Color Image Encryption Method Based on DNA Strand Displacement Analog Circuit

Abstract

The invention relates to the field of strand displacement, and provides a color image encryption method based on a DNA strand displacement analog circuit. Firstly, a reaction module with a light-emitting group and a quenching group is designed through Visual DSD software, and by utilizing the equivalence of a DNA strand displacement reaction module and an ideal reaction module, an analog circuit formed by the DNA strand displacement reaction module can perform analog on the dynamics characteristics of an ideal reaction network formed by the ideal reaction module, wherein the Rssler chaotic system can be described by the idealized reaction network. Secondly, data generated by the DNA strand displacement analog circuit is converted into a chaotic sequence matched with a plaintext image in size after being extended, and finally, the color image encryption effect is achieved through scrambling and diffusion operations.

Claims

1. A color image encryption method based on a DNA strand displacement analog circuit, which essentially combines a DNA strand displacement technology with an image chaotic encryption method by utilizing the compilability of a DNA strand sequence, and the method comprises the following specific steps: step 1: determining an idealized reaction network that can describe a Rssler chaotic system; step 2: determining an idealized reaction module and a DNA strand displacement reaction module corresponding thereto according to an idealized reaction equation; step 3: constructing a DNA strand displacement analog circuit according to the idealized reaction network and the reaction module; step 4: adopting an encryption method, and the detailed steps (1)-(5) of the encryption method are as follows: (1) generating a secret key by using the plaintext image; (2) setting the measurement accuracy of the concentration of a DNA strand as 0.1 nM, wherein the measurement is performed every 3 seconds; (3) extending the measured data to obtain a new chaotic sequence; (4) scrambling the color plaintext image at the level of the three components of R, G, B in consideration of the relation between the three components of R, G, B in a color image; (5) performing scrambling at a pixel level by utilizing the extended chaotic sequence; (6) generating a scrambling sequence U by using the chaotic sequence; (7) generating a scrambling sequence V by using the chaotic sequence; and (8) performing diffusion processing on the scrambled image; step 5: adopting a decryption method, which comprises: removing the diffusion effect on the encrypted image according to the inverse process of the encryption method to obtain a plaintext image;

2. The color image encryption technology based on a DNA strand displacement analog circuit according to claim 1, wherein the color image encryption is performed by using the DNA strand displacement chaotic analog circuit for the first time.

Description

BRIEF DESCRIPTION OF THE DRAWINGS AND TABLES

[0007] FIG. 1 Encryption flow

[0008] FIG. 2 Catalytic reaction module 1: X.fwdarw.2X

[0009] FIG. 3 Catalytic reaction module 2: X+Y.fwdarw.2Y

[0010] FIG. 4 Annihilation reaction module: X+Y.fwdarw.

[0011] FIG. 5 Degradation reaction module 1: X+X.fwdarw.X

[0012] FIG. 6 Degradation reaction module 2: Y.fwdarw.

[0013] FIG. 7 Experimental results obtained by using encryption and decryption schemes

[0014] Table 1 Values of parameters of a Rssler chaotic system

[0015] Table 2 Correlation coefficient of a lena ciphertext image and adjacent pixels thereof

[0016] Table 3 Information entropy

[0017] Table 4 NPCR and UACI values for encrypted images

DETAILED DESCRIPTION OF THE INVENTION

[0018] The present invention will be described further below with reference to the drawings.

[0019] The detailed steps are as follows:

Step 1: determining an idealized reaction network that can describe the Rssler chaotic system as shown in Formula (1).

[00001]$\begin{array}{cc}{X}_1.Math.\stackrel{.Math.k_{1.Math.}}{.fwdarw.}.Math.2.Math.X_1& \left(1.Math.a\right)\\ 2.Math.X_1.Math.\stackrel{.Math.k_{2.Math.}}{.fwdarw.}.Math.X_1& \left(1.Math.b\right)\\ X_2+X_1.Math.\stackrel{.Math.k_3.Math.}{.fwdarw.}.Math.2.Math.X_2& \left(1.Math.c\right)\\ X_2.Math.\stackrel{.Math.k_4.Math.}{.fwdarw.}.Math.& \left(1.Math.d\right)\\ X_1+X_3.Math.\stackrel{.Math.k_5.Math.}{.fwdarw.}.Math.& \left(1.Math.e\right)\\ X_3.Math.\stackrel{.Math.k_{6.Math.}}{.fwdarw.}.Math.2.Math.X_3& \left(1.Math.f\right)\\ 2.Math.X_3.Math.\stackrel{.Math.k_7.Math.}{.fwdarw.}.Math.X_3& \left(1.Math.g\right)\end{array}$

Step 2: determining an idealized reaction module and a DNA strand displacement reaction module corresponding thereto, for example, a catalytic reaction module, a degradation reaction module and an annihilation reaction module according to an idealized reaction equation.
Step 3: constructing a DNA strand displacement analog circuit according to the idealized reaction network and the reaction modules.
Step 4: adopting an encryption method. The detailed steps (1)-(5) of the encryption method are as follows:
(1) obtaining a secret key d.sub.k according to plaintext information, wherein K[4,5,6, . . . , ];
(2) obtaining chaotic sequences x.sub.1(i), x.sub.2(i) and x.sub.3(i) from the concentration measurement, and obtaining sequences matched with plaintext images from the extended sequences) {circumflex over (X)}.sub.1(i) {circumflex over (X)}.sub.2(i) and {circumflex over (X)}.sub.3(i);
(4) scrambling the color plaintext images at the level of the three components R, G, B in consideration of the relation between the three components R, G, B in a color image;
(5) obtaining scrambling sequences [1,N], ={.sup.r,.sup.g,.sup.b} and ={.sup.r,.sup.g,.sup.b} by using the extended chaotic sequences;
(6) scrambling the plaintext images to obtain a scrambled image P;
(7) obtaining a scrambling sequence U by utilizing the extended chaotic sequences;
(8) obtaining a scrambling sequence V by utilizing the extended chaotic sequences; and
(9) performing diffusion operation on the image P by utilizing sequences U={U.sub.r,U.sup.g,U.sup.b} and V={V.sup.r,V.sup.g,V.sup.b} to obtain an encrypted image C={C.sup.r,C.sup.g,C.sup.b}.
Step 5: adopting a decryption method. The detailed steps (1)-(2) of the decryption method are as follows:
(1) removing the diffusion effect on the encrypted image from the last pixel to the first pixel; and
(2) removing the diffusion effect from the last column (row) to the first column (row) to obtain a plaintext image;

EXAMPLE 1

[0020] The embodiments of the present invention are implemented on the premise of the technical proposal of the present invention, and detailed embodiments and specific operation processes are given, but the scope of protection of the present invention is not limited to the following embodiments.

Step 1: substituting the parameters in table 1 into the DNA strand displacement analog circuit to obtain chaotic sequences x.sub.1(i), x.sub.2(i) and x.sub.3(i).
Step 2: detecting the encryption scheme by using color images of sizes 256256 including Lena, Pepper and Baboon, wherein s.sub.1=800, s.sub.2=1500.
Step 3: arranging the pixel values of the plaintext image according to the size, then representing the pixel values by p.sup.r, p.sup.g and p.sup.b, and recording the positions of the pixel values respectively by q.sup.r{q.sub.1.sup.r,q.sub.2.sup.r, . . . ,q.sub.MN.sup.r}, q.sup.q={q.sub.1.sup.g,q.sub.2.sup.g, . . . ,q.sub.MN.sup.g} and q.sup.b={q.sub.1.sup.b,q.sub.2.sup.b, . . . ,q.sub.MN.sup.b, then

[00002]$\begin{array}{cc}{\mathrm{sum}}_r=\underset{i=1}{\overset{MN}{.Math.}}.Math.p_i^r.Math.q_i^r& \left(21\right)\\ {\mathrm{sum}}_g=\underset{i=1}{\overset{MN}{.Math.}}.Math.p_i^g.Math.q_i^g& \left(22\right)\\ {\mathrm{sum}}_b=\underset{i=1}{\overset{MN}{.Math.}}.Math.p_i^b.Math.q_i^b& \left(23\right)\\ d_k=\mathrm{mod}\left({\mathrm{sum}}_r+{\mathrm{sum}}_g+{\mathrm{sum}}_b,k+0.1\right).Math..Math.\left(1kK\right)& \left(24\right)\end{array}$

[0021] wherein, 0<.sub.k10, K[4,5,6, . . . , ].

Step 4: extending x.sub.1(i), x.sub.2(i), and x.sub.3(i) into three sets of sequences and {circumflex over (X)}.sub.1(i), {circumflex over (X)}.sub.2(i) and {circumflex over (X)}.sub.3(i) matched with the plaintext images as follows,

[00003]$\begin{array}{cc}\{\begin{array}{c}{\hat{X}}_1\left(i\right)=X_1\left(m+1\right)\\ {\hat{X}}_2\left(i\right)=X_2\left(m+1\right)\\ {\hat{X}}_3\left(i\right)=X_3\left(m+1\right)\end{array}.Math..Math.1i{r}_2& \left(25\right)\\ \{\begin{array}{c}{\hat{X}}_1\left(r_2+b{r}_1-j\right)=X_1\left(m+1+b\right)\\ {\hat{X}}_2\left(r_2+b{r}_1-j\right)=X_2\left(m+1+b\right)\\ {\hat{X}}_3\left(r_2+b{r}_1-j\right)=X_3\left(m+1+b\right)\end{array}& \left(26\right)\\ r_1=.Math.MN/\left(-1\right).Math.& \left(27\right)\\ r_2=\mathrm{mod}\left(MN,-1\right)& \left(28\right)\\ 1b-1,0r_1-1& \left(29\right)\end{array}$

the first m data are discarded, and the detection time can be obtained by the following equation:

T=(+m)3(seconds) (30)

Step 5: scrambling the color plaintext images at the level of the three components R, G, B as follows in consideration of the relation among the three components R, G, B in a color image:

[00004]$\begin{array}{cc}\{\begin{array}{cc}{p}^r\left(i\right).Math.p^g\left(q_i^r\right)& \mathrm{if}.Math..Math.{\hat{X}}_1\left(i\right)>10.Math..Math.\mathrm{nM}\\ \mathrm{No}.Math..Math.\mathrm{exchange}& \mathrm{if}.Math..Math.{\hat{X}}_1\left(i\right)10.Math..Math.\mathrm{nM}\end{array}& \left(31\right)\\ \{\begin{array}{cc}{p}^g\left(i\right).Math.p^b\left(q_i^g\right)& \mathrm{if}.Math..Math.{\hat{X}}_2\left(i\right)>10.Math..Math.\mathrm{nM}\\ \mathrm{No}.Math..Math.\mathrm{exchange}& \mathrm{if}.Math..Math.{\hat{X}}_2\left(i\right)10.Math..Math.\mathrm{nM}\end{array}& \left(32\right)\\ \{\begin{array}{cc}{p}^b\left(i\right).Math.p^r\left(q_i^b\right)& \mathrm{if}.Math..Math.{\hat{X}}_3\left(i\right)>10.Math..Math.\mathrm{nM}\\ \mathrm{No}.Math..Math.\mathrm{exchange}& \mathrm{if}.Math..Math.{\hat{X}}_3\left(i\right)10.Math..Math.\mathrm{nM}\end{array}& \left(33\right)\end{array}$

wherein 1MN
Step 6: repetitively iterating equations (34) and (35) until 6 one-dimensional arrays are obtained, wherein [1,M], [1,N], ={.sup.r,.sup.g,.sup.b} and ={.sup.r,.sup.g,.sup.b}.

[00005]$\begin{array}{cc}\{\begin{array}{c}{}^r=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_1}{d}{10}^{14}\right),M\right)+1\\ {}^g=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_1}{d}{10}^{14}\right),M\right)+1\\ {}^b=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_3}{d}{10}^{14}\right),M\right)+1\end{array}& \left(34\right)\\ \{\begin{array}{c}{}^r=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_1}{d}{10}^{14}\right),N\right)+1\\ {}^g=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_2}{d}{10}^{14}\right),N\right)+1\\ {}^b=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_3}{d}{10}^{14}\right),N\right)+1\end{array}& \left(35\right)\end{array}$

step 7: obtaining a scrambled image P according to the following operation:

f(i,j)f((i+s.sub.1),(j+s.sub.2)) (36)

Step 8, generating a diffusion sequence U by using the chaotic sequences;

[00006]$\begin{array}{cc}\{\begin{array}{c}{U}^r=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_1}{d}{10}^{14}\right),256\right)\\ U^g=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_1}{d}{10}^{14}\right),256\right)\\ U^b=\mathrm{mod}\left(\mathrm{floor}\left(\frac{{\hat{X}}_3}{d}{10}^{14}\right),256\right)\end{array}& \left(37\right)\end{array}$

Step 9: generating a diffusion sequence V by using the chaotic sequences;

[00007]$\begin{array}{cc}\{\begin{array}{cc}{V}^r=255& \mathrm{if}.Math..Math.{\hat{X}}_1>10.Math..Math.\mathrm{nM}\\ V^r=0& \mathrm{if}.Math..Math.{\hat{X}}_{1}10.Math..Math.\mathrm{nM}\end{array}& \left(38\right)\\ \{\begin{array}{cc}{V}^g=255& \mathrm{if}.Math..Math.{\hat{X}}_2>10.Math..Math.\mathrm{nM}\\ V^g=0& \mathrm{if}.Math..Math.{\hat{X}}_{2}10.Math..Math.\mathrm{nM}\end{array}& \left(39\right)\\ \{\begin{array}{cc}{V}^b=255& \mathrm{if}.Math..Math.{\hat{X}}_3>10.Math..Math.\mathrm{nM}\\ V^b=0& \mathrm{if}.Math..Math.{\hat{X}}_{3}10.Math..Math.\mathrm{nM}\end{array}& \left(40\right)\end{array}$

step 10: performing diffusion operation on the image p by using the matrix U={U.sup.r,U.sup.g,U.sup.b} and V={V.sup.r,V.sup.g,V.sup.b} to obtain an encrypted image C={C.sup.r,C.sup.g,C.sup.b}.

[00008]$\begin{array}{cc}{C}_1=P_1^{}{U}_i{V}_1& \left(41\right)\\ \{\begin{array}{c}{C}_i^r=P_i^{.Math..Math.r}{C}_{i-1}^r{U}_i^r{V}_i^r\\ C_i^g=P_i^{.Math..Math.g}{C}_{i-1}^g{U}_i^g{V}_i^g{C}_i^r\\ C_i^b=P_i^{.Math..Math.b}{C}_{i-1}^b{U}_i^b{V}_i^b{C}_i^r{C}_i^g\end{array}.Math..Math.MNi>1& \left(42\right)\end{array}$

step 11: adopting a decryption method. The detailed steps: (1)-(2) of the decryption method are as follows:

[0022] (1) removing the diffusion effect on the encrypted image from the last pixel to the first pixel;

[00009]$\begin{array}{cc}\{\begin{array}{c}{E}_i^r=C_i^r{C}_{i-1}^r{U}_i^r{V}_i^r\\ E_i^g=C_i^g{C}_{i-1}^g{U}_i^g{V}_i^g{C}_i^r\\ E_i^b=C_i^b{C}_{i-1}^b{U}_i^b{V}_i^b{C}_i^r{C}_i^g\end{array}.Math..Math.i>1& \left(43\right)\\ E_1=C_1{U}_1{V}_1& \left(44\right)\end{array}$

[0023] (2) removing the scrambling effect from the last column (row) to the first column (row) to obtain a plaintext image;

[0024] The effects of encryption and decryption of Lena, Pepper and Babook images are shown in FIG. 7, and the indices of the encrypted images are shown in tables 2-4.

[0025] The above is only the specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto, and any changes or substitutions without creative efforts shall fall within the protection scope of the present invention. Therefore, the claimed protection extent of the invention shall be determined with reference to the appended claims.