CN114362918B

CN114362918B - Image encryption method based on central law and three-dimensional bit plane

Info

Publication number: CN114362918B
Application number: CN202210030022.7A
Authority: CN
Inventors: 张晓强; 田婧希
Original assignee: China University of Mining and Technology CUMT
Current assignee: China University of Mining and Technology CUMT
Priority date: 2022-01-12
Filing date: 2022-01-12
Publication date: 2024-11-26
Anticipated expiration: 2042-01-12
Also published as: CN114362918A

Abstract

A large number of images are generated and distributed throughout the various fields each day. In order to protect image information from being stolen in the network transmission process, an image encryption method based on a genetic center rule and a three-dimensional bit plane is provided. The invention simulates a genetic center rule and defines a three-dimensional bit plane. Firstly, converting an original image into an 8-bit binary image and converting the 8-bit binary image into a standard three-dimensional matrix; secondly, replacing the three-dimensional matrix by rotating bit planes and replacing between the bit planes; thirdly, coding a chaotic three-dimensional matrix into a DNA code, introducing RNA mutation by simulating a genetic center rule, and combining with chaos to realize diffusion; finally, an encrypted image is obtained by an RNA decoding operation. Experimental results and method analysis show that the method has strong safety and good performance.

Description

Image encryption method based on central rule and three-dimensional bit plane

Technical Field

The present invention relates to an information encryption technology, and in particular, to an image encryption method.

Background

In recent years, security problems of networks and information systems have been increasingly emphasized, and images have become important information carriers in daily life of people. It can intuitively and vividly transmit a large amount of information and is widely applied to the fields of communication, military and medical treatment. However, due to the openness of the internet, information is easily intercepted or leaked during network transmission. Data hiding and image encryption are common methods of maintaining image security, but the former suffers from some limitations due to insufficient embedding capability, in contrast to image encryption which can effectively protect images. Therefore, how to encrypt an image effectively and securely becomes very important.

Because the image has the characteristics of large data capacity and high correlation between pixels and data redundancy, the traditional data encryption algorithm cannot encrypt the digital image. In recent years, various encryption methods based on chaos have been proposed, such as chaos-based image encryption, compressed sensing-based image encryption, genetic algorithm-based image encryption. With the advent of the big data age, the network information transmission capability is improved, and the requirements on the efficiency and the security of the encryption method are further improved.

In order to protect image information from being stolen and improve the security and efficiency of encryption in the network transmission process, an image encryption method based on a central rule and a three-dimensional bit plane is provided. The method simulates a central rule, defines a three-dimensional bit plane and improves the safety and the high efficiency of the encryption process.

Disclosure of Invention

The purpose of the invention is that: in order to protect image information from being stolen and improve the security and efficiency of encryption in the network transmission process, an image encryption method based on a central rule and a three-dimensional bit plane is provided.

The technical scheme of the invention is as follows: in order to achieve the aim of the invention, the adopted technical scheme is an image encryption method based on a central rule and a three-dimensional bit plane, and the encryption steps are detailed as follows:

Step 1: constructing a three-dimensional matrix: the interactive image is I, the size is m multiplied by n, each pixel value in the I is converted into an 8-bit binary value, and the I can be constructed into a three-dimensional matrix C multiplied by d by C= [ C _ij],c_ij =0 or 1 through zero padding operation, wherein d is a positive integer, d ³ is more than or equal to 8mn, and d takes the smallest value;

step 2: generating a key: calculating 256-bit hash value K of I by using SHA-256 secure hash algorithm, dividing the 256-bit hash value K into blocks according to 8 bits, obtaining K=k ₁, k₂,…, k₃₂, randomly selecting c ₁, c₂, c₃, c₄, c₅, c₆ as external key input, and calculating an initial value u ₀,v₀ and a control parameter mu of a two-dimensional Logistic adjustment Sine Map (Two Dimension Logistic-Adjusted-Sine Map, 2D-LASM) shown in formula (4) and an initial value x ₀, y₀, z₀ and control parameters a, b and c of a three-dimensional Sine chaotic system shown in formula (5) by using a key generator shown in formulas (1) - (3); u ₀, v₀,μ, x₀, y₀, z₀, a, b, c are keys;

，（1）

Wherein ∈ represents an exclusive or operation;

，（2）

，（3）

Wherein mod ()' represents a modulo operation;

，（4）

Wherein μ ε [0, 1] is the control parameter, u ₀, v₀ ε (0, 1) is the initial value;

，（5）

wherein a, b, c epsilon [1, 4] is a control parameter, x ₀, y₀, z₀ epsilon [0,1] is an initial value;

Step 3: generating a chaotic sequence: according to the initial value X ₀, y₀, z₀ and the control parameters a, b and c, iterating the three-dimensional Sine chaotic system 1000+d times shown in the formula (5), discarding the previous 1000 iteration values, and generating 3 chaotic sequences X, Y and Z with the lengths d; according to the initial value U ₀,v₀ and the control parameter mu, 2D-LASM1000+d ³/2 times shown in the iterative formula (4), discarding the previous 1000 iterative values, and generating 2 chaotic sequences U and V with the lengths of D ³/2;

step 4: three-dimensional bit plane scrambling: three-dimensional bit plane sets of C are respectively scrambled by using X, Y and Z, wherein the three-dimensional bit plane sets comprise an X bit plane set P ^x={p^x (i), a Y bit plane set P ^y={p^y (i) and a Z bit plane set P ^z={p^z (i), and a three-dimensional scrambling matrix P ⁶ can be finally obtained; the specific operation is as follows: using X and formulas (6) - (9), rotating and scrambling P ^x={p^x (i),

[X¹, S₁]=sort(x(i))，i=1, 2,…, d，（6）

T₁=mod(floor(x(i)×10¹⁶), 4)×90，（7）

Wherein, sort (-) is an ascending sort function, floor (-) is a downward rounding function, X (i) ∈x, X ¹ is a new sequence after sorting, S ₁ is an index value of X ¹;

P¹(i, :, :)=imrotate(C(i, :, :), t₁(i))，i=1, 2,…, d，（8）

Wherein imrotatet ()' is a rotation function, C (i,:) is the ith X bit plane of C, t ₁(i)∈T₁ is the rotation angle value of the bit plane, t ₁ (i) takes the value of 0 degrees, 90 degrees, 180 degrees or 270 degrees, and P ¹ (i,:) is the ith X bit plane of the three-dimensional matrix P ¹;

P²(i, :, :)=P¹(s₁(i), :, :)，i=1, 2,…, d，（9）

wherein s ₁(i)∈S₁,P² (i,:) is the ith X-bit plane of the three-dimensional matrix P ²;

using Y and formulas (10) - (13), rotate and scramble P ^y={p^y (i) },

[Y¹, S₂]=sort(y(i))，i=1, 2,…, d，（10）

T₂=mod(floor(y(i)×10¹⁶), 4)×90，（11）

Wherein Y (i) ∈y, Y ¹ is the new sequence after sorting, S ₂ is the index value of Y ¹;

P³(:, i, :)=imrotate(P²(:, i, :), t₂(i))，i=1, 2,…, d，（12）

Wherein P ² (: i,:) is the ith Y-bit plane of the three-dimensional matrix P ², and t ₂(i)∈T₂,P³ (: i,:) is the ith Y-bit plane of the three-dimensional matrix P ³;

P⁴(:, i, :)=P³(:, s₂(i), :)，i=1, 2,…, d，（13）

Wherein s ₂(i)∈S₂,P⁴ (: i,:) is the ith Y-bit plane of the three-dimensional matrix P ⁴;

Using Z and equations (14) - (17), rotate and scramble P ^z={p^z (i) },

[Z¹, S₃]=sort(z(i))，i=1, 2,…, d，（14）

T₃=mod(floor(z(i)×10¹⁶), 4)×90，（15）

Wherein Z (i) ∈z, Z ¹ is the new sequence after ordering, S ₃ is the index value of Z ¹;

P⁵(:, :, i)=imrotate(P⁴(:, :, i), t₃(i))，i=1, 2,…, d，（16）

Wherein P ⁴ (: i) is the ith Z-bit plane of the three-dimensional matrix P ⁴, and t ₃(i)∈T₃,P⁵ (: i) is the ith Z-bit plane of the three-dimensional matrix P ⁵;

P⁶(:, :, i)=P⁵(:, :, s₃(i))，i=1, 2,…, d，（17）

Wherein s ₃(i)∈S₃,P⁶ (: i) is the ith Z bit plane of the three-dimensional matrix P ⁶;

step 5: DNA coding: the DNA coding rules are as follows:

And (3) calculating:

l_i=mod(sum(P⁶(i, :, :), 8)，i=1, 2,…, d，（18）

wherein P ⁶ (i,:)) is the ith X bit plane of the three-dimensional matrix P ⁶, sum is a summation function, and the ith X bit plane of P ⁶ is encoded according to the first _i encoding rules in the DNA encoding rules, so as to obtain a three-dimensional DNA encoding matrix P ⁷ with the size of d/2X d;

step 6: transcription of DNA: the DNA transcription rules are:

According to the DNA transcription rule, P ⁷ is transcribed to obtain a three-dimensional RNA matrix P ⁸ with the size of d/2×d×d;

step 7: RNA variation: the RNA mutation rule is as follows:

u is integer by means of formula (19),

U¹=floor(mod(U×10¹⁶, 4)，（19）

U ¹ is an integer chaotic sequence, the value of which is 0,1,2 or 3, corresponds to four modes of RNA variation, and converts U ¹ into a matrix U ² with the size of d/2 x d according to a certain rule; RNA variation was performed on P ⁸ using U ² and equation (20),

P⁹(w₁, w₂, w₃)=Mutation(P⁸(w₁, w₂, w₃), U²(w₁, w₂, w₃)), （20）

Wherein w ₁=1, 2,…, d/2,w₂=1, 2,…, d,w₃ =1, 2, …, d, mutation (x, y) indicates that the base x is mutated according to the y-th Mutation mode of the RNA Mutation rule, so as to obtain an RNA Mutation matrix P ⁹ with the size of d/2×d×d;

step 8: RNA translation: the RNA translation rules are:

According to the RNA translation rule, translating the P ⁹ to obtain a three-dimensional matrix P ¹⁰ with the size of d/2 multiplied by d;

Step 9: RNA calculation: the RNA encoding rule is:

The RNA exclusive OR rule is:

The first d ²/8 elements of V are selected to form a chaotic subsequence V ¹, V ¹ is integer by using a formula (21),

V²=floor(mod(V¹×10¹⁶, 256)，（21）

Wherein V ² is the generated integer chaotic sequence; v ² is encoded according to the 1 st RNA encoding rule, so that a two-dimensional RNA matrix V ³ with the size of d ²/8 multiplied by 4 can be obtained; according to a certain rule, V ³ is converted into a matrix V ⁴ with the size of d/2 x d; performing a diffusion operation as shown in formula (22) to obtain a diffusion matrix P ¹¹ with a size of d/2×d×d;

，（22）

wherein ☉ denotes an RNA exclusive OR operation, P ¹⁰ (j:) is the j-th X-bit plane of the three-dimensional matrix P ¹⁰, and P ¹¹ (j:) is the j-th X-bit plane of the three-dimensional matrix P ¹¹;

step 10: and (3) RNA decoding: the RNA decoding rules are:

And (3) calculating:

r_i=mod(sum(P¹¹(:, :, i), 8)，i=1, 2,…, d，（23）

Wherein P ¹¹ (: i) is the ith Z bit plane of the three-dimensional matrix P ¹¹; decoding the ith Z bit plane of P ¹¹ according to the r _i decoding rules in the RNA decoding rules to obtain a decoding matrix C _p with the size of d multiplied by d; and (3) removing zero elements added in the step (1) in the matrix, and converting 8-bit binary values in the matrix into decimal pixel values to obtain an encryption image E with the size of m multiplied by n.

In the decryption process, the same chaotic sequence is used for decrypting the encrypted image, so that the original image can be restored, and the decryption process is the inverse process of the encryption process.

The beneficial effects are that: in order to protect image information from being stolen and improve the security and efficiency of encryption in the network transmission process, an image encryption method based on a central rule and a three-dimensional bit plane is provided, and the following five points are mainly contributed: (1) Three-dimensional bit planes are defined, a three-dimensional scrambling mode is designed, and a plurality of bit planes can be scrambled synchronously; (2) Generating an initial value and a control parameter of the chaotic system by the SHA-256 hash value of the plaintext image and the external parameter; (3) The central rule including DNA coding, transcription, translation and amino acid synthesis is simulated, so that the image encryption is tightly combined with the biological genetic process; (4) Introducing RNA mutation in the encryption process, simulating the mutation process in the nature, and further improving the safety of the encryption method by mutation mode and position randomness, and combining RNA operation with the RNA matrix generated by chaos to realize further diffusion; (5) Experimental results and method analysis verify the feasibility and safety of the proposed method.

Drawings

Fig. 1: an encryption flow chart;

Fig. 2: an original image;

fig. 3: the image is encrypted.

Detailed Description

The practice of the invention is described in further detail below with reference to the attached drawings and examples.

Fig. 1 is an encryption flow chart of the present method.

The programming software used was Matlab R2016a and the Lena gray scale image of size 512 x 512 shown in fig. 2 was selected as the subject.

Step 1: constructing a three-dimensional matrix: inputting 1 image of Lena gray scale with size 512×512 as plaintext image I, converting each pixel value in I into 8-bit binary value, by means of the zero-filling operation, I can be constructed to be 128X 128 in size x 128 three-dimensional matrix c= [ C _ij],c_ij =0 or 1.

Step 2: generating a key: calculating 256-bit hash value K of I by using SHA-256 secure hash algorithm, dividing the hash value K into blocks according to 8 bits to obtain K=k ₁, k₂,…, k₃₂, selecting c₁=0.6723,c₂=0.1839,c₃=0.2343,c₄=0.0928,c₅=0.5623,c₆=0.2613 as external key input, and calculating initial value u ₀, v₀ of 2D-LASM and control parameter mu, and initial value x ₀, y₀, z₀ of the three-dimensional Sine chaotic system and control parameters a, b and c by using a key generator.

Step 3: generating a chaotic sequence: according to the initial value X ₀, y₀, z₀ and the control parameters a, b and c, iterating the three-dimensional Sine chaotic system 1128 times, and discarding the previous 1000 iteration values, 3 chaotic sequences X, Y and Z with the lengths of 128 can be generated; according to the initial value U ₀,v₀ and the control parameter mu, 2D-LASM1049576 times are iterated, and the previous 1000 iteration values are discarded, so that 2 chaotic sequences U and V with the lengths of 1048576 can be generated.

Step 4: three-dimensional bit plane scrambling: three-dimensional bit plane sets of C, including X bit plane set P ^x={p^x (i), Y bit plane set P ^y={p^y (i) and Z bit plane set P ^z={p^z (i), are scrambled with X, Y and Z, respectively, to finally obtain a three-dimensional scrambling matrix P ⁶.

Step 5: DNA coding: by using the formula (18), the ith X bit plane of P ⁶ is encoded according to the first _i coding rules in the DNA coding rules, so as to obtain a three-dimensional DNA coding matrix P ⁷ with the size of 64×128×128.

Step 6: transcription of DNA: according to the DNA transcription rule, P ⁷ is transcribed to obtain a three-dimensional RNA matrix P ⁸ with the size of 64×128×128.

Step 7: RNA variation: u ¹ is an integer chaotic sequence of U, the value of U is 0,1,2 or 3, and the four modes correspond to RNA variation; according to a certain rule, U ¹ is converted into a matrix U ² with the size of 64 multiplied by 128, and RNA mutation is carried out on P ⁸ by using U ², so that an RNA mutation matrix P ⁹ with the size of 64 multiplied by 128 can be obtained.

Step 8: RNA translation: according to the RNA translation rule, P ⁹ is translated to obtain a three-dimensional matrix P ¹⁰ with the size of 64 multiplied by 128.

Step 9: RNA calculation: the first 2048 elements of V are selected to form an integer chaotic sequence with a chaotic subsequence V ¹,V² being V ¹; v ² is encoded according to the 1 st RNA encoding rule, so that a two-dimensional RNA matrix V ³ with the size of 2048 multiplied by 4 can be obtained; according to a certain rule, V ³ is converted into a matrix V ⁴ with the size of 64 multiplied by 128; the diffusion operation is performed on P ¹⁰ by using V ⁴, and a diffusion matrix P ¹¹ with a size of 64×128×128 can be obtained.

Step 10: and (3) RNA decoding: according to the (_i) th decoding rule of the RNA decoding rules by using the formula (23), decoding the ith Z bit plane of P ¹¹, a size of 128×128 can be obtained a decoding matrix C _p of x 128; the zero elements added in step 1 in the matrix are removed, and the 8-bit binary values in the matrix are converted into decimal pixel values, so that an encrypted image E with the size of 512×512 can be obtained, as shown in fig. 3.

In the decryption process, the same chaotic sequence is utilized to decrypt the encrypted image E, so that the original image can be restored, and the decryption process is the inverse process of the encryption process.

Claims

1. An image encryption method based on the central law and a three-dimensional bit plane, characterized in that it comprises the following steps:

Step 1: Construct a three-dimensional matrix: Let the interactive image be I with a size of m × n . Convert each pixel value in I into an 8-bit binary value. Through the zero-filling operation, I can be constructed into a three-dimensional matrix C = [ c _ij ] with a size of d × d × d , where c _ij = 0 or 1, where d is a positive integer that satisfies d ³ ≥ 8 mn and d takes the minimum value.

Step 2: Generate key: Use the SHA-256 secure hash algorithm to calculate the 256 _- bit hash value K of I , divide it into blocks of 8 bits each, and obtain K=k1 _, k2 ,…, k32 . Randomly select c1 , _c2 , _c3 , c4 , c5 _, c6 _as external key inputs. Use the key generator shown in formulas (1)-(3) to calculate the initial values u0 _, _v0 and _control parameters μ of the two-dimensional Logistic-Adjusted-Sine Map (2D-LASM) shown in formula (4), as well _as the initial values x0, y0, z0 and control parameters a, b, c _of _the three _- _dimensional Sine chaotic system _shown in formula ( 5) ; u0 , v0 , μ , x0 , _y0 _, z0 _, a , b , _c are the keys ;

, (1)

Among them, ⊕ represents the exclusive OR operation;

, (2)

, (3)

Where, mod (•) represents the modulo operation;

, (4)

Among them, μ ∈[0, 1] is the control parameter, u ₀ , v ₀ ∈(0, 1) is the initial value;

, (5)

Among them, a , b , c ∈[1, 4] are control parameters, x ₀ , y ₀ , z ₀ ∈[0, 1] are initial values;

Step 3: Generate chaotic sequences: Iterate the three-dimensional Sine chaotic system shown in formula (5) 1000+ d times according to the initial values x ₀ , y ₀ , z ₀ and control parameters a , b , c, and discard the first 1000 iteration values to generate three chaotic sequences X , Y and Z with a length of d ; iterate the 2D-LASM shown in formula (4) 1000+ d ³ /2 times according to the initial values u ₀ , v ₀ and control parameters μ , and discard the first 1000 iteration values to generate two chaotic sequences U and V with a length of d ³ /2;

Step 4: Three-dimensional bit plane scrambling: Use X , Y and Z to scramble the three-dimensional bit plane sets ^of C , including ^the X bit plane set Px = { px ( i )}, ^the Y bit plane set Py = ^{py ( i )} and ^the Z bit plane set Pz = { pz ( i )}, ^and finally obtain ^the three-dimensional scrambled matrix P6 ; the specific operation is: ^use X and formulas (6)-(9) to rotate and scramble Px ⁼ { px ( i )},

[ X ¹ , S ₁ ] =sort ( x ( i )), i= 1, 2, … , d , (6)

T ₁ =mod ( floor ( x ( i )×10 ¹⁶ ), 4)×90, (7)

Among them, sort (•) is the ascending sorting function, floor (•) is the floor rounding function, x ( i )∈ X , X ¹ is the new sequence after sorting, and S ₁ is the index value of X ¹ ;

P ¹ ( i , :, :) =imrotate ( C ( i , :, :), t ₁ ( i )), i= 1, 2, … , d , (8)

where imrotatet (•) is the rotation function, C ( i , :, :) is the i- th X- bit plane of C , t ₁ ( i )∈ T ₁ is the rotation angle value of the bit plane, t ₁ ( i ) takes the value of 0°, 90°, 180° or 270°, and P ¹ ( i , :, :) is the i- th X -bit plane of the three-dimensional matrix P ¹ ;

P ² ( i , :, :) =P ¹ ( s ₁ ( i ), :, :), i= 1, 2, … , d , (9)

Where, s ₁ ( i )∈ S ₁ , P ² ( i , :, :) is the i- th X -plane of the three-dimensional matrix P ² ;

Using Y and formulas (10)-(13), rotate and scramble P ^y ={ p ^y ( i )},

[ Y ¹ , S ₂ ] =sort ( y ( i )), i= 1, 2, … , d , (10)

T ₂ =mod ( floor ( y ( i )×10 ¹⁶ ), 4)×90, (11)

Among them, y ( i )∈ Y , Y ¹ is the new sequence after sorting, S ₂ is the index value of Y ¹ ;

P ³ (:, i , :) =imrotate ( P ² (:, i , :), t ₂ ( i )), i= 1, 2, … , d , (12)

Wherein, P ² (:, i , :) is the i- th Y -bit plane of the three-dimensional matrix P ² , t ₂ ( i )∈ T ₂ , P ³ (:, i , :) is the i- th Y -bit plane of the three-dimensional matrix P ³ ;

P ⁴ (:, i , :) =P ³ (:, s ₂ ( i ), :), i= 1, 2, … , d , (13)

Where, s ₂ ( i )∈ S ₂ , P ⁴ (:, i , :) is the i- th Y -bit plane of the three-dimensional matrix P ⁴ ;

Using Z ^and formulas (14)-( ¹⁷ ), rotate and scramble Pz = { pz ( i )},

[ Z ¹ , S ₃ ] =sort ( z ( i )), i= 1, 2, … , d , (14)

T ₃ =mod ( floor ( z ( i )×10 ¹⁶ ), 4)×90, (15)

Among them, z ( i )∈ Z , Z ¹ is the new sequence after sorting, S ₃ is the index value of Z ¹ ;

P ⁵ (:, :, i ) =imrotate ( P ⁴ (:, :, i ), t ₃ ( i )), i= 1, 2, … , d , (16)

Wherein, P ⁴ (:, :, i ) is the i- th Z- bit plane of the three-dimensional matrix P ⁴ , t ₃ ( i )∈ T ₃ , P ⁵ (:, :, i ) is the i -th Z -bit plane of the three-dimensional matrix P ⁵ ;

P ⁶ (:, :, i ) =P ⁵ (:, :, s ₃ ( i )), i= 1, 2, … , d , (17)

Where, s ₃ ( i )∈ S ₃ , P ⁶ (:, :, i ) is the i- th Z -plane of the three-dimensional matrix P ⁶ ;

Step 5: DNA encoding: The DNA encoding rules are:

calculate:

l _i =mod ( sum ( P ⁶ ( i , :, :), 8), i= 1, 2, … , d , (18)

Wherein, P ⁶ ( i , :, :)) is the i- th X -bit plane of the three-dimensional matrix P ⁶ , sum (•) is the summation function, and according to the l _i -th coding rule in the DNA coding rule, the i- th X- bit plane of P ⁶ is encoded to obtain a three-dimensional DNA coding matrix P ⁷ of size d /2× d × d ;

Step 6: DNA transcription: The rules of DNA transcription are:

According to the DNA transcription rules, P ⁷ is transcribed to obtain a three-dimensional RNA matrix P ⁸ of size d /2 × d × d ;

Step 7: RNA mutation: The RNA mutation rules are:

Using formula (19) to convert U into an integer,

U ¹ =floor ( mod ( U ×10 ¹⁶ , 4), (19)

Among them, U ¹ is the generated integer chaotic sequence, with values of 0, 1, 2 or 3, corresponding to the four modes of RNA mutation. According to a certain rule, U ¹ is converted into a matrix U ² of size d /2× d × d . Using U ² and formula (20), RNA mutation is performed on P ⁸ .

P ⁹ ( w ₁ , w ₂ , w ₃ ) =Mutation ( P ⁸ ( w ₁ , w ₂ , w ₃ ), U ² ( w ₁ , w ₂ , w ₃ )), (20)

Wherein, w ₁ = 1, 2, … , d /2, w ₂ = 1, 2, … , d , w ₃ = 1, 2, … , d , Mutation ( x , y ) means that base x mutates according to the yth mutation pattern of the RNA mutation rule, and an RNA mutation matrix P ⁹ of size d /2× d × d can be obtained;

Step 8: RNA translation: The RNA translation rules are:

According to the RNA translation rules, P ⁹ is translated to obtain a three-dimensional matrix P ¹⁰ of size d /2 × d × d ;

Step 9: RNA calculation: The RNA encoding rule is:

The RNA XOR rule is:

Select the first d ² /8 elements of V to form the chaotic subsequence V ¹ , and use formula (21) to integerize V ¹ ,

V ² =floor ( mod ( V ¹ ×10 ¹⁶ , 256), (21)

Wherein, V ² is the generated integer chaotic sequence; according to the first RNA encoding rule, V ² is encoded to obtain a two-dimensional RNA matrix V ³ of size d ² /8×4; according to a certain rule, V ³ is converted into a matrix V ⁴ of size d /2× d ; performing the diffusion operation shown in formula (22), a diffusion matrix P ¹¹ of size d /2× d × d is obtained;

, (twenty two)

Wherein, ☉ represents RNA XOR operation, P ¹⁰ ( j , :, :) is the j -th X -bit plane of the three-dimensional matrix P ¹⁰ , and P ¹¹ ( j , :, :) is the j -th X -bit plane of the three-dimensional matrix P ¹¹ ;

Step 10: RNA decoding: The RNA decoding rules are:

calculate:

r _i =mod ( sum ( P ¹¹ (:, :, i ), 8), i= 1, 2, … , d , (23)

Wherein, P ¹¹ (:, :, i ) is the i- th Z -bit plane of the three-dimensional matrix P ¹¹ ; according to the r _i- th decoding rule in the RNA decoding rule, the i - th Z -bit plane of P ¹¹ is decoded to obtain a decoding matrix C _p of size d × d × d ; the zero elements added in step 1 in the matrix are removed, and the 8-bit binary values in the matrix are converted into decimal pixel values, to obtain an encrypted image E of size m × n .

2. The method according to claim 1, characterized in that: in step 4, the three-dimensional bit plane includes an X bit plane, a Y bit plane and a Z bit plane; wherein the X bit plane is a bit plane composed of all elements with equal X coordinate values in the first dimension in a three-dimensional matrix composed of 0/1; the Y bit plane is a bit plane composed of all elements with equal Y coordinate values in the second dimension in a three-dimensional matrix composed of 0/1; and the Z bit plane is a bit plane composed of all elements with equal Z coordinate values in the third dimension in a three-dimensional matrix composed of 0/1.