-29 重庆邮电大学 Plaintext associated images Encryption Algorithm based on Hyperchaotic Chen System

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Application publication date: 20221101