CN109214972B - Image encryption method based on chaos pseudorandom DNA enhancement - Google Patents
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Abstract
The invention discloses an image encryption method based on chaos pseudorandom DNA enhancement, which comprises the following steps: s1, inputting a common image and a permutator; s2, obtaining a random permutation sequence; s3, carrying out random replacement to obtain a random replacement image matrix; s4, generating a key matrix; s5, obtaining a new chaotic image condition value by using direct logic mapping; s6, rounding down to obtain a constant value; s7, selecting a DNA coding rule; s8, obtaining a DNA sequence of the replacement image matrix; s9, obtaining a DNA sequence of the key matrix; s10, selecting a DNA linear operation corresponding to the current constant value; s11, obtaining a DNA sequence of the password image; s12, selecting a DNA encryption rule corresponding to the current constant value; and S13, obtaining the password image and realizing image encryption. The invention solves the problems of low efficiency, insecurity and unavailability in the prior art.
Description
Technical Field
The invention belongs to the technical field of image encryption, and particularly relates to an image encryption method based on chaos pseudorandom DNA enhancement.
Background
With the rapid development of computer technology and network technology, people are urgently required to research and develop more safe, efficient and reliable methods for protecting the data security. The chaotic system has many good properties such as sensitivity to initial conditions and control parameters, consistency of periodic point sets and topological transitivity. These properties and the confusion in cryptography are closely related to diffusion characteristics. Since the 80 s of the last century, the research of chaotic cryptography has attracted increasing attention, and a large number of chaotic-based encryption algorithms have been proposed, and have made many hopeful developments. However, recent studies have shown that chaotic cryptographic schemes, previously considered to be highly practical and safe, have proven to be inefficient, unsafe, and unusable. Through deep analysis and research, the chaos password scheme with strong practicability and high safety is designed to become a prominent problem to be solved urgently.
Disclosure of Invention
Aiming at the defects in the prior art, the image encryption method based on chaos pseudorandom DNA enhancement, which is provided by the invention and has the advantages of combination of chaos and DNA coding, high efficiency, high safety and strong practicability, improves the encryption effect and solves the problems of low efficiency, unsafety and unavailability in the prior art.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
an image encryption method based on chaos pseudorandom DNA enhancement comprises the following steps:
s1: acquiring a common image and a displacer, and obtaining the dimensionality of the common image;
s2: obtaining a random permutation sequence by using a permutation sub and a random permutation function according to the dimensionality of the common image;
s3: carrying out random replacement on pixels in the image according to the random replacement sequence to obtain a random replacement image matrix;
s4: generating an initial condition value and a control variable of the chaotic image by using a hash function according to the random permutation image matrix, and generating a key matrix by using pseudo-random enhanced logic mapping;
s5: obtaining a new chaotic image condition value by using direct logic mapping according to the chaotic image initial condition value and the control variable;
s6: obtaining a constant value by rounding down according to the current chaotic image condition value;
s7: selecting a DNA coding rule corresponding to the current constant value and coding all pixels on all lines of the image;
s8: obtaining a DNA sequence of a displacement image matrix;
s9: repeating the steps S5 to S7 according to the key matrix to obtain a DNA sequence of the key matrix;
s10: repeating the step S5, and performing DNA linear operation on the chaotic image condition value to obtain linear parameters;
s11: according to the DNA sequence of the displaced image matrix and the DNA sequence of the key matrix, using the DNA linear operation corresponding to the linear parameters to obtain the DNA sequence of the password image;
s12: repeating steps S5 to S6, selecting a DNA encryption rule corresponding to the current constant value;
s13: and encrypting each line of the DNA sequence of the password image according to the DNA encryption rule to obtain the password image, thereby realizing image encryption.
Further, in step S2, the formula of the random permutation order is:
O=randperm(M×N)
wherein O is a random permutation order; randderm (·) is a random permutation order function; m and N are the dimensions of the common image.
Further, in step S3, the formula of the permuted image matrix is:
I'=reshape(I(O),M,N)
in the formula, I' is a permutation image matrix; i is an input common image; reshape (·) is a permuted image matrix function; o is a random permutation order; m and N are the dimensions of the common image.
Further, in step S4, the method for generating the key matrix includes the following steps:
s4-1: executing a hash function SHA-256 on the replacement image matrix to obtain a 64-bit 16-system data string;
s4-2: converting the 16-system data string into a 256-bit data stream;
s4-3: respectively putting the data streams into 4 64-bit different blocks, and processing each block to obtain a processed block value, wherein the formula is as follows:
in the formula, #1、ψ2、ψ3、ψ4Is the processed block value; biIs a corresponding data stream; j is an indication quantity, j belongs to {1, 2., 256 };
s4-4: obtaining an initial condition value and a control variable of the chaotic image according to the processed block value;
the calculation formula of the initial condition value of the chaotic image is as follows:
xo=(ψ1+ψ2)mod1
in the formula, xoThe initial condition value of the chaotic image is obtained; psi1、ψ2Is the processed block value; mod is a modulo operation;
the calculation formula of the control variable is as follows:
p=3.999+(((ψ3+ψ4)mod1)×0.001)
wherein p is a control variable; psi3、ψ4Is the processed block value; mod is a modulo operation;
s4-5: according to the initial condition value and the control variable of the chaotic image, iteration is carried out by using pseudo-random enhanced logic mapping to obtain a chaotic sequence;
the formula for the calculation of the pseudo-randomly enhanced logical mapping is:
xi+1=((pxi(1-xi))100000)mod1
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe current chaotic image condition value; p is a control variable; mod is a modulo operation; i is an indication quantity, i belongs to {1, 2., MN };
s4-6: converting the chaotic sequence into a digital sequence, and obtaining a key matrix according to the digital sequence;
in the formula, kiIs a digital sequence of pixels, and kiE.g. K, wherein K is a key matrix; siIs a corresponding chaotic sequence; i is the indicated quantity, i ∈ {1, 2., MN }.
Further, in step S5, a new chaotic image condition value is obtained by using direct logic mapping, and the calculation formula is:
xi+1=pxi(1-xi)
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe current chaotic image condition value; p is a control variable; i is an indicator quantity, i ∈ {1,2,. multidot.m }.
Further, in step S6, the calculation formula of the constant value is:
R=floor(xM×8)+1
in the formula, R is a current constant value; floor (·) is a downward rounding operation; x is the number ofMIs the current chaotic image condition value.
Further, in step S10, performing DNA linear operation on the chaotic image condition value to obtain a linear parameter, wherein the linear parameter is calculated by the following formula:
Y=floor(xM×3)+1
in the formula, Y is a linear parameter; floor (·) is a downward rounding operation; x is the number ofMIs the current chaotic image condition value.
Further, in step S11, the calculation formula of the DNA sequence of the password image is:
in the formula, QδA DNA sequence that is a cryptographic image; l'δIs a DNA sequence of a displaced image matrix; kδDNA sequences that are key matrices;linear manipulation for arbitrarily selected DNA.
The beneficial effect of this scheme does:
(1) the scheme has the advantages of simple structure, discreteness, high output processing, less arithmetic operation and relatively easy low-dimensional system, saves the computing power, time and resources during use, has better attack recovery rate and improves the practicability;
(2) the DNA coding and decoding rules and the DNA algebra operation are randomly selected by direct logic mapping and operated on a row basis, so that the safety is improved, the execution time is greatly reduced, and the encryption efficiency is improved.
Drawings
FIG. 1 is a flow chart of an image encryption method based on chaos pseudorandom DNA enhancement;
FIG. 2 is a flow diagram of a method for generating a key matrix using pseudo-randomly enhanced logical mapping;
FIG. 3 is a prior art encryption method histogram;
FIG. 4 is a histogram of the encryption method according to the present embodiment;
FIG. 5 is a comparison graph of pixel correlation between an encrypted image and a generic image;
fig. 6 is a graph comparing the noise immunity of the present embodiment and the prior art.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
In the embodiment of the invention, an image encryption method based on chaos pseudorandom DNA enhancement, as shown in FIG. 1, comprises the following steps:
s1: acquiring a common image and a displacer, and obtaining the dimensionality of the common image;
s2: according to the dimensionality of the common image, a random permutation sequence is obtained by using a permutator and a random permutation function, and the formula is as follows:
O=randperm(M×N)
wherein O is a random permutation order; randderm (·) is a random permutation order function; m and N are the dimensionalities of the common image;
s3: carrying out random replacement on pixels in the image according to a random replacement sequence to obtain a random replacement image matrix, wherein the formula is as follows:
I'=reshape(I(O),M,N)
in the formula, I' is a permutation image matrix; i is an input common image; reshape (·) is a permuted image matrix function; o is a random permutation order; m and N are the dimensionalities of the common image;
s4: according to the random permutation image matrix, a hash function is used for generating an initial condition value and a control variable of the chaotic image, and a pseudo-random enhanced logic mapping is used for generating a key matrix, as shown in fig. 2, the method comprises the following steps:
s4-1: executing a hash function SHA-256 on the replacement image matrix to obtain a 64-bit 16-system data string; h ═ H1,h2,...,h64
S4-2: converting the 16-system data string into a 256-bit data stream; psi ═ b1,b2,...,b256
S4-3: respectively putting the data streams into 4 64-bit different blocks, and processing each block to obtain a processed block value, wherein the formula is as follows:
in the formula, #1、ψ2、ψ3、ψ4Is the processed block value; biIs a corresponding data stream; j is an indication quantity, j belongs to {1, 2., 256 };
s4-4: obtaining an initial condition value and a control variable of the chaotic image according to the processed block value;
the calculation formula of the initial condition value of the chaotic image is as follows:
xo=(ψ1+ψ2)mod1
in the formula, xoAs a chaotic imageAn initial condition value of; psi1、ψ2Is the processed block value; mod is a modulo operation;
the calculation formula of the control variable is as follows:
p=3.999+(((ψ3+ψ4)mod1)×0.001)
wherein p is a control variable; psi3、ψ4Is the processed block value; mod is a modulo operation;
s4-5: according to the initial condition value and the control variable of the chaotic image, iteration is carried out by using the logic mapping enhanced by the pseudo-random to obtain a chaotic sequence S ═ S1,s2,...,sMN};
The formula for the calculation of the pseudo-randomly enhanced logical mapping is:
xi+1=((pxi(1-xi))100000)mod1
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe current chaotic image condition value; p is a control variable; mod is a modulo operation; i is an indication quantity, i belongs to {1, 2., MN };
s4-6: converting the chaotic sequence into a digital sequence, and obtaining a key matrix according to the digital sequence;
in the formula, kiIs a digital sequence of pixels, and kiE.g. K, wherein K is a key matrix; siIs a corresponding chaotic sequence; i is an indication quantity, i belongs to {1, 2., MN };
s5: according to the use of the initial condition value and the control variable of the chaotic image, a new chaotic image condition value is obtained by direct logic mapping, and the calculation formula is as follows:
xi+1=pxi(1-xi)
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe current chaotic image condition value; p is a control variable; i is an indication quantity, i belongs to {1, 2.., M };
s6: obtaining a constant value by rounding down according to the current chaotic image condition value;
the calculation formula for the constant values is:
R=floor(xM×8)+1
in the formula, R is a current constant value; floor (·) is a downward rounding operation; x is the number ofMThe current chaotic image condition value;
s7: selecting a DNA coding rule corresponding to the current constant value and coding all pixels on all lines of the image;
s8: obtaining a DNA sequence of a displacement image matrix;
s9: repeating the steps S5 to S7 according to the key matrix to obtain a DNA sequence of the key matrix;
s10: repeating the step S5 to obtain the chaotic image condition value xMPerforming DNA linear operation to obtain a linear parameter Y, wherein the calculation formula of the linear parameter Y is as follows:
Y=floor(xM×3)+1
in the formula, floor (·) is a downward rounding operation; x is the number ofMThe current chaotic image condition value;
s11: according to the DNA sequence of the displaced image matrix and the DNA sequence of the key matrix, the DNA sequence of the password image is obtained by using the DNA linear operation corresponding to the linear parameter Y, and the calculation formula is as follows:
in the formula, QδA DNA sequence that is a cryptographic image; l'δIs a DNA sequence of a displaced image matrix; kδDNA sequences that are key matrices;linear manipulation for arbitrarily selected DNA;
s12: repeating steps S5 to S6, selecting a DNA encryption rule corresponding to the current constant value;
s13: and encrypting each line of the DNA sequence of the password image according to the DNA encryption rule to obtain the password image, thereby realizing image encryption.
And (3) analyzing experimental data:
the histogram obtained by the traditional encryption method is shown in fig. 3, which highly reflects the size of information contained in each pixel point, and the histogram obtained by the encryption method of the scheme is shown in fig. 4, and the chaos degree (i.e. the degree of containing information) of each part is the same, so that an attacker is more difficult to obtain information in an image, i.e. the histogram has strong impact resistance and high safety.
Comparing the pixel correlation between the encrypted image and the normal image in the present scheme, as shown in fig. 5, the correlation is almost disappeared in the encrypted image, which shows that our scheme is also very resistant to data attack.
As shown in fig. 6, comparing the noise immunity of the present scheme with that of the prior art, it can be seen that the encryption method not only has a great improvement in encryption effect and stability, but also has better performance in noise immunity, compared with the prior art.
The image encryption method based on chaos pseudorandom DNA enhancement, which is provided by the invention and combines chaos with DNA coding, has high efficiency, high safety and strong practicability, improves the encryption effect, and solves the problems of low efficiency, insecurity and unavailability in the prior art.
Claims (7)
1. An image encryption method based on chaos pseudorandom DNA enhancement is characterized by comprising the following steps:
s1: acquiring a common image and a displacer, and obtaining the dimensionality of the common image;
s2: obtaining a random permutation sequence by using a permutation sub and a random permutation function according to the dimensionality of the common image;
s3: carrying out random replacement on pixels in the image according to the random replacement sequence to obtain a random replacement image matrix;
s4: generating an initial condition value and a control variable of the chaotic image by using a hash function according to the random permutation image matrix, and generating a key matrix by using pseudo-random enhanced logic mapping;
in step S4, the method for generating a key matrix includes the following steps:
s4-1: executing a hash function SHA-256 on the replacement image matrix to obtain a 64-bit 16-system data string;
s4-2: converting the 16-system data string into a 256-bit data stream;
s4-3: respectively putting the data streams into 4 64-bit different blocks, and processing each block to obtain a processed block value, wherein the formula is as follows:
in the formula, #1、ψ2、ψ3、ψ4Is the processed block value; biIs a corresponding data stream; j is an indication quantity, j belongs to {1, 2., 256 };
s4-4: obtaining an initial condition value and a control variable of the chaotic image according to the processed block value;
the calculation formula of the initial condition value of the chaotic image is as follows:
xo=(ψ1+ψ2)mod 1
in the formula, xoThe initial condition value of the chaotic image is obtained; psi1、ψ2Is the processed block value; mod is a modulo operation;
the calculation formula of the control variable is as follows:
p=3.999+(((ψ3+ψ4)mod1)×0.001)
wherein p is a control variable; psi3、ψ4Is the processed block value; mod is a modulo operation;
s4-5: according to the initial condition value and the control variable of the chaotic image, iteration is carried out by using pseudo-random enhanced logic mapping to obtain a chaotic sequence;
the formula for the calculation of the pseudo-randomly enhanced logical mapping is:
xi+1=((pxi(1-xi))100000)mod1
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiIs as followsA pre-chaotic image condition value; p is a control variable; mod is a modulo operation; i is an indication quantity, i belongs to {1, 2., MN };
s4-6: converting the chaotic sequence into a digital sequence, and obtaining a key matrix according to the digital sequence;
in the formula, kiIs a digital sequence of pixels, and kiE.g. K, wherein K is a key matrix; siIs a corresponding chaotic sequence; i is an indication quantity, i belongs to {1, 2., MN }; s5: obtaining a new chaotic image condition value by using direct logic mapping according to the chaotic image initial condition value and the control variable;
s6: obtaining a constant value by rounding down according to the current chaotic image condition value;
s7: selecting a DNA coding rule corresponding to the current constant value and coding all pixels on all lines of the image;
s8: obtaining a DNA sequence of a displacement image matrix;
s9: repeating the steps S5 to S7 according to the key matrix to obtain a DNA sequence of the key matrix;
s10: repeating the step S5, and performing DNA linear operation on the chaotic image condition value to obtain linear parameters;
s11: according to the DNA sequence of the displaced image matrix and the DNA sequence of the key matrix, using the DNA linear operation corresponding to the linear parameters to obtain the DNA sequence of the password image;
s12: repeating steps S5 to S6, selecting a DNA encryption rule corresponding to the current constant value;
s13: and encrypting each line of the DNA sequence of the password image according to the DNA encryption rule to obtain the password image, thereby realizing image encryption.
2. The image encryption method based on chaos pseudo-random DNA enhancement as claimed in claim 1, wherein in step S2, the formula of random permutation sequence is:
O=randperm(M×N)
wherein O is a random permutation order; randderm (·) is a random permutation order function; m and N are the dimensions of the common image.
3. The image encryption method based on chaos pseudo-random DNA enhancement as claimed in claim 1, wherein in step S3, the formula of the permutation image matrix is:
I'=reshape(I(O),M,N)
in the formula, I' is a permutation image matrix; i is an input common image; reshape (·) is a permuted image matrix function; o is a random permutation order; m and N are the dimensions of the common image.
4. The image encryption method based on chaos pseudo-random DNA enhancement according to claim 1, wherein in step S5, a new chaos image condition value is obtained by using direct logic mapping, and the calculation formula is:
xi+1=pxi(1-xi)
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe current chaotic image condition value; p is a control variable; i is an indicator quantity, i ∈ {1,2,. multidot.m }.
5. The image encryption method based on chaos pseudo-random DNA enhancement according to claim 1, wherein in step S6, the calculation formula of the constant value is:
R=floor(xM×8)+1
in the formula, R is a current constant value; floor (·) is a downward rounding operation; x is the number ofMIs the current chaotic image condition value.
6. The image encryption method based on chaos pseudo-random DNA enhancement according to claim 1, wherein in step S10, DNA linear operation is performed on the chaos image condition value, and the calculation formula of the linear parameter is:
Y=floor(xM×3)+1
in which Y is a linear parameter, flor (-) is a round-down operation; x is the number ofMIs the current chaotic image condition value.
7. The image encryption method based on chaos pseudo-random DNA enhancement as claimed in claim 1, wherein in step S11, the calculation formula of the DNA sequence of the password image is:
Qδ=l'δ⊕Kδ
in the formula, QδA DNA sequence that is a cryptographic image; l'δIs a DNA sequence of a displaced image matrix; kδDNA sequence of key matrix ⊕ is the linear operation of arbitrarily chosen DNA.
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