CN115834788A

CN115834788A - Color image encryption method for visualized DNA fulcrum-mediated strand displacement reaction

Info

Publication number: CN115834788A
Application number: CN202211435627.0A
Authority: CN
Inventors: 邹成业
Original assignee: Anyang Normal University
Current assignee: Anyang Normal University
Priority date: 2022-11-16
Filing date: 2022-11-16
Publication date: 2023-03-21
Anticipated expiration: 2042-11-16
Also published as: CN115834788B

Abstract

The invention provides a color image encryption method for visualized DNA pivot mediated strand displacement reaction, which comprises the following steps: constructing a Rnano chaotic system facing to a DNA fulcrum mediated strand displacement reaction; by imaging in plain colourR、G、BThe channel matrixes are respectively converted into sequences and arranged in ascending order to obtain sub-keys; endowing an initial value to the R-shaped sneaker chaotic system by utilizing a sub-secret key, splicing the generated three data groups, and obtaining three chaotic sequences according to the sub-secret key; using data sets to respectively align color plaintext imagesPThe corresponding sequences are scrambled with color components, and the three chaotic sequences are utilized to scramble elements in the scrambled matrix respectively to obtain a scrambling matrix; and diffusing the scrambling matrixes by the three chaotic sequences respectively to obtain an encrypted image. The invention obtains the chaotic sequence by deformation splicing of the detection result, is applied to the R, G, B component and pixel two layers of the image, and can effectively ensureThe security and the attack resistance of the encryption of the images are prevented.

Description

Color image encryption method for visualized DNA fulcrum-mediated strand displacement reaction

Technical Field

The invention relates to the technical field of biological calculation, information processing and data encryption, in particular to a color image encryption method for visualized DNA pivot mediated strand displacement reaction, which ensures the safety of an image encryption technology.

Background

While a conventional electronic computer performs serial computation, a new computer represented by a biological computer, an optical computer, a quantum computer, a nano computer performs an operation mode of parallel computation or distributed computation, and has attracted great interest and attention of scientists. DNA is an important carrier of biological computers, and has attracted attention due to its characteristics such as parallelism of reaction, large information storage capacity, and low energy consumption, and has attracted intensive research by scientists in the fields of artificial intelligence, biological engineering, mathematics, physics, chemistry, and information processing. In recent years, DNA pivot mediated strand displacement reaction has been widely used in a variety of fields as a novel biological computing technique. The DNA fulcrum-mediated strand displacement reaction conforms to the Watson-Crick base pairing principle, does not need external electromagnetic field influence and annealing operation, and can be realized at normal temperature, so the DNA fulcrum-mediated strand displacement reaction has the controllable and predictable kinetic characteristics, and complicated and various DNA digital circuits and DNA analog circuits can be constructed through a cascade mode.

The DNA digital circuit belongs to a binary circuit, and when the concentration of a signal DNA chain is higher than a threshold value, the output value is 1, otherwise, the output value is 0. Compared with a DNA digital circuit, the DNA analog circuit has higher requirements on the concentration detection precision of a DNA chain, and because the detection concentration of a signal DNA chain is an output value, the realization of the application of the DNA analog circuit is particularly important under the condition of limited concentration detection precision of the DNA chain at present.

In the conventional chaotic encryption algorithm, the sensitivity of the chaotic system to an initial value and a parameter is utilized to expand the space of a secret key so as to resist the violent attack of an attacker, but the method is not suitable for a semi-synthetic biological system because the detection precision of concentration is limited. To address this challenge, the present invention expands the key space with a sub-key.

Disclosure of Invention

Aiming at the technical problems that the DNA chain concentration detection precision of the existing DNA analog circuit is limited, and the sensitivity requirement of a general chaotic circuit on initial conditions is difficult to realize, the invention provides a color image encryption method for visualized DNA fulcrum-mediated chain displacement reaction.

In order to achieve the purpose, the technical scheme of the invention is realized as follows: a color image encryption method for visualized DNA pivot mediated strand displacement reaction comprises the following steps:

the method comprises the following steps: construction of a DNA-based strand displacement reaction mediated by a DNA fulcrum

A chaotic system;

step two, key generation: respectively converting the R, G, B channel matrixes of the colorful plaintext image P into sequences and arranging the sequences in an ascending order to obtain sub-keys;

step three, generating a chaotic sequence: using a sub-key to give

The chaotic system gives an initial value to

Splicing three data sets generated by the chaotic system, and obtaining three chaotic sequences according to the sub secret keys;

step four: color image scrambling: respectively scrambling the color components of the sequences corresponding to the R, G, B channel matrix of the color plaintext image P by using the three data groups, and scrambling the elements in the matrix after the color components are scrambled by using the three chaotic sequences to obtain a scrambling matrix

Step five: image diffusion: respectively aligning the three chaotic sequences to a scrambling matrix

And diffusing to obtain an image consisting of the matrix as an encrypted image.

Preferably, in the first step

The ideal chemical reaction network of the chaotic system is as follows:

wherein X, Y and Z are signal reaction participants, k _α α =1, …,7 is the reaction rateAnd Φ represents a useless substance.

The differential equation for an idealized chemical reaction network is:

wherein ,

representing the differential of variables X, Y and Z, respectively.

Preferably, the DNA compiling method of the idealized chemical reaction network is:

(I)

and

belongs to a catalytic reaction module I, and is compiled into a DNA strand displacement reaction:

wherein ,X_i Is a signal DNA strand, i is a positive integer, A _i ,P _i ,N _i And C _i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m (ii) a Reaction rate q _i and k_i Satisfy q _i ≤q _m ，k _i ＝q _i C _m ，q _m Represents the maximum reaction rate; design of Signal DNA chain X _i Has a DNA single-stranded structure of<x3^x2 x1^>Helper DNA strand A _i ,P _i ,N _i And C _i The complex chain structures of the DNA are respectively as follows: { x3^ x }: x2 x1^ x }, and]::<s1 s2^x1^k2^>、{x1^*}:[s1 s2^]<t6 x2 x1^k2^>:<s1 s2^t6 x2>[x1^k2^]、[x2 x1^]:{k2^*}::<k3^t1^>and<x3^>::[x2 x1^]{ k3^ t1^ wherein }, wherein,<>represents a top chain structural portion of a DNA chain, [ 2 ]]Representing the double-stranded part of the DNA strand that has been complementarily paired, for joining two double-stranded domains, and { } representing the lower-strand domain of the DNA strand, for labeling the upper-strand domain, { character } B* Used to label the down-chain domain; waste indicates an unusable DNA strand, T _i 、Ta _i 、Pa _i Respectively representing products generated by DNA reaction;

(II)

belongs to a catalytic reaction module II, and is compiled as a DNA strand displacement reaction:

wherein ,X_i 、Y _i As a signal DNA strand, B _i ,Am _i ,E _i ,Ea _i ,Eb _i And Fa _i Is an auxiliary DNA strand; reaction rate q _i ,q′ _i and k_i Satisfy q _i ,q′ _i ≤q _m ，k _i ＝q _i (ii) a Designing input signal Y _i The DNA single strand structure of<y1^y2 y3^>Auxiliary DNA chain B _i ,E _i ,Ea _i And Fa _i The complex chain structures of the DNA are respectively as follows: { x3^ x } [ x2 x1^ y } ]]:[y2 y3^]::<b2 b3^r1 r2^>、{y3^*}:<r1 r2^b1 y2>[b2 b3^]:[r1 r2^]::<b1 y2 b2 b3^>、[x2 x1^]:{k2^*}::<k3^t1^>And<x3^>::[x2 x1^]{ k3^ t1^ and { c1^ c2^ are }:<y1^>[y2 y3^]；Ma _i products formed by DNA reactions, fa _i Indicates the DNA strand that should be added before the reaction starts;

(III)

belongs to an annihilation reaction module, and is compiled into a DNA strand displacement reaction:

wherein ,Fb_i And Fc _i Is an auxiliary DNA strand; design of helper DNA strand Fb _i The double-stranded structure of the DNA is { x3^ x }: x2 x1^ y]:[y2 y3^]；Ad _i Represents a product produced by a DNA reaction;

(IV)

and

belongs to a degradation reaction module I, and is compiled into a DNA strand displacement reaction:

wherein ,G_i ,Ac _i And Tp _i Is an auxiliary DNA strand; designed helper DNA strand G _i And Tp _i The double-stranded structure of the DNA is { x3^ x }: x2 x1^ x3^ x]:[x2 x1^]::<c2^c3^>And [ x3^ x2 x1^ x]{c2^*c3^*}；Da _i Represents a product produced by a DNA reaction;

(V)

belongs to a degradation reaction module II, and is compiled into a DNA strand displacement reaction:

wherein ,Ka_i Is an auxiliary DNA strand; designed helper DNA strand Ka _i The DNA double-stranded structure is { y1^ x }: y2 y3^ x ^ y]；

(VI) DNA Strand Displacement reaction

Belongs to a regulation reaction module and is used for removing the buffer effect:

wherein ,Va_i and Wa_i For the auxiliary DNA strand, omega _i Generating a product for the DNA; design of auxiliary DNA strands Va _i The DNA double-chain structure is [ h1^ y2]:{y3^*}，qx _i 、qy _i Respectively representing forward reaction rate and backward reaction rate;

wherein x1, x2, x3, y1, y2, y3, z1, z2, z3, b1, b2, b3, c1, c2, c3, r1, r2, s1, s2, t6, k2, k3, and t1 each represents a different DNA base sequence;

the above-mentionedSignal DNA strand X in DNA strand displacement reaction _i Signal DNA strand Y _i Signal DNA strand Z _i Auxiliary DNA strand C _i 、Fa _i 、Tp _i Provided with fluorophores of different colors, a signal DNA chain X _i Signal DNA strand Z _i Auxiliary DNA strand A _i 、C _i 、Fa _i 、B _i 、Fb _i 、G _i 、Ka _i 、Va _i 、Tp _i The quenching group is arranged on the fluorescent probe, the quenching group can absorb fluorescence emitted by the fluorophore, when the fluorophore is far away from the quenching group, the fluorescence is not absorbed, and the luminous intensity can be detected to be used as a marker; when the fluorophore is near the quenching bolus, fluorescence is absorbed and no luminescence intensity is detected.

Preferably, the method for obtaining the sub-key comprises:

step 21: the R, G, B channel matrix P of the color plaintext image P ^R 、P ^G and P^B Are respectively reconstructed into sequences P ^1R 、P ^1G and P^1B The method comprises the following steps:

where reshape (,) represents the reconstruction function and the sequence

And

are respectively a sequence P ^1R M × N pixel values;

step 22: will sequence P ^1R 、P ^1G and P^1B The pixel values in (1) are arranged:

wherein sort (#) represents an ascending sort function, wherein

And

are respectively a sequence P ^1R 、P ^1G and P^1B A new sequence after the ascending order arrangement,

and

are respectively a new sequence h ^r 、h ^g and h^b The index value of (a);

step 23: then the key is key = sum _r +sum _g +sum _b Wherein, sum _r 、sum _g and sum_b The calculation method comprises the following steps:

obtaining K sub-keys by using the key:

d _k ＝mod(key,a _k ),k＝1≤k≤K；

wherein ,sum_r 、sum _g and sum_b The sum of pixel values representing R, G, B components, respectively, mod represents a function for the remainder, a _k ＝k+0.1，K＝4,5,…,∞。

Preferably, the method for generating the chaotic sequence comprises:

step 31: according to the sub-key pair

Initial values of signal DNA chains X, Y and Z of the chaotic system are given as follows:

wherein ,[X]₀ 、[Y] ₀ 、[Z] ₀ Initial values for DNA signal chains X, Y and Z, respectively, d ₁ (nM)、d ₂ (nM)、d ₃ (nM) is the sub-key d _k nM is nanomolar;

step 32: splicing signal DNA chains X, Y and Z to obtain data groups X ', Y ' and Z ', wherein the splicing method comprises the following steps:

wherein ,

index values representing the sequence, sum

I' =1,2, …, ω, j =1,2, …, r, representing the absolute value and the rounded-down sign, respectively ₂ Omega is the number of splices, an

Represents rounding up; s is the number of test data sets to discard, r ₁ 、r ₂ Is an intermediate variable;

step 33: obtaining chaotic sequences U according to the data groups X ', Y ' and Z ' respectively ^r 、U ^g 、U ^b ：

wherein ,

preferably, the

Three groups of data groups obtained by signal DNA chains X, Y and Z of chaotic system

And

each set of data of (1) contains 1+r ₂ Data when the DNA strand displacement reaction formally started sxT ₀ After second, the first s detection data sets are discarded and every T ₀ The concentration of the signal DNA chains X, Y and Z is detected once in seconds, and the total detection time is T = (1 + s + r) ₂ )×T ₀ Wherein the splicing times are

Intermediate variable r ₂ ＝(M×N-r ₁ ) Omega, intermediate variable r ₁ ＝mod(M×N,ω)。

Preferably, the method for performing color component scrambling on the sequence corresponding to the R, G, B channel matrix of the color plaintext image P by using three data sets in the fourth step is: respectively aligning the sequence P according to the concentration of the signal chain on the R, G, B component level ^1R 、P ^1G and P^1B Scrambling the medium elements:

the R, G, B component obtained after scrambling is the sequence

And

and

are respectively a sequence P ^1R 、P ^1G and P^1B The elements of (1); x' _l 、Y′ _l 、Z′ _l The I-th elements of data sets X ', Y ' and Z ' are shown, respectively, and 1nM and 2nM are the DNA strand concentrations.

Preferably, the obtaining a scrambling matrix

And

the method comprises the following steps:

will be sequenced

And

are respectively reconstructed into a matrix

And

matrix of

And

scrambling is performed on a pixel level, respectively:

wherein ,s₁ and s₂ Is a positive integer and is a non-zero integer,

and

respectively represent matrices

And

an element of (1);

scrambling matrix Γ = [ Γ = [ Γ ] ^r ,Γ ^g ,Γ ^b] and Ψ＝[Ψ^r ,Ψ ^g ,Ψ ^b ]Comprises the following steps:

wherein m and n respectively represent the row and the column; u shape ^r (m)、U ^g (m)、U ^b (m)、U ^r (n)、U ^g (n)、U ^b (n) respectively represent chaotic sequences U ^r 、U ^g 、U ^b The mth and nth elements of (a);

the scrambled scrambling matrix is

And

are respectively scrambling matrices

And

row m and column n.

Preferably, the image diffusion method in the step five is as follows:

step 51: to the scrambling matrix

And

and (3) reconstruction:

wherein ,

and

are respectively a matrix

And

a reconstructed sequence;

step 52: by a chaotic sequence U ^r 、U ^g and U^b Obtaining a diffusion sequence V ^r 、V ^g and V^b The method comprises the following steps:

wherein ,

respectively represent diffusion sequences V ^r 、V ^g and V^b 1nM, 2nM represent the concentration of DNA strands;

step 53: using diffusion sequences V ^r 、V ^g and V^b Separate diffusion sequences

And

obtaining an encrypted image, wherein the calculation method comprises the following steps:

wherein ,

in order to perform the exclusive-or operation,

respectively represent chaotic sequences U ^r 、U ^g 、U ^b Diffusion sequence V ^r 、V ^g 、V ^b And post-diffusion sequence E ^1r 、E ^1g 、E ^1b The value of the ith element of (c);

post-diffusion sequence E ^1r 、E ^1g 、E ^1b Respectively reconstructing to obtain a matrix E ^r ,E ^g ,E ^b Then the matrix E is formed ^r ,E ^g ,E ^b And splicing the three channels R, G, B to obtain a ciphertext image.

Preferably, the corresponding image decryption method is:

step 1: using diffusion sequences V ^r 、V ^g and V^b Removing the diffusion effect:

wherein ,

r, G, B sequences corresponding to the three channel components respectively representing the decrypted image;

step 2: for sequence D ^r 、D ^g and D^b Go on heavilyStructure:

wherein ,Λ^R 、Λ ^G 、Λ ^B Respectively represent D ^r 、D ^g and D^b Reconstructing to obtain a matrix;

and step 3: at the pixel level, the scrambling effect is eliminated from the last row to the first row, and the last column to the first column:

wherein M '= M, M-1,M-2, …,1,n' = N, N-1,N-2, …,1;

and 4, step 4: matrix Λ after eliminating scrambling effect ^1R 、Λ ^1G 、Λ ^1B Respectively reconstructing to obtain the sequences Lambda of canceling scrambling effect ^2R 、Λ ^2G 、Λ ^2B Comprises the following steps:

and 5: de-scrambling effect sequence Λ at the R, G and B levels ^2R 、Λ ^2G 、Λ ^2B Comprises the following steps:

wherein ,Λ^2R (l)、Λ ^2G (l)、Λ ^2B (l) Respectively represent the sequence Λ ^2R 、Λ ^2G 、Λ ^2B The l element of (1);

and 6: and reconstructing the sequence without the scrambling effect back to the matrix, and splicing the sequence as the information of R, G, B three channels to obtain a decrypted image.

Compared with the prior art, the invention has the following beneficial effects: designing DNA sequence code of data DNA chain and several reaction modules for generating DNA circuit and constructing DNA chain displacement reaction based on DNA fulcrum

The chaotic system is used for generating a chaotic sequence and realizing the image encryption of the DNA circuit; the generated chaotic sequence pair is utilized to not only implement the scrambling of the pixel level but also add the scrambling of the R, G, B component level, and the dual scrambling can enhance the scrambling effect; the invention obtains the chaotic sequence by deforming and splicing the detection result obtained in the effective detection time, and applies the chaotic sequence to the image scrambling and diffusing process to realize the image encryption algorithm, wherein the image scrambling is implemented on two layers of R, G, B components and pixels of the image, and the security and the attack resistance of the image encryption can be effectively ensured.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a schematic flow diagram of the present invention;

FIG. 2 is a reaction schematic of catalytic reaction module I of the present invention;

FIG. 3 is a reaction schematic of catalytic reaction module II of the present invention;

FIG. 4 is a reaction scheme of an annihilation reaction module of the invention;

FIG. 5 is a reaction scheme of the degradation reaction module I of the present invention;

FIG. 6 is a reaction scheme of the degradation reaction module II of the present invention;

FIG. 7 is a reaction schematic of a conditioning reaction module of the present invention;

FIG. 8 is a schematic diagram of the DNA coding design in catalytic reaction module I of the present invention;

FIG. 9 is a schematic diagram of a DNA coding design in catalytic reaction module II of the present invention;

FIG. 10 is a schematic diagram of DNA coding design in other reaction modules of the present invention;

FIG. 11 is a diagram illustrating the encryption effect of the Lena color plaintext image according to the present invention, wherein (a) is the original image and (b) is the encrypted image.

Fig. 12 is a sector histogram of the pixel distribution of the present invention, in which (a) is a plaintext image and (b) is a ciphertext image.

FIG. 13 is a comparison graph of the correlation between adjacent pixels of a plaintext image and a ciphertext image, where (a) is a red component of the plaintext image, (b) is a red component of the ciphertext image, (c) is a green component of the plaintext image, (d) is a green component of the ciphertext image, (e) is a blue component of the plaintext image, and (f) is a blue component of the ciphertext image.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art based on the embodiments of the present invention without inventive step, are within the scope of the present invention.

The invention constructs the DNA-based support point mediated strand displacement reaction

A chaotic system with a DNA analog circuit as a pseudo-random number generator comprising a plurality of reaction modules, wherein a fluorophore is designed at an end of a signal DNA strand, and the emission intensity of the fluorophore is measuredSo that the dynamic change of the DNA circuit signal becomes visible and the concentration of the signal DNA chain is convenient to detect. As a large amount of leakage reaction exists in the biochemical circuit and a large amount of DNA chains are continuously degraded, the dynamic characteristics of the DNA circuit are continuously degraded, so that the concentration detection of the signal DNA chains needs to be completed within a limited time, and the detected data is spliced to meet the requirement of the chaotic sequence. At present, the DNA chain concentration detection precision is limited, the sensitivity requirement of a general chaotic circuit on initial conditions is difficult to realize, the problem is overcome through the design of a sub-secret key, and the secret key space is effectively expanded.

Fig. 1 shows a color image encryption method for visualized DNA pivot mediated strand displacement reaction, which is specifically implemented as follows:

the method comprises the following steps: construction of DNA-directed strand displacement reaction mediated by DNA pivot

The chaos system, DNA fulcrum mediated strand displacement reaction, is that the footing point is used to provide the fulcrum for the reaction between the invading DNA strand and the substrate DNA strand, through the free energy difference of DNA molecule hybridization, one single strand sequence is used to replace the other single strand from the double helix structure of the hybridized DNA for the subsequent reaction, has accurate sequence orthogonality, wherein the reaction rate can be adjusted by the length of the footing point. Application of DNA pivot mediated strand displacement reaction to

Model-derived chaotic system can use its pair

And carrying out DNA compiling on the model to realize a DNA circuit.

Step 1:

the idealized chemical reaction network of the system is designed to be:

wherein X, Y and Z are signal reaction participants, k _α α =1, …,7 is the reaction rate, Φ represents a useless substance.

According to the characteristics of the idealized chemical reaction network, the differential equation of the idealized chemical reaction network is as follows:

wherein ,

representing the differential of variables X, Y and Z, respectively. The differential equation is used to illustrate the rate of change of chemicals X, Y and Z.

Step 2: and (3) DNA compiling of the idealized chemical reaction network, wherein each part in the chemical reaction network can be compiled into a corresponding DNA reaction module, and the specific compiling process is as follows:

(I) As shown in figure 2 of the drawings, in which,

and

belonging to catalytic reaction module I, it can be compiled as the following DNA strand displacement reaction:

wherein ,X_i Is a signal DNA strand, i is a positive integer, A _i ,P _i ,N _i And C _i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m (ii) a Reaction Rate q _i and k_i Satisfy q _i ≤q _m ，k _i ＝q _i C _m ，q _m Indicating the maximum reaction rate. Design of input Signal DNA chain X _i The DNA single strand structure of<x3^x2 x1^>，A _i ,P _i ,N _i And C _i The complex chain structures of the DNA are respectively as follows: { x3^ X }: [ x2 x1^ s]::<s1 s2^x1^k2^>、{x1^*}:[s1 s2^]<t6 x2 x1^k2^>:<s1 s2^t6 x2>[x1^k2^]、[x2 x1^]:{k2^*}::<k3^t1^>And<x3^>::[x2 x1^]{ k3^ t1^ wherein }, wherein,<>represents an upper chain structural portion of a DNA chain, [ 2 ]]Means for linking two double-stranded domains, { } means for labeling the upper strand domain, and ^ means for labeling the lower strand domain.

waste denotes the useless DNA strand, T _i 、Ta _i 、Pa _i Indicates the DNA strand that should be added before the reaction. As shown in FIG. 2, the structure of each signal chain is added with a fluorophore and a fire extinguishing group, and the detection of the DNA strand concentration is facilitated by using different colors of the fluorophore as a label. Wherein x1, x2, x3, x, s1, s2, t6, k2, k3, and t1 each represent a different DNA base sequence.

(II) as shown in FIG. 3,

belonging to catalytic reaction module II, it can be compiled as the following DNA strand displacement reaction:

wherein ,Y_i As a signal DNA strand, B _i ,Am _i ,E _i ,Ea _i ,Eb _i And Fa _i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m (ii) a Reaction rate q _i ,q′ _i and k_i Satisfy q _i ,q′ _i ≤q _m ，k _i ＝q _i . Designing input signal Y _i The DNA single-stranded structures of (A) are respectively<y1^y2 y3^>，B _i ,E _i ,Ea _i And Fa _i The complex chain structures of the DNA are respectively as follows: { x3^ x } [ x2 x1^ y } ]]:[y2 y3^]::<b2 b3^r1 r2^>、{y3^*}:<r1 r2^b1 y2>[b2 b3^]:[r1 r2^]::<b1 y2 b2 b3^>、[x2 x1^]:{k2^*}::<k3^t1^>And<x3^>::[x2 x1^]{ k3^ t1^ and { c1^ c2^ are }:<y1^>[y2 y3^]。X _i 、Ma _i 、Fa _i each represents a DNA strand to be added before the reaction starts. Wherein y1, y2, y3, b1, b2, b3, r1, r2, c1 and c2 each represent a different DNA base sequence. As shown in FIG. 3, the structure of each signal chain is added with a fluorophore and a fire extinguishing group, and the detection of the DNA chain concentration is facilitated by using different colors of the fluorophores as labels.

(III) As shown in FIG. 4,

belonging to an annihilation reaction module, it can be compiled as the following DNA strand displacement reaction:

wherein ,Fb_i And Fc _i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m (ii) a Reaction rate q _i and k_i Satisfy q _i ≤q _m ，k _i ＝q _i I =5. Designed helper DNA complex strand Fb _i The double-stranded structure of the DNA is { x3^ x }: x2 x1^ y]:[y2y3^]。Ad _i Indicates the DNA strand that should be added before the reaction. Wherein z1, z2 and z3 each represent a different DNA base sequence. As shown in FIG. 4, the structure of each signal chain is added with a fluorophore and a fire extinguishing group, and the detection of the DNA chain concentration is facilitated by using different colors of the fluorophore as markers.

(IV) as shown in figure 5,

and

belonging to a degradation reaction module I, it can be compiled into the following DNA strand displacement reaction:

wherein ,G_i ,Ac _i And Tp _i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m (ii) a Reaction rate q _i and k_i Satisfy q _i ≤q _m ，k _i ＝q _i . Designed helper DNA Complex strand G _i And Tp _i The double-stranded structure of the DNA is { x3^ x }: x2 x1^ x3^ x]:[x2 x1^]::<c2^c3^>And [ x3^ x2 x1^ x]{c2^*c3^*}。

wherein ,Da_i Indicates the product of the DNA reaction. As shown in FIG. 5, the structure of each signal chain adds a fluorophore and a fire extinguishing group, the detection of the concentration of the DNA chain is facilitated by using different colors of the fluorophores as labels, and c3 is a fragment or a region of the DNA chain.

(V) as shown in figure 6,

belongs to a degradation reaction module II, which can be compiled into the following DNA strand displacement reaction:

wherein ,Ka_i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m . Reaction rate q _i and k_i Satisfy q _i ≤q _m ，k _i ＝q _i C _m . Designed auxiliary DNA complex chain Ka _i The DNA double-stranded structure of (a) is { y1^ x }: [ y2 y3^ 3]. As shown in FIG. 6, the structure of each signal DNA strand is added with a fluorophore and a fire extinguishing group, and the detection of the DNA strand concentration is facilitated by using different colors of the fluorophores as markers.

(VI) As shown in FIG. 7, the DNA strand displacement reaction (7) belongs to the regulatory reaction module for removing the buffer effect:

wherein ,Va_i and Wa_i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m 。ω _i Products were generated for the DNA. Design of helper DNA Complex chain Va _i The DNA double-chain structure is [ h1^ y2]:{y3^*}。qx _i 、qy _i Respectively representing forward and backward reaction rates. As shown in FIG. 7, the structure of each signal DNA strand is added with a fluorophore and a fire extinguishing group, and the detection of the DNA strand concentration is facilitated by using different colors of the fluorophores as markers.

DNA codes are shown in FIGS. 8-10, in which the materials used in biochemical reactions are shown, red, blue and yellow fluorophores are luminescent materials with different colors, the quenching mass can absorb fluorescence emitted by the fluorophores, and when the fluorophores are far away from the quenching mass, the fluorescence is not absorbed, and the luminescence intensity can be detected as a marker; when the fluorophore is near the quenching bolus, fluorescence is absorbed and no luminescence intensity is detected.

Step two, generating a secret key: assuming that a color plain text image P has a size of M × N, it is composed of R, G, B components, which are respectively composed of a color component matrix P ^R 、P ^G and P^B The three portions are all M × N in size, where the pixel values range from 0 to 255. Converting R, G, B channel matrix of color plaintext image P into sequence P ^1R 、P ^1G and P^1B And the sub-keys are obtained by ascending order arrangement, and the specific implementation is as follows:

step 1: the color component matrix P ^R 、P ^G and P^B The reconstruction into the sequence is as follows:

where reshape (, mxn, 1) represents the reconstruction function, the matrix is transformed into a sequence of 1 row mxn columns, and the sequence

And

are respectively a sequence P ^1R M × N pixel values.

And 2, step: will sequence P ^1R 、P ^1G and P^1B Pixel value in (1) is as commonFormula (9) is arranged:

wherein sort (, i.e., the sequence of numbers is arranged in the order from small to large; wherein

And

and

is a new sequence h ^r 、h ^g and h^b The index value of (c).

And step 3: key = sum is defined as a key of an encryption algorithm _r +sum _g +sum _b, wherein sum_r 、sum _g and sum_b This can be obtained from equation (10):

obtaining K sub-keys by using the key:

d _k ＝mod(key,a _k ),(k＝1≤k≤K) (11)

wherein ,sum_r 、sum _g and sum_b The summation of pixel values representing R, G, B components, respectively, mod represents a function for remainder, key is the dividend, a _k Is a divisor. a is a _k ＝k+0.1，K＝4,5,…,∞。

Step three, generating a chaotic sequence: since the DNA strand concentration detection technique is limited, the accuracy of DNA strand concentration detection is set to 0.0001nM in the present invention. And the concentration of signal DNA strands X, Y and Z is every T ₀ Time of secondAnd detecting once. Since the detection of the signal DNA strand needs to be completed within the effective time, the effective time is set in the present invention

Second, therefore, the number of concentration detections is necessarily limited, and the detected number of signal DNA strands X, Y and Z needs to be spliced to meet the requirement of the chaotic sequence. When the DNA reaction formally starts s X T ₀ After second, the first s detection data groups are discarded to ensure the pseudo-randomness of the detection data, and the pseudo-randomness is ensured every T ₀ The concentration of the signal DNA chains X, Y and Z is detected once in seconds, and the concentration detection is needed

Second, three sets of data were obtained from the signal DNA strands X, Y and Z

And

then each set of data contains 1+r ₂ For data, the total detection time T can be estimated as T = (1 + s + r) ₂ )×T ₀ Wherein the number of splices is

r ₂ ＝(M×N-r ₁ )/ω，r ₁ = mod (M × N, ω), s denotes the first s detection data groups that need to be discarded to ensure the pseudo-randomness of the detection data. s is the number of set test data to discard. T is ₀ Denotes the detection time interval, r ₂ Represents an intermediate variable, r ₁ Is also an intermediate variable. Given the splicing times omega, the intermediate variable r can be calculated ₁ Calculating an intermediate variable r ₁ The intermediate variable r can be calculated ₂ Calculating an intermediate variable r ₂ The total detection time can be estimated finally.

Step 1: to give

The chaotic system gives an initial value, the generated three groups of data are spliced, three chaotic sequences are obtained according to the sub key, and the three chaotic sequences are obtained according to the sub keyKey pair according to equation (12)

wherein ,[X]₀ 、[Y] ₀ 、[Z] ₀ Initial values for DNA signal chains X, Y and Z, respectively, d ₁ (nM)、d ₂ (nM)、d ₃ (nM) is given in equation (11) as the sub-key d _k The first three items of (1) were assigned to initial concentrations of signal DNA strand X, Y, Z, respectively, in nM, the stoichiometric unit of nanomolar.

Step 2: the signal DNA strands X, Y and Z are spliced according to equations (13) and (14) to yield data sets X ', Y ' and Z ':

wherein ,

index values representing the sequence, sum

And 3, step 3: the chaotic sequence is obtained from equation (15):

wherein ,

obtaining the chaotic sequence by using d can effectively increase the key space.

Step four: color image scrambling: sequence P corresponding to R, G, B channel matrix of color plaintext image P by using three groups of data ^1R 、P ^1G and P^1B Color component scrambling is carried out, and the three chaotic sequences are utilized to carry out scrambling on elements in the matrix after the color component scrambling respectively to obtain a scrambling matrix

And

step 1: for sequence P at the R, G, B component level according to equations (16) - (18) ^1R 、P ^1G and P^1B Scrambling the medium elements:

wherein the R, G, B component obtained after scrambling is formed by the sequence

And

and (4) showing. The scrambling of the pixel layer is realized, and the position of the original pixel is changed.

Step 2: to the sequence

And

reconstructed as a matrix according to equation (19):

and 3, step 3: scrambling is performed at the pixel level according to equation (20):

wherein ,s₁ and s₂ Is a positive integer and is a non-zero integer,

and

respectively represent matrices

And

an element of (1); scrambling matrix Γ = [ Γ = [ Γ ] ^r ,Γ ^g ,Γ ^b] and Ψ＝[Ψ^r ,Ψ ^g ,Ψ ^b ]The definition is as follows:

where m and n represent the rows and columns, respectively, the benefit is enhanced diffusion. The scrambled matrix is

And

are respectively

And

row m and column n. Step five: image diffusion: three chaotic sequences U obtained by formula (15) ^r、Ug and U^b Separately opposite scrambling matrices

And

Step 1: matrix pair according to equation (21)

And

and (3) reconstruction:

wherein ,

and

is a matrix

And

the reconstructed sequence.

Step 2: by a chaotic sequence U ^r 、U ^g and U^b Obtaining the diffusion sequence V according to the formulas (22) to (24) ^r 、V ^g and V^b ：

wherein ,X′_l 、Y′ _l 、Z′ _l The I-th elements of data sets X ', Y ' and Z ' are indicated, respectively, and 1nM, 2nM indicate the concentration of DNA strand;

and step 3: using diffusion sequences V ^r 、V ^g and V^b Separate de-diffusion sequence

And

obtaining an encrypted image E = { E = { [ E ] ^r ,E ^g ,E ^b And the calculation method comprises the following steps:

wherein ,

is an exclusive or operation.

Respectively representing the values of the l-th element of the corresponding sequence, obtaining a matrix E by sequence reconstruction ^r ,E ^g ,E ^b Then the matrix E is formed ^r ,E ^g ,E ^b The three channels R, G, B are spliced respectively to obtain the ciphertext image.

The image decryption method corresponding to the invention comprises the following steps:

step 1: using diffusion sequences V ^r 、V ^g and V^b The diffusion effect is removed according to equations (27) and (28):

wherein ,

the components of the three channels of the decrypted image R, G, B are respectively represented, and because the decryption algorithm is the inverse process of the encryption algorithm, the processing is verified through experiments, and the ciphertext image can be decrypted to obtain the plaintext image.

And 2, step: for sequence D ^r 、D ^g and D^b The reconstruction is performed according to equation (29):

wherein ,Λ^R 、Λ ^G 、Λ ^B Respectively represent D ^r 、D ^g and D^b The resulting matrix is reconstructed.

And step 3: at the pixel level, the scrambling effect is eliminated from the last row (column) to the first row (column) according to equation (30):

wherein M '= M, M-1,M-2, …,1,n' = N, N-1,N-2, …,1.

And 4, step 4: to matrix Λ according to equation (31) ^R 、Λ ^G and Λ^B And (3) reconstruction:

and 5: the scrambling effect is canceled at the R, G and B level according to equations (32) - (34), and a decrypted image is obtained.

And 6: will be Λ ^R 、Λ ^G and Λ^B Reconstructing the shape of M multiplied by N, and splicing the shape as the information of R, G, B three channels to obtain a decrypted image.

The following provides a security analysis of the encryption method of the present invention as follows: when in use

The DNA compilation of the chaotic system takes values as shown in Table 1, s =500, s ₁ ＝800、s ₂ ＝800、T ₀ Fig. 11 (a) and 11 (b) are respectively a plaintext image and an encrypted image of Lena when =15 seconds, and fig. 12 (a) and 12 (b) are respectively sector histograms of pixel value distributions of the plaintext image and the ciphertext image, and it can be seen from fig. 12 that the histogram of the plaintext image presents a non-uniform characteristic, and the histogram of the ciphertext image after encryption presents a circular and uniform distribution situation, which illustrates that the encryption method of the present invention can make the pixel value distribution of the ciphertext image have good balance, can completely hide useful information of the plaintext image, and can effectively prevent statistical attack of pixel values of an attacker.

TABLE 1

DNA compiling parameter value of chaotic system

Fig. 13 (a), 13 (c) and 13 (e) show the correlation between adjacent pixels in the horizontal direction, vertical direction and diagonal direction of R, G, B component of Lena plaintext image, respectively, and fig. 13 (b), 13 (d) and 13 (f) show the correlation between adjacent pixels in the horizontal direction, vertical direction and diagonal direction of R, G, B component of ciphertext image, respectively. As can be seen from fig. 13, the pairs of adjacent pixel points of the plaintext image are concentrated on the diagonal lines, and the adjacent pixel points of the ciphertext image are uniformly distributed in the rectangular region, which indicates that the plaintext image has strong correlation in each direction, while the ciphertext image does not have correlation in each direction.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims

1. A color image encryption method for visualized DNA pivot mediated strand displacement reaction is characterized by comprising the following steps:

A chaotic system;

step two, key generation: respectively converting R, G, B channel matrixes of the color plaintext image P into sequences and arranging the sequences in an ascending order to obtain sub-keys;

step three, generating a chaotic sequence: using the sub-key to give

The chaotic system gives an initial value to

Splicing three data groups generated by the chaotic system, and obtaining three chaotic sequences according to the sub-secret key;

And

And

2. The method for encrypting the color image for visualizing the DNA pivot mediated strand displacement reaction according to claim 1, wherein the first step is a step

The ideal chemical reaction network of the chaotic system is as follows:

wherein X, Y and Z are signal reaction participants, k _α α =1, …,7 is the reaction rate, Φ represents a useless material;

the differential equation for an idealized chemical reaction network is:

wherein ,

representing the differential of variables X, Y and Z, respectively.

3. The color image encryption method for visualized DNA pivot mediated strand displacement reaction according to claim 2, wherein the DNA compiling method of the idealized chemical reaction network is as follows:

(I)

and

wherein ,X_i Is a signal DNA strand, i is a positive integer, A _i ,P _i ,N _i And C _i Is an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C _m (ii) a Reaction rate q _i and k_i Satisfy q _i ≤q _m ，k _i ＝q _i C _m ，q _m Represents the maximum reaction rate; design of Signal DNA chain X _i The DNA single strand structure of<x3^ x2 x1^>Helper DNA strand A _i ,P _i ,N _i And C _i The complex chain structures of the DNA are respectively as follows: { x3^ x }: x2 x1^ x }, and]::<s1 s2^ x1^ k2^>、{x1^*}:[s1 s2^]<t6 x2 x1^ k2^>:<s1 s2^ t6 x2>[x1^ k2^]、[x2 x1^]:{k2^*}::<k3^ t1^>and<x3^>::[x2 x1^]{ k3^ t1^ where,<>represents an upper chain structural portion of a DNA chain, [ 2 ]]Means double-stranded structural parts of the DNA strands which have been complementarily paired, for joining the two double-stranded structural domains, and { } means DNA strandsUsed to label the uplink domain, used to label the downlink domain; waste denotes the useless DNA strand, T _i 、Ta _i 、Pa _i Respectively representing products generated by DNA reaction;

(II)

belongs to a catalytic reaction module II, and is compiled into a DNA strand displacement reaction as follows:

wherein ,X_i 、Y _i As a signal DNA strand, B _i ,Am _i ,E _i ,Ea _i ,Eb _i And Fa _i Is an auxiliary DNA strand; reaction rate q _i ,q′ _i and k_i Satisfy q _i ,q′ _i ≤q _m ，k _i ＝q _i (ii) a Designing an input signal Y _i The DNA single strand structure of<y1^ y2 y3^>Helper DNA strand B _i ,E _i ,Ea _i And Fa _i The complex chain structures of the DNA are respectively as follows: { x3^ x }: x2 x1^ y]:[y2 y3^]::<b2 b3^ r1 r2^>、{y3^*}:<r1 r2^ b1 y2>[b2 b3^]:[r1 r2^]::<b1 y2 b2 b3^>、[x2 x1^]:{k2^*}::<k3^ t1^>And<x3^>::[x2 x1^]{ k3^ t1^ and { c1^ c2^ are }:<y1^>[y2 y3^]；Ma _i products formed by DNA reactions, fa _i Indicates the DNA strand to be added before the reaction starts;

(III)

wherein ,Fb_i And Fc _i Is an auxiliary DNA strand; design aidHelper DNA chain Fb _i The double-stranded structure of the DNA is { x3^ x }: x2 x1^ y]:[y2 y3^]；Ad _i Represents a product produced by a DNA reaction;

(IV)

and

wherein ,G_i ,Ac _i And Tp _i Is an auxiliary DNA strand; designed helper DNA strand G _i And Tp _i The DNA double-chain structure is { x3^ x }: x2 x1^ x3^ x]:[x2 x1^]::<c2^ c3^>And [ x3^ x2 x1^ x]{c2^* c3^*}；Da _i Represents a product produced by a DNA reaction;

(V)

wherein ,Ka_i Is an auxiliary DNA strand; designed auxiliary DNA chain Ka _i The DNA double-stranded structure of (a) is { y1^ x }: [ y2 y3^ 3]；

(VI) DNA Strand Displacement reaction

wherein ,Va_i and Wa_i For the auxiliary DNA strand, omega _i Generating a product for the DNA; design of auxiliary DNA strands Va _i DNA of (2)The chain structure is [ h1^ y2]:{y3^*}，qx _i 、qy _i Respectively representing forward reaction rate and backward reaction rate;

in the DNA strand displacement reaction, a signal DNA strand X _i Signal DNA strand Y _i Signal DNA strand Z _i Auxiliary DNA strand C _i 、Fa _i 、Tp _i Fluorophores with different colors and signal DNA chain X _i Signal DNA strand Z _i Auxiliary DNA strand A _i 、C _i 、Fa _i 、B _i 、Fb _i 、G _i 、Ka _i 、Va _i 、Tp _i The quenching group is arranged on the fluorescent probe, the quenching group can absorb fluorescence emitted by the fluorophore, when the fluorophore is far away from the quenching group, the fluorescence is not absorbed, and the luminous intensity can be detected to be used as a marker; when the fluorophore is near the quenching bolus, fluorescence is absorbed and no luminescence intensity is detected.

4. The color image encryption method for visualized DNA pivot mediated strand displacement reaction according to any one of claims 1 to 3, wherein the method for obtaining the sub-key is as follows:

where reshape (,) represents the reconstruction function and the sequence

And

are respectively a sequence P ^1R M × N pixel values;

wherein sort (#) represents an ascending sort function, wherein

And

are respectively a sequence P ^1R 、P ^1G and P^1B A new sequence after the ascending sequence arrangement,

and

are respectively a new sequence h ^r 、h ^g and h^b An index value of (d);

obtaining K sub-keys by using the key:

d _k ＝mod(key,a _k ),k＝1≤k≤K；

5. The color image encryption method for visualized DNA pivot mediated strand displacement reaction according to claim 4, wherein the chaotic sequence is generated by a method comprising the following steps:

step 31: according to the sub-key pair

step 32: splicing the signal DNA chains X, Y and Z to obtain data groups X ', Y ' and Z ', wherein the splicing method comprises the following steps:

wherein ,

index values, | and | representing sequences

wherein ,

6. the method for encrypting the color image for visualizing the DNA pivot mediated strand displacement reaction according to claim 5, wherein the method is characterized in that

And

each set of data of (1) contains 1+r ₂ Data when DNA strand displacement reaction is formalStart sxT ₀ After second, the first s detection data sets are discarded and every T ₀ The concentration of the signal DNA chains X, Y and Z is detected once in seconds, and the total detection time is T = (1 + s + r) ₂ )×T ₀ Wherein the splicing times are

7. The color image encryption method for the visualized DNA pivot-mediated strand displacement reaction according to claim 5 or 6, wherein in the fourth step, the method for respectively scrambling the color components of the sequence corresponding to the R, G, B channel matrix of the color plaintext image P by using three data sets comprises: respectively aligning the sequence P according to the concentration of the signal chain on the R, G, B component level ^1R 、P ^1G and P^1B Scrambling the medium elements:

the R, G, B component obtained after scrambling is the sequence

And

and

are respectively a sequence P ^1R 、P ^1G and P^1B The element (1) in (1); x' _l 、Y _l ′、Z′ _l The I-th elements of data sets X ', Y ' and Z ' are shown, respectively, and 1nM and 2nM are the DNA strand concentrations.

8. The method for encrypting the color image oriented to the visualized DNA pivot-mediated strand displacement reaction according to claim 7, wherein the scrambling matrix is obtained

And

the method comprises the following steps:

will be sequenced

And

are respectively reconstructed into a matrix

And

matrix array

And

scrambling is performed on a pixel level, respectively:

wherein ,s₁ and s₂ Is a positive integer and is a non-zero integer,

and

respectively represent matrices

And

an element of (1);

the scrambled scrambling matrix is

And

are respectively scrambling matrices

And

row m and column n.

9. The color image encryption method for visualized DNA pivot mediated strand displacement reaction according to claim 8, wherein the image diffusion method in the fifth step is:

step 51: to the scrambling matrix

And

and (3) reconstruction:

wherein ,

and

are respectively a matrix

And

a reconstructed sequence;

wherein ,V_l ^r 、V _l ^g 、V _l ^b Respectively represent diffusion sequences V ^r 、V ^g and V^b 1nM, 2nM represent the concentration of DNA strands;

And

wherein ,

in order to perform the exclusive-or operation,

V _l ^r 、V _l ^g 、V _l ^b 、

10. The color image encryption method for visualized DNA pivot mediated strand displacement reaction according to claim 9, wherein the corresponding image decryption method is as follows:

wherein ,

step 2: for sequence D ^r 、D ^g and D^b And (3) carrying out reconstruction:

wherein M '= M, M-1,M-2, …,1,n' = N, N-1,N-2, …,1;

and 4, step 4: matrix Lambda after eliminating scrambling effect ^1R 、Λ ^1G 、Λ ^1B Respectively reconstructing to obtain the sequences Lambda of canceling scrambling effect ^2R 、Λ ^2G 、Λ ^2B Comprises the following steps:

step 6: and reconstructing the sequence without the scrambling effect back to the matrix, and splicing the sequence as the information of R, G, B three channels to obtain a decrypted image.