CN109242751B - Image encryption method based on chaotic tent mapping and DNA decoding - Google Patents

Image encryption method based on chaotic tent mapping and DNA decoding Download PDF

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CN109242751B
CN109242751B CN201810933329.1A CN201810933329A CN109242751B CN 109242751 B CN109242751 B CN 109242751B CN 201810933329 A CN201810933329 A CN 201810933329A CN 109242751 B CN109242751 B CN 109242751B
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chaotic
value
dna
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李建平
顾小丰
胡健
苌浩阳
薛庆弢
陆亚男
周望
孙睿男
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University of Electronic Science and Technology of China
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    • G—PHYSICS
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    • G06T1/0021—Image watermarking
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
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Abstract

The invention discloses an image encryption method based on chaotic tent mapping and DNA decoding, which comprises the following steps: s1, acquiring an ASCII sequence, a tent map and parameters of the common image, and obtaining the dimensionality of the common image; s2, generating a key image and a chaotic image initial condition value by using chaotic tent mapping; s3, obtaining a new chaotic image condition value by using logic mapping; s4, rounding down to obtain a constant value; s5, selecting a DNA coding rule; s6, obtaining a DNA sequence of the common image; s7, obtaining a DNA sequence of the key image; s8, selecting DNA algebra operation; s9, obtaining a DNA sequence of the semi-password image by using DNA algebraic operation; s10, selecting a DNA decoding rule; s11, carrying out DNA decoding according to the DNA decoding rule to obtain a password image; the invention solves the problems of low safety and practicability and direct generation of the secret key in the prior art.

Description

Image encryption method based on chaotic tent mapping and DNA decoding
Technical Field
The invention belongs to the technical field of image encryption, and particularly relates to an image encryption method based on chaotic tent mapping and DNA decoding.
Background
Chaos in combination with DNA coding for image encryption has attracted considerable interest in recent years because it has proven to provide powerful image ciphers. The DNA coding is widely applied to chaotic systems in recent years due to the characteristics of large storage capacity, good parallelism and low power consumption. For example, an encryption algorithm combining DNA sequence manipulation and chaotic mapping has recently been proposed as part of a cross-receive system for medical image security, using 1D logical mapping to select DNA encoding and decoding rules, and PWLCM for pixel scrambling. Chaotic tent mapping is an image cryptosystem developed in recent years. In the proposed cryptosystem, the chaotic sequence is mixed with the ordinary image pixels and directly applied to the ordinary image to generate the cryptoimage.
The prior art has the following problems:
(1) in the system of the chaos sequence and the common image pixel in the prior art, once an attacker knows the initial conditions and the control parameters, the attacker can easily recognize important information in the chaos sequence and the common image pixel is low in safety and practicability.
(2) Furthermore, some of the drawbacks found in most low-dimensional chaos based schemes are the direct generation of keys.
Disclosure of Invention
Aiming at the defects in the prior art, the chaos tent mapping and DNA decoding-based image encryption method provided by the invention has high safety and practicability, can randomly generate the key image, can resist statistical attack and has strong anti-noise attack capability, and solves the problems of low safety and practicability and direct generation of the key 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 chaotic tent mapping and DNA decoding comprises the following steps:
s1: acquiring a 16-bit ASCII sequence, a tent map and parameters of the common image, and obtaining the dimensionality of the common image;
s2: generating a key image and a chaotic image initial condition value by using chaotic tent mapping according to the dimensionality of a common image, an ASCII sequence and a tent map;
s3: obtaining a new chaotic image condition value by using logic mapping according to the chaotic image initial condition value and the tent map parameter;
s4: obtaining a constant value by rounding down according to the current chaotic image condition value;
s5: selecting a DNA coding rule corresponding to the current constant value and coding all pixels on all lines of the image;
s6: obtaining a DNA sequence of a common image;
s7: repeating the steps S3 to S5 according to the key image to obtain a DNA sequence of the key image;
s8: repeating the steps S3 to S4, and selecting a DNA algebraic operation corresponding to the current constant value;
s9: obtaining a DNA sequence of the semi-password image by using DNA algebraic operation according to the DNA sequence of the common image and the DNA sequence of the key image;
s10: repeating steps S3 to S5, selecting a DNA decoding rule corresponding to the current constant value;
s11: and performing DNA decoding on each line of the DNA sequence of the password image according to the DNA decoding rule to obtain the password image, thereby realizing image encryption.
Further, in step S2, the method for generating the key image and the chaotic image initial condition value using the chaotic tent map includes the following steps:
s2-1: converting the first eight characters of the ASCII sequence into a 16-system form, and converting the last eight characters into a 64-system form;
s2-2: processing the value in the 16-system form to obtain a first chaotic image value, wherein the formula is as follows:
Figure BDA0001767181720000031
in the formula, xaIs a first chaotic image value; h isqA value in 16-ary form; q is an indicated amount;
s2-3: processing the value in the 64-system form to obtain a second chaotic image value, wherein the formula is as follows:
Figure BDA0001767181720000032
in the formula, xbIs a second chaotic image value; bpA value in 16-ary form; p is an indicated amount;
s2-4: obtaining an initial condition value of the chaotic image according to the first chaotic image value and the second chaotic image value, wherein the formula is as follows:
x0＝(xa+xb)mod 1
in the formula, x0The initial condition value of the chaotic image is obtained; x is the number ofaIs a first chaotic image value; x is the number ofbIs a second chaotic image value; mod is a modulo operation;
s2-5: according to the initial condition value of the chaotic image and the tent map, using the chaotic tent map to carry out iteration to generate a chaotic sequence X ═ { X ═ X1,x2,...,xMNThe chaotic tent mapping formula is:
Figure BDA0001767181720000033
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe image is a current chaotic image condition value, r is a tent map, i is an indicating quantity, i ∈ {1, 2.., MN }, and M and N are dimensions of a common image;
s2-6: generating a chaotic key image according to the chaotic sequence, wherein a calculation formula is as follows:
Figure BDA0001767181720000034
in the formula, kiIs a key image factor, and ki∈ K, K being a key image, xiIs the current chaotic image condition value, and xi∈ X, X is the chaotic sequence and mod is the modulo operation.
Further, in step S3, a new chaotic image condition value is obtained by using logical mapping, and the calculation formula is:
xi+1＝uxi(1-xi)
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiIs the current chaotic image condition value, u is a tent map parameter, i is an indicating quantity, i ∈ {1, 2.
Further, in step S4, a constant value is obtained by rounding down the current chaotic image condition value, and the calculation formula is:
Z＝floor(xM×7)+1
in the formula, Z 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 S8, the calculation formula of the constant value is:
Y＝floor(xM×3)+1
in the formula, Y is a current constant value corresponding to the selected DNA algebraic operation; floor (·) is a downward rounding operation; x is the number ofMIs the current chaotic image condition value.
Further, in step S9, the calculation formula of the DNA sequence of the half-cipher image is:
Figure BDA0001767181720000041
in the formula, I' is a DNA sequence of a semi-password image; lδA DNA sequence that is a generic image; kδA DNA sequence that is a key image;
Figure BDA0001767181720000042
is an algebraic operation of the DNA selected arbitrarily.
The beneficial effect of this scheme does:
(1) pixels in the password image are uniformly distributed, and an attacker can hardly recognize any meaningful information in the password image because the password image cannot recognize the mode of the password image, so that the safety and the practicability are improved;
(2) the key image is randomly generated, so that the direct generation of the key image is avoided, and the safety is further improved;
(3) the password image of the scheme destroys the correlation between adjacent pixels, has enough oppressiveness and enough robustness to statistical attack, and can resist the statistical attack;
(4) the scheme can recover the image after the noise attack and has the capability of resisting the noise attack.
Drawings
FIG. 1 is a flow chart of an image encryption method based on chaotic tent mapping and DNA decoding;
FIG. 2 is a flow chart of generating a key image and chaotic image initial condition values using chaotic tent mapping;
FIG. 3 is a graph of the results of histogram analysis;
FIG. 4 is a comparison graph of pixel correlation of pepper test images;
FIG. 5 is a comparison graph of the correlation of pixels in a Lena test image;
FIG. 6 is a diagram of the results of decrypting an image after introducing Gaussian noise;
fig. 7 is a diagram of the results of decrypting an image after introduction of salt and pepper noise.
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 chaotic tent mapping and DNA decoding comprises the following steps:
s1: acquiring a 16-bit ASCII sequence, a tent map and parameters of the common image, and obtaining the dimensionality of the common image;
s2: generating a key image and an initial condition value of the chaotic image by using chaotic tent mapping according to the dimensionality of a common image, an ASCII sequence and a tent map, and comprising the following steps of:
s2-1: converting the first eight characters of the ASCII sequence into a 16-system form, and converting the last eight characters into a 64-system form;
s2-2: processing the value in the 16-system form to obtain a first chaotic image value, wherein the formula is as follows:
Figure BDA0001767181720000061
in the formula, xaIs a first chaotic image value; h isqA value in 16-ary form; q is an indicated amount;
s2-3: processing the value in the 64-system form to obtain a second chaotic image value, wherein the formula is as follows:
Figure BDA0001767181720000062
in the formula, xbIs a second chaotic image value; bpA value in 16-ary form; p is an indicated amount;
s2-4: obtaining an initial condition value of the chaotic image according to the first chaotic image value and the second chaotic image value, wherein the formula is as follows:
x0＝(xa+xb)mod 1
in the formula, x0The initial condition value of the chaotic image is obtained; x is the number ofaIs a first chaotic image value; x is the number ofbIs a second chaotic image value; mod is a modulo operation;
s2-5: according to the initial condition value of the chaotic image and the tent map, performing iteration by using chaotic tent mapping to generate a chaotic sequence, wherein the chaotic tent mapping formula is as follows:
Figure BDA0001767181720000063
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe image is a current chaotic image condition value, r is a tent map, i is an indicating quantity, i ∈ {1, 2.., MN }, and M and N are dimensions of a common image;
s2-6: generating a chaotic key image according to the chaotic sequence, wherein a calculation formula is as follows:
Figure BDA0001767181720000064
in the formula, kiIs a key image factor, and ki∈ K, K being a key image, xiIs the current chaotic image condition value, and xi∈ X, X is the chaos sequence, mod is the modulus operation;
s3: obtaining a new chaotic image condition value by using logic mapping according to the chaotic image initial condition value and the tent map parameter, wherein the calculation formula is as follows:
xi+1＝uxi(1-xi)
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe image is a current chaotic image condition value, u is a tent map parameter, i is an indication quantity, i ∈ {1, 2., M };
s4: obtaining a constant value by rounding down according to the current chaotic image condition value, wherein the current chaotic image condition value comprises a chaotic image condition value corresponding to a common image and a chaotic image condition value corresponding to a key image, and the calculation formula is as follows:
Z＝floor(xM×7)+1
in the formula, Z is a current constant value; floor (·) is a downward rounding operation; x is the number ofMThe current chaotic image condition value;
s5: selecting a DNA coding rule corresponding to the current constant value and coding all pixels on all lines of the image;
s6: obtaining a DNA sequence of a common image;
s7: repeating the steps S3 to S5 according to the key image to obtain a DNA sequence of the key image;
s8: repeating steps S3 to S4, and selecting a DNA algebra operation corresponding to the current constant value, wherein the calculation formula of the constant value is as follows:
Y＝floor(xM×3)+1
wherein Y is the current norm corresponding to the selected DNA algebra operationA numerical value; floor (·) is a downward rounding operation; x is the number ofMThe current chaotic image condition value;
s9: obtaining the DNA sequence of the semi-password image by using DNA algebraic operation according to the DNA sequence of the common image and the DNA sequence of the key image, wherein the calculation formula is as follows:
Figure BDA0001767181720000071
in the formula, I' is a DNA sequence of a semi-password image; lδA DNA sequence that is a generic image; kδA DNA sequence that is a key image;
Figure BDA0001767181720000072
algebraically operating for arbitrarily selected DNA;
s10: repeating steps S3 to S5, selecting a DNA decoding rule corresponding to the current constant value;
s11: and performing DNA decoding on each line of the DNA sequence of the password image according to the DNA decoding rule to obtain the password image, thereby realizing image encryption.
And (3) analyzing experimental data:
a robust image encryption scheme will produce a cryptographic image with a uniform histogram distribution. The results of the histogram analysis are shown in fig. 3 (a) and (b), and it is apparent from the figure that the proposed encryption scheme uniformly distributes pixels in the password image. Since the pattern is not seen in the histogram of the password image, it is difficult for an attacker to recognize any meaningful information therein. It can be concluded that: the scheme provides sufficient resistance to statistical attacks.
Two thousand pairs of adjacent pixels are randomly selected from an original image and an encrypted image, and the horizontal, vertical and diagonal correlation coefficients of the pixels are calculated, fig. 4 and 5 show the correlation graphs of two test images, namely pepper (512 × 512) and Lena (256 × 256), and as is obvious from the correlation coefficient table of the common image and the password image in table 1, the scheme sufficiently destroys the correlation between the adjacent pixels, so that the scheme has enough oppressibility to statistical attacks, has enough robustness and can resist the statistical attacks.
TABLE 1
Figure BDA0001767181720000081
The cryptographic image is subjected to various noises during transmission, which may cause difficulties in decryption and restoration of the image. Two different levels of noise (gaussian noise, salt and pepper noise) are introduced into the cryptographic image before decryption. Fig. 6, 7 and table 2 noise impact comparison tables show the results of decrypting images after different degrees of noise introduction. As can be seen from the figure, the proposed scheme is still able to recover the image after a noise attack, and thus has the ability to resist noise attacks.
TABLE 2
Figure BDA0001767181720000091
The image encryption method based on chaotic tent mapping and DNA decoding, which is provided by the invention, has high safety and practicability, random generation of key images, and strong capability of resisting statistical attack and anti-noise attack, solves the problems of low safety and practicability and direct generation of keys in the prior art.

Claims (5)

1. An image encryption method based on chaotic tent mapping and DNA decoding is characterized by comprising the following steps:
s1: acquiring a 16-bit ASCII sequence, a tent map and parameters of the common image, and obtaining the dimensionality of the common image;
s2: generating a key image and a chaotic image initial condition value by using chaotic tent mapping according to the dimensionality of a common image, an ASCII sequence and a tent map;
in step S2, the method for generating the key image and the chaotic image initial condition value using the chaotic tent map includes the following steps:
s2-1: converting the first eight characters of the ASCII sequence into a 16-system form, and converting the last eight characters into a 64-system form;
s2-2: processing the value in the 16-system form to obtain a first chaotic image value, wherein the formula is as follows:
Figure FDA0002386448040000011
in the formula, xaIs a first chaotic image value; h isqA value in 16-ary form; q is an indicated amount;
s2-3: processing the value in the 64-system form to obtain a second chaotic image value, wherein the formula is as follows:
Figure FDA0002386448040000012
in the formula, xbIs a second chaotic image value; bpA value in 16-ary form; p is an indicated amount;
s2-4: obtaining an initial condition value of the chaotic image according to the first chaotic image value and the second chaotic image value, wherein the formula is as follows:
x0＝(xa+xb)mod1
in the formula, x0The initial condition value of the chaotic image is obtained; x is the number ofaIs a first chaotic image value; x is the number ofbIs a second chaotic image value; mod is a modulo operation;
s2-5: according to the initial condition value of the chaotic image and the tent map, performing iteration by using chaotic tent mapping to generate a chaotic sequence, wherein the chaotic tent mapping formula is as follows:
Figure FDA0002386448040000021
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiThe image is a current chaotic image condition value, r is a tent map, i is an indicating quantity, i ∈ {1, 2.., MN }, and M and N are dimensions of a common image;
s2-6: generating a chaotic key image according to the chaotic sequence, wherein a calculation formula is as follows:
Figure FDA0002386448040000022
in the formula, kiIs a key image factor, and ki∈ K, K being a key image, xiIs the current chaotic image condition value, and xi∈ X, X is the chaos sequence, mod is the modulus operation;
s3: obtaining a new chaotic image condition value by using logic mapping according to the chaotic image initial condition value and the tent map parameter;
s4: obtaining a constant value by rounding down according to the current chaotic image condition value;
s5: selecting a DNA coding rule corresponding to the current constant value and coding all pixels on all lines of the image;
s6: obtaining a DNA sequence of a common image;
s7: repeating the steps S3 to S5 according to the key image to obtain a DNA sequence of the key image;
s8: repeating the steps S3 to S4, and selecting a DNA algebraic operation corresponding to the current constant value;
s9: obtaining a DNA sequence of the semi-password image by using DNA algebraic operation according to the DNA sequence of the common image and the DNA sequence of the key image;
s10: repeating steps S3 to S5, selecting a DNA decoding rule corresponding to the current constant value;
s11: and performing DNA decoding on each line of the DNA sequence of the password image according to the DNA decoding rule to obtain the password image, thereby realizing image encryption.
2. The image encryption method based on chaotic tent mapping and DNA decoding of claim 1, wherein in step S3, a new chaotic image condition value is obtained using logical mapping, and the calculation formula is:
xi+1＝uxi(1-xi)
in the formula, xi+1The next generation chaotic image condition value; x is the number ofiIs the current chaotic image condition value, u is a tent map parameter, i is an indicating quantity, i ∈ {1, 2.
3. The image encryption method based on chaotic tent mapping and DNA decoding of claim 1, wherein in step S4, a constant value is obtained by rounding down according to the current chaotic image condition value, and the calculation formula is:
Z＝floor(xM×7)+1
in the formula, Z is a current constant value; floor (·) is a downward rounding operation; x is the number ofMIs the current chaotic image condition value.
4. The image encryption method based on chaotic tent mapping and DNA decoding as claimed in claim 1, wherein in step S8, the constant value is calculated as:
Y＝floor(xM×3)+1
in the formula, Y is a current constant value corresponding to the selected DNA algebraic operation; floor (·) is a downward rounding operation; x is the number ofMIs the current chaotic image condition value.
5. The image encryption method based on chaotic tent mapping and DNA decoding of claim 1, wherein in step S9, the calculation formula of the DNA sequence of the semi-cipher image is:
Figure FDA0002386448040000031
in the formula, I' is a DNA sequence of a semi-password image; lδA DNA sequence that is a generic image; kδA DNA sequence that is a key image;
Figure FDA0002386448040000032
is an algebraic operation of the DNA selected arbitrarily.
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