CN113313621B

CN113313621B - Image encryption watermark embedding method based on hybrid chaotic system and closed-loop diffusion

Info

Publication number: CN113313621B
Application number: CN202110406825.3A
Authority: CN
Inventors: 刘吉伟; 吴笛; 尹湘舟; 张沅
Original assignee: Great Wall Information Co Ltd
Current assignee: Great Wall Information Co Ltd
Priority date: 2021-04-15
Filing date: 2021-04-15
Publication date: 2022-06-28
Anticipated expiration: 2041-04-15
Also published as: CN113313621A

Abstract

The invention discloses a digital image encryption watermark embedding method, an extraction method and a device based on a hybrid chaotic system and closed-loop diffusion, wherein the embedded watermark cannot be perceived by naked eyes by the watermark embedding method based on a chaotic sequence and the closed-loop diffusion, a key is constructed and a scrambled image is generated by using a high-order image and a low-order image respectively in the embedding process, the scrambled image is subjected to closed-loop diffusion by using the key formed by the image, the digital image encryption watermark can be used for digital images with any content, and the image quality and the extracted watermark quality are hardly influenced; the watermark is embedded in the low three-bit information of the original image, the density of the watermark information is low, and an invisible watermark is formed; the method is extremely sensitive to the secret key and the image data embedded with the watermark, and slight modification can cause the extracted watermark to lose identifiability, so that the method has sensitivity; by adopting the novel conservative chaotic system, various cracking methods including reconstruction attack can be resisted.

Description

Image encryption watermark embedding method based on hybrid chaotic system and closed loop diffusion

Technical Field

The invention belongs to the technical field of digital watermarks, and particularly relates to a digital image encrypted watermark embedding method, an extraction method and an extraction device based on a hybrid chaotic system and closed-loop diffusion.

Background

In recent years, with the rapid development of computer science and network technology, more and more data information, especially digital images, circulating at high speed involve intellectual property and data protection problems. The protection of intellectual property (especially digital work content) by the nation and the people is increasingly important, and simultaneously, the protection of the intellectual property and the protection of the digital work content put higher and higher requirements on related technologies (such as copyright protection and data tampering detection) on the intellectual property and the data tampering detection. As an important means for copyright labeling and data protection, scholars at home and abroad make a great deal of intensive research on embedding and extracting digital image watermarks.

Digital image watermarks can be divided into two types according to robustness, one is robust watermarks which still can maintain partial integrity and can be accurately identified after undergoing various unintentional or intentional signal processing processes; possible signal processing procedures include channel noise, filtering, digital/analog and analog/digital conversion, resampling, shearing, displacement, scale change, lossy compression coding and the like; this type of digital image watermarking is commonly used for copyright identification; the other is fragile watermark, which has extremely high sensitivity to external modification, and after the marked works are distributed, transmitted and used, the data can be accurately judged whether to be tampered by the digital watermark, so that the watermark is usually used for data integrity detection and tamper resistance; also known as fingerprints. Generally, digital image watermarking needs to have security and concealment, and is also robust or sensitive according to different applications. The security means that the information of the digital image watermark is safe and difficult to be falsified or forged; this is ensured by the watermark itself. The imperceptibility refers to the hidden digital image watermark in the target digital image which can not be perceived by human senses; meanwhile, the digital image watermark does not influence the normal use of the protected data and can not cause the degradation of the target digital image. Robustness refers to the ability of a digital image watermark in a target digital image to maintain partial integrity and be accurately extracted and authenticated after undergoing various unintentional or intentional image processing (e.g., noise attack) procedures. Sensitivity means that the digital image watermark in the target digital image cannot be distinguished after any image processing process. Concealment and robustness/sensitivity are guaranteed by the watermark embedding and extraction algorithms.

In order to meet the requirements, in recent years, scholars at home and abroad propose a plurality of watermark embedding and extracting algorithms. For example, Chong Yu, university of Reddish 2015, proposed an SSDW algorithm based on an artificial neural network and Arnold screening. The algorithm has the advantages that Blind Extraction (Blind Extraction) is adopted, and an original watermark image is not needed when the watermark is extracted; the disadvantages are that: the image embedded with the watermark based on the algorithm has obvious fine noise points, and only anti-noise attack test is carried out at present. Ashok Kumar et al proposed a WLSBWM algorithm based on discrete wavelet transform and LSB in 2017, also had the advantage of blind extraction, and was able to resist a variety of attacks other than image rotation. The method has the disadvantages that the image after the watermark is embedded has obvious worm-like noise, and the algorithm links are more and more complex. In 2017, Raheleh KHORSAND MOVAGGAR et al propose a watermark embedding and extracting algorithm based on an artificial neural network, discrete wavelet transform and Singular Value Decomposition (SVD), and have small influence on the quality of a target digital image, but the original watermark picture is required for watermark extraction, so that the application range of the original watermark picture is limited. In addition, the algorithm has poor effect on resisting clipping and noise attack, and a rotation attack test is not carried out. Baharak Ahmaderaghi et al propose a watermark embedding and extracting algorithm based on discrete shear transform and statistical decision theory, similar to the above algorithm, the watermark extraction requires the original watermark picture, and no anti-scaling attack test is performed. In 2021, based on different considerations of requirements and purposes, the algorithm described in the published patent "a digital image watermark embedding method, extracting method, device, storage medium" is suitable for robust watermarking, and is used for copyright identification, but cannot be used for data tamper detection.

Disclosure of Invention

The invention provides a digital image encryption watermark embedding method, an extraction method and a device based on a hybrid chaotic system and closed loop diffusion, aiming at realizing the watermark embedding sensitivity, resisting various cracking methods including reconstruction attack and adapting to digital images with any content.

The technical scheme provided by the invention is as follows:

in one aspect, a digital image encryption watermark embedding method based on a hybrid chaotic system and closed-loop diffusion comprises the following steps:

image segmentation, namely segmenting an image to be embedded with a watermark according to bits to obtain a high five-bit image and a low three-bit image;

generating a key, namely obtaining a hash value of the image with the five high bits to be embedded with the watermark by adopting a hash algorithm, and obtaining a synthetic key based on the hash value and an appointed key;

generating a sequence, and generating a fusion chaotic sequence by using a synthesis key and a chaotic sequence iterative formula, wherein the fusion chaotic sequence comprises a scrambling sequence and a diffusion sequence;

image scrambling, namely extracting pixel components from the lower three-digit image by using a scrambling sequence, and synthesizing 256 × 256 scrambled images; recording the position of each pixel component in the lower three-bit image to form an in-situ matrix;

the original matrix records the positions of the pixels of the extracted components in the lower three-bit image;

Embedding the watermark of the scrambled image, namely embedding the watermark of the specified digital image into the scrambled image by using a watermark embedding mode based on channel data;

the watermark embedding mode based on the channel data is determined by adopting the disclosed digital image watermark embedding method, the disclosed digital image watermark extracting method, the disclosed digital image watermark embedding device and the disclosed digital image watermark embedding method in the storage medium;

image diffusion, namely performing closed-loop diffusion on the scrambled image embedded with the watermark by using a diffusion sequence to form a diffused scrambled image;

restoring the low three-bit image, namely restoring each pixel component of the diffused scrambled image into the low three-bit image according to the in-situ matrix to generate the diffused low three-bit image;

and acquiring a target image embedded with the watermark, and combining the diffused lower three-bit image and the diffused upper five-bit image to generate the target image embedded with the digital watermark.

In the specific processing process of the image, the matrix corresponding to the image is used for operation;

the watermark embedded by the scheme can not be perceived by naked eyes, a key is constructed and a scrambled image is generated by respectively using a high-order image and a low-order image in the embedding process, the scrambled image is subjected to closed-loop diffusion by using the key formed by the image, the digital image with any content can be used, and the image quality and the extracted watermark quality can hardly be influenced; the watermark is embedded in the low three-bit information of the original image, the watermark information density is very low, and an invisible watermark is formed; the method is extremely sensitive to the secret key and the image data embedded with the watermark, and slight modification can cause the extracted watermark to lose identifiability, so that the method has sensitivity; by adopting the novel conservative chaotic system, various cracking methods including reconstruction attack can be resisted (reconstruction attack cannot be resisted by adopting an encryption algorithm of a dissipative chaotic system);

Further, the generation steps of the fused chaotic sequence are as follows:

step A1: generating 8 double-precision floating point numbers by using the synthetic key as initial values of the chaotic sequence;

step A2: performing iterative computation from an initial value by using a chaotic sequence iterative formula to obtain a 5D-HCCS chaotic sequence and a 3D-LASM chaotic sequence;

the chaotic sequence iterative formula comprises a 5D-HCCS and a 3D-LASM iterative formula, wherein the 3D-LASM iterative formula is obtained by performing three-dimensional expansion on a 2D-LASM iterative formula;

the 3D-LASM iterative formula is extended from 2D-LASM as follows:

x(t+1)＝sin(μ(z(t)+3)x(t)(1-x(t)))

y(t+1)＝sin(μ(x(t+1)+3)y(t)(1-y(t)))

z(t+1)＝sin(μ(y(t+1)+3)z(t)(1-z(t)))

wherein t represents iteration times, mu is 0.9, the chaotic iteration formula is extremely sensitive to an initial value, and x (0), y (0) and z (0) represent the initial value of the 3D-LASM iteration formula;

the 5D-HCCS iterative formula is proposed in 2019, and the mathematical expression is as follows:

x’＝ay+cv

y’＝-ax+bxu

z’＝du

u’＝-bxy–dz

v’＝-cx

wherein, a is 30, b is 30, c is 10, and d is 30; when the initial value is two negative numbers and three positive numbers, the system generates hyper-chaotic (hyper-chaotic) behavior without chaotic attractors, see (A novel image encryption scheme based on coherent hyper-chaotic systems and closed-loop diffusion between blocks);

step A3: according to the sequence of the elements and the components in the chaotic sequence, sequentially measuring the random index value ind (c) by the element components of the 3D-LASM chaotic sequence:

Taking out the element components of the 5D-HCCS chaotic sequence according to the random index value ind (c), and sequentially adding the element components to a pseudo-random number sequence with N elements, wherein each element comprises M components to obtain a fusion chaotic sequence;

where c represents the selected element component, m is the modulus, n is a constant, and the value is 10.

Sequentially taking three components of elements of the 3D-LASM chaotic sequence, calculating a random index when each component is taken, taking a component of an element from the 5D-HCCS sequence by using the index (sequentially taking one component at a time), and sequentially putting the component into a component of an element of the fused chaotic sequence (sequentially putting one component at a time);

further, when the fused chaotic sequence is a scrambling sequence, N is 256 × 256+ 512; m ═ 12; keys for generating the initial value of the fused chaotic sequence are H1-H16 and K17-K32;

when the fused chaotic sequence is a diffusion sequence, N is 256 × 256+4 × 4, and M is 6; keys for generating the initial value of the fused chaotic sequence are H17-H32 and K1-K16;

H1-H16 and H17-H32 are respectively the first 16 8-bit integers and the last 16 8-bit integers of the hash value of the image top five-bit image to be embedded with the watermark obtained by the hash algorithm, and K1-K16 and K17-K32 are respectively the first 16 8-bit integers and the last 16 8-bit integers of the 256-bit designated key.

Further, the generation formula for generating 8 double-precision floating point numbers by using the synthetic key is as follows:

b_j∈{-224.0,-244.0,-236.0,-216.0,-222.0,1.0,1.4,0.7}

c_j∈{0,1.5,0,-1.5,0,0,0.0037,0.0012}

when the fused chaotic sequence is a scrambled sequence, a_i,j∈{H1-H16,K17-K32}；

When the fused chaotic sequence is a diffusion sequence, a_i,j∈{H17-H32,K1-K16}。

Further, the specific process of image scrambling is as follows:

step B1: setting 256 × 256 initial scrambled images, and setting all element values of red channels of the initial scrambled images to 128;

step B2: updating the element value of the green channel and the element value of the blue channel of each pixel in the initial scrambled image according to the following formulas respectively:

B＝b1*2⁶+b2*2³+b3

G＝b4*2⁶+b5*2³+b6

sequentially selecting an element c in the scrambling sequence, taking a random index value s1 of the sum of the first 6 components c1-c6 of c, taking a low 2-bit value b1 of an element (p1, p2) in the (s1+1) th channel of the image to be embedded with the watermark, and taking a low 3-bit value b2 of an element (p3, p4) in the ((s1+1) mod3+1) th channel of the image to be embedded with the watermark; taking a low 3-bit value b3 of an element with a position of (p5, p6) in the ((s1+2) mod3+1) th channel of the image to be embedded with the watermark; and recording (p1, p2), (p3, p4) and (p5, p6) to the in-situ matrix;

selecting an element c in the scrambling sequence in sequence, taking a random index value s2 of the sum value of the last 6 components c7-c12 of c, taking a low 2-bit value b4 of an element (q1, q2) in the (s2+1) th channel of the image to be embedded with the watermark, and taking a low 3-bit value b5 of an element (q3, q4) in the ((s2+1) mod3+1) th channel of the image to be embedded with the watermark; taking a low 3-bit value b6 of an element with a position of (q5, q6) in the ((s2+2) mod3+1) th channel of the image to be embedded with the watermark; and recording (q1, q2), (q3, q4) and (q5, q6) to the in-situ matrix;

p1, p2 are respectively the random index values corresponding to c1 and c2, p3, p4 are respectively the random index values corresponding to c3 and c4, p5, p6 are respectively the random index values corresponding to c5 and c 6; q1, q2 are respectively the random index values corresponding to c7 and c8, q3, q4 are respectively the random index values corresponding to c9 and c10, and q5, q6 are respectively the random index values corresponding to c11 and c 12;

when calculating the random index value, the modulus m is 3, and the same random index function as that in the step A3 is adopted;

step B3: traversing all pixels to obtain a matrix T1 composed of all pixel green channel element values and a matrix T2 composed of all pixel blue channel element values;

step B4: respectively changing the probability distribution of all elements of the matrix T1 and the matrix T2 by using a Box-Muller method, so that all element values of T1 and T2 conform to normal distribution;

the expected value of the normal distribution is set to 128, and the standard deviation is set to 4;

step B5: the modified matrix T1 and matrix T2 are combined with the initial scrambled image red channel matrix to generate the scrambled image.

Further, the process of image diffusion is as follows:

step C1: dividing the diffusion sequence into three subsequences according to component average, wherein each subsequence comprises 256 × 256+4 × 4 elements, and each element has two components;

Step C2: arranging the elements of the ith subsequence in groups into 256 × 256 diffusion matrices P and Q, and 4 × 4 unlocking matrices U and locking matrices L, i being 1,2, 3;

step C3: taking the ith channel matrix M of the scrambled image embedded with the watermark; vertically indexing the sub-matrixes of the channel matrix M from left to right and from top to bottom;

step C4: taking out 4 x 4 sub-matrixes at the upper left corner of the channel matrix M and 4 x 4 sub-matrixes at the lower right corner of the channel matrix M, combining the unlocking matrix U and the unlocking matrix U through matrix XOR operation, and outputting a first 4 x 4 encryption matrix;

step C5: locking the jth 4 x 4 sub-matrix A, wherein j is more than or equal to 2, taking the previous 4 x 4 sub-matrix A1 of the matrix A in the channel matrix M, taking the 4 x 4 sub-matrix B1 at the corresponding position from the diffusion matrix P according to the selected position of the sub-matrix A1, and adding the two to output a middle matrix V1;

step C6: taking a 4 x 4 submatrix A2 in front of the matrix A in the channel matrix M, taking a 4 x 4 submatrix B2 at a corresponding position from the diffusion matrix Q according to the selected position of the submatrix A2, and adding the two to output a middle matrix V2;

step C7: combining the matrix A, the intermediate matrix V1 and the intermediate matrix V2 through matrix XOR operation to output a 4 x 4 encryption matrix corresponding to the matrix A;

Step C8: repeating the steps C5-C8 until all 4 x 4 sub-matrixes except the first sub-matrix in the channel matrix M are traversed, and all output encryption matrixes form a set C, wherein the set C comprises the encryption matrix corresponding to the last sub-matrix and is called a last 4 x 4 encryption matrix;

step C9: combining the first 4 x 4 encryption matrix, the last 4 x 4 encryption matrix and the locking matrix L through matrix XOR operation to output a second-order first 4 x 4 encryption matrix;

step C10: splicing all encryption matrixes and second-order first 4 x 4 encryption matrixes in the set C into the diffused ith channel matrix according to the original corresponding index sequence;

step C11: and C3-C10 are repeated until all channel matrixes of the scrambled image embedded with the watermark are traversed, and the diffused scrambled image is obtained.

In another aspect, a digital image encryption watermark embedding device based on a hybrid chaotic system and closed-loop diffusion comprises:

the image segmentation module is used for segmenting the image to be embedded with the watermark according to the position to obtain a high five-bit image and a low three-bit image;

the first key generation module is used for obtaining a hash value of an image top five-bit image to be embedded with the watermark by adopting a hash algorithm and obtaining a synthetic key based on the hash value and a specified key;

The first sequence generating module is used for generating a fused chaotic sequence by utilizing a synthetic key and a chaotic sequence iterative formula, wherein the fused chaotic sequence comprises a scrambling sequence and a diffusion sequence;

an image scrambling module which extracts pixel components from the lower three-bit image by using a scrambling sequence and synthesizes 256 × 256 scrambled images; recording the position of each pixel component in the low three-dimensional image to form an in-situ matrix;

the scrambled image watermark embedding module is used for embedding the specified digital image watermark into the scrambled image by using a channel data-based watermark embedding mode;

the image diffusion module is used for performing closed-loop diffusion on the scrambled image embedded with the watermark by using a diffusion sequence to form a diffused scrambled image;

the low three-bit image restoration module is used for restoring each pixel component of the diffused scrambled image into a low three-bit image according to the in-situ matrix to generate a diffused low three-bit image;

and the target image module for acquiring the embedded watermark is used for combining the diffused lower three-bit image and the diffused upper five-bit image to generate a target image embedded with the digital watermark.

On the other hand, the digital image encryption watermark extraction method based on the mixed chaotic system and the closed loop diffusion is used for extracting the watermark of the digital image of which the watermark is to be extracted, wherein the watermark in the digital image of which the watermark is to be extracted is embedded by adopting the digital image encryption watermark embedding method based on the mixed chaotic system and the closed loop diffusion;

the extraction method comprises the following steps:

image segmentation, namely segmenting the target image embedded with the watermark according to positions to obtain a high five-bit image and a low three-bit image;

and (3) generating a key: calculating the hash value of the five-bit image through a hash algorithm, and generating a synthetic key with a specified key;

generating a sequence, and generating a fused chaotic sequence by using a synthetic key and a chaotic sequence iterative formula, wherein the fused chaotic sequence comprises a scrambling sequence and a diffusion sequence;

image scrambling, namely extracting pixel components from the lower three-bit image by using a scrambling sequence, and synthesizing 256 × 256 scrambled images; recording the position of each pixel component in the lower three-bit image to form an in-situ matrix; closed-loop back diffusion: carrying out closed-loop back diffusion on the 256 × 256 scrambled images embedded with the watermarks by using a diffusion sequence to form a back-diffused scrambled image matrix;

and (4) watermark extraction, namely extracting a digital watermark from the anti-diffused scrambled image by using a watermark extraction mode based on channel data.

The watermark extraction mode based on the channel data is determined by adopting the disclosed digital image watermark embedding method, extraction method, device and storage medium;

further, the image back diffusion process is as follows:

step D1: dividing the diffusion sequence into three subsequences according to component average, wherein each subsequence comprises 256 × 256+4 × 4 elements, and each element has two components;

step D2: arranging the elements of the ith subsequence in groups into 256 × 256 diffusion matrices P and Q, and 4 × 4 unlocking matrices U and locking matrices L, i being 1,2, 3;

step D3: taking the ith 256 x 256 channel matrix M of the scrambled image embedded with the watermark; vertically indexing the sub-matrixes of the channel matrix M from left to right and from top to bottom;

step D4: taking out 4 x 4 sub-matrixes at the upper left corner of the channel matrix M and 4 x 4 sub-matrixes at the lower right corner of the channel matrix M, combining the unlocking matrix U and the unlocking matrix U through matrix XOR operation, and outputting a first 4 x 4 decryption matrix;

step D5: locking the jth 4 x 4 sub-matrix A, wherein j is more than or equal to 2, taking the previous 4 x 4 sub-matrix A1 of the matrix A in the channel matrix M, taking the corresponding 4 x 4 sub-matrix B1 from the diffusion matrix P according to the selection mode of the sub-matrix A1, adding the two, and outputting a middle matrix V1;

Step D6: taking any one 4 x 4 sub-matrix A2 in front of the matrix A in the channel matrix M, taking the corresponding 4 x 4 sub-matrix B2 from the diffusion matrix Q according to the selection mode of the sub-matrix A2, and adding the two to output an intermediate matrix V2;

step D7: combining the matrix A, the intermediate matrix V1 and the intermediate matrix V2 through matrix XOR operation, and outputting a 4 x 4 decryption matrix corresponding to the matrix A;

step D8: repeating the steps D6-D8 until all 4 x 4 sub-matrixes except the first sub-matrix in the channel matrix M are traversed, and all output decryption matrixes form a set C, wherein the set C comprises the decryption matrix corresponding to the last sub-matrix and is called the last 4 x 4 decryption matrix;

step D9: combining the first 4 x 4 decryption matrix, the last 4 x 4 decryption matrix and the locking matrix L through matrix XOR operation to output a second-order first 4 x 4 decryption matrix;

step D10: splicing all decryption matrixes and second-order first 4 x 4 decryption matrixes in the set C into the ith channel matrix after back diffusion according to the original corresponding index sequence;

step D11: and D3-D10 are repeated until all channel matrixes of the scrambled image embedded with the watermark are traversed, and the scrambled image after back diffusion is obtained.

On the other hand, the digital image encryption watermark extraction device based on the hybrid chaotic system and the closed-loop diffusion is used for extracting the watermark of the digital image of which the watermark is to be extracted, wherein the watermark in the digital image of which the watermark is to be extracted is embedded by adopting the digital image encryption watermark embedding method based on the hybrid chaotic system and the closed-loop diffusion;

The extraction device comprises:

the target image segmentation module is used for segmenting the target image embedded with the watermark according to bits to obtain a high five-bit image and a low three-bit image;

the second key generation module is used for calculating the hash value of the upper five-bit image through a hash algorithm and generating a synthetic key with the specified key;

the second sequence generation module generates a fused chaotic sequence comprising a scrambling sequence and a diffusion sequence by utilizing a synthesis key and a chaotic sequence iterative formula;

a target image scrambling module for synthesizing 256 × 256 scrambled images by extracting pixel components from the lower three-bit images using a scrambling sequence; recording the position of each pixel component in the lower three-bit image to form an in-situ matrix;

a closed-loop back diffusion module: carrying out closed-loop back diffusion on the 256 × 256 scrambled images embedded with the watermarks by using a diffusion sequence to form a back-diffused scrambled image matrix;

and the watermark extraction module is used for extracting the digital watermark from the anti-diffused scrambled image by using a channel data-based watermark extraction mode.

The channel data-based watermark extraction mode is determined by adopting the disclosed digital image watermark embedding method, digital image watermark extraction device and digital image watermark storage medium.

Advantageous effects

The invention discloses a digital image encryption watermark embedding method, an extraction method and a device based on a hybrid chaotic system and closed-loop diffusion, wherein the embedded watermark cannot be perceived by naked eyes and is difficult to perceive and acquire by a common technical means through the watermark embedding method based on a chaotic sequence and the closed-loop diffusion; the watermark is embedded in the low three-bit information of the original image, the watermark information density is very low, and the invisible watermark is formed; the method is extremely sensitive to the secret key and the image data embedded with the watermark, and slight modification can cause the extracted watermark to lose identifiability, so that the method has sensitivity; by adopting the novel conservative chaotic system, various cracking methods including reconstruction attack can be resisted, and many encryption algorithms adopting the dissipative chaotic system are difficult to resist the attack.

Drawings

Fig. 1 is a flowchart of a watermark embedding method provided by an embodiment of the present invention;

FIG. 2 is a flow chart of a closed loop diffusion provided by an embodiment of the present invention;

fig. 3 is a flowchart of a watermark extraction method provided in an embodiment of the present invention;

FIG. 4 is a flow chart of a closed loop back diffusion process provided by an embodiment of the present invention;

FIG. 5 is a schematic diagram of embedding random watermarks into different digital images by using a random 256-bit key according to the method of the present embodiment, and then extracting watermarks from each target image by using a correct key and a randomly modified key with one bit according to the method of the present embodiment, where (a) is a schematic diagram of comparing a random key 1 with a watermark extracted by 1-bit modification of the random key 1, (b) is a schematic diagram of comparing a random key 2 with a watermark extracted by 1-bit modification of the random key 2, (c) is a schematic diagram of comparing a random key 3 with a watermark extracted by 1-bit modification of the random key 3, (d) is a schematic diagram of comparing a random key 4 with a watermark extracted by 1-bit modification of the random key 4, (e) is a schematic diagram of comparing a random key 5 with a watermark extracted by 1-bit modification of the random key 5, and (f) is a schematic diagram of comparing a random key 6 with a watermark extracted by 1-bit modification of the random key 6, (g) a schematic diagram of comparing a random key 7 with a watermark extracted by 1-bit modification of the random key 7, (h) a schematic diagram of comparing a random key 8 with a watermark extracted by 1-bit modification of the random key 8, (i) a schematic diagram of comparing a random key 9 with a watermark extracted by 1-bit modification of the random key 9, (j) a schematic diagram of comparing a random key 10 with a watermark extracted by 1-bit modification of the random key 10, (k) a schematic diagram of comparing a random key 11 with a watermark extracted by 1-bit modification of the random key 11, (l) a schematic diagram of comparing a random key 12 with a watermark extracted by 1-bit modification of the random key 12, (m) a schematic diagram of comparing a random key 13 with a watermark extracted by 1-bit modification of the random key 13, and (n) a schematic diagram of comparing a random key 14 with a watermark extracted by 1-bit modification of the random key 14;

Fig. 6 is schematic diagrams of watermarks before and after modification of a target image extracted by the method according to the embodiment of the present invention, where (a) is a schematic diagram of the watermark extracted for the target image, (b) is a schematic diagram of the watermark extracted after randomly modifying the target image by one pixel and randomly modifying the lowest one of the five upper bits of one channel, (c) is a schematic diagram of the watermark extracted after randomly modifying all (25% -40%) of the pixels (all channels) by the target image by the lowest two bits, (d) is a schematic diagram of the watermark extracted after randomly modifying all (25% -40%) of the pixels (all channels) by the target image by the lowest three bits, and (e) is a schematic diagram of the watermark extracted after adding 0.1% salt and pepper noise to the target image.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. It should be apparent that the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the examples given herein without making any creative effort, shall fall within the protection scope of the present invention.

It is noted that the terms "first," "second," and the like in the description of the present invention are used for descriptive purposes only and are not intended to indicate or imply relative importance or order. Further, in the description of the present invention, the meaning of "a plurality" means at least two unless otherwise specified.

As shown in fig. 1, a digital image encryption watermark embedding method based on a hybrid chaotic system and closed-loop diffusion includes:

image segmentation, namely segmenting an image to be embedded with a watermark according to positions to obtain a high five-bit image and a low three-bit image;

generating a key, namely obtaining a hash value of the image with the five high bits to be embedded with the watermark by adopting a hash algorithm, and obtaining a synthetic key based on the hash value and a specified key;

embedding a scrambled image watermark, namely embedding a specified digital image watermark into the scrambled image by using a channel data-based watermark embedding mode;

In the specific processing process of the image, calculating by using a matrix corresponding to the image;

the watermark embedded by the scheme can not be perceived by naked eyes, a key is constructed and a scrambled image is generated by respectively using a high-order image and a low-order image in the embedding process, the scrambled image is subjected to closed-loop diffusion by using the key formed by the image, the digital image with any content can be used, and the image quality and the extracted watermark quality can hardly be influenced; the watermark is embedded in the low three-bit information of the original image, the watermark information density is very low, and the invisible watermark is formed; the method is extremely sensitive to the secret key and the image data after the watermark is embedded, and slight modification can cause the extracted watermark to lose identifiability, so that the method has sensitivity; by adopting the novel conservative chaotic system, various cracking methods including reconstruction attacks can be resisted (the reconstruction attacks can not be resisted by adopting an encryption algorithm of a dissipative chaotic system);

The generation steps of the fusion chaotic sequence are as follows:

step A1: generating 8 double-precision floating point numbers by using the synthetic key as an initial value of the chaotic sequence;

the chaotic sequence iteration formula comprises a 5D-HCCS and a 3D-LASM iteration formula, wherein the 3D-LASM iteration formula is obtained by performing three-dimensional expansion on a 2D-LASM iteration formula;

the 3D-LASM iterative formula is extended from 2D-LASM as follows:

x(t+1)＝sin(μ(z(t)+3)x(t)(1-x(t)))

y(t+1)＝sin(μ(x(t+1)+3)y(t)(1-y(t)))

z(t+1)＝sin(μ(y(t+1)+3)z(t)(1-z(t)))

wherein t represents the iteration number, mu is 0.9, the chaotic iteration formula is extremely sensitive to an initial value, and x (0), y (0) and z (0) represent the initial value of the 3D-LASM iteration formula;

the chaos iterative formula of 5D-HCCS is proposed in 2019, and the mathematical expression is as follows:

x’＝ay+cv

y’＝-ax+bxu

z’＝du

u’＝-bxy–dz

v’＝-cx

wherein, a is 30, b is 30, c is 10, d is 30; when the initial value is two negative numbers and three positive numbers, the system generates hyper-chaotic (hyper-chaotic) behavior without chaotic attractors, see "improved image encryption scheme based on coherent hyper-chaotic systems and closed-loop diffusion between blocks";

Taking out the element components of the 5D-HCCS chaotic sequence according to the random index value ind (c), and sequentially adding the element components to a pseudo-random number sequence with N elements, wherein each element comprises M components, namely the fusion chaotic sequence;

wherein c represents the selected element component, m is the modulus, n is the constant, and the value is 10.

when the fused chaotic sequence is a scrambling sequence, N is 256 × 256+ 512; m-12; keys for generating the initial value of the fused chaotic sequence are H1-H16 and K17-K32;

The generation formula for generating 8 double-precision floating point numbers by using the synthetic key is as follows:

b_j∈{-224.0,-244.0,-236.0,-216.0,-222.0,1.0,1.4,0.7}

c_j∈{0,1.5,0,-1.5,0,0,0.0037,0.0012}

The specific process of image scrambling is as follows:

step B1: setting 256 × 256 initial scrambled images, and setting all element values of the red channels of the initial scrambled images to 128;

B＝b1*2⁶+b2*2³+b3

G＝b4*2⁶+b5*2³+b6

As shown in fig. 2, the process of image diffusion is as follows:

Step C8: repeating the steps C5-C8 until all 4 x 4 sub-matrixes except the first sub-matrix in the channel matrix M are traversed, and all output encryption matrixes form a set C, wherein the set C comprises the encryption matrix corresponding to the last sub-matrix and is called the last 4 x 4 encryption matrix;

The embodiment of the invention also provides a digital image encryption watermark embedding device based on a hybrid chaotic system and closed loop diffusion, which comprises the following steps:

the scrambled image watermark embedding module is used for embedding the specified digital image watermark into the scrambled image by using a watermark embedding mode based on channel data;

the watermark embedding mode based on the channel data is determined by the disclosed method in the digital image watermark embedding method, the digital image watermark extracting method, the digital image watermark embedding device and the storage medium;

As shown in fig. 3, a digital image encryption watermark extraction method based on a hybrid chaotic system and closed-loop diffusion is used for extracting a watermark from a digital image to be subjected to watermark extraction, wherein the watermark in the digital image to be subjected to watermark extraction is embedded by using the digital image encryption watermark embedding method based on the hybrid chaotic system and the closed-loop diffusion;

the extraction method comprises the following steps:

image scrambling, namely extracting pixel components from the lower three-digit image by using a scrambling sequence, and synthesizing 256 × 256 scrambled images; recording the position of each pixel component in the lower three-bit image to form an in-situ matrix; closed-loop back diffusion: carrying out closed-loop back diffusion on the 256 × 256 scrambled images embedded with the watermarks by using a diffusion sequence to form a back-diffused scrambled image matrix;

as shown in fig. 4, the process of the image back diffusion is as follows:

step D2: arranging the elements of the ith subsequence in component order as a 256 × 256 spreading matrix P and Q, and a 4 × 4 unlocking matrix U and locking matrix L, i ═ 1,2, 3;

step D3: taking the ith 256 × 256 channel matrix M of the scrambled image embedded with the watermark; vertically indexing sub-matrixes of the channel matrix M from left to right and from top to bottom;

The embodiment of the invention also provides a digital image encryption watermark extraction device based on the hybrid chaotic system and closed-loop diffusion, which is used for extracting the watermark of the digital image of which the watermark is to be extracted, wherein the watermark in the digital image of which the watermark is to be extracted is embedded by adopting the digital image encryption watermark embedding method based on the hybrid chaotic system and the closed-loop diffusion;

The extraction device comprises:

the second key generation module is used for calculating the hash value of the five-bit image through a hash algorithm and generating a synthetic key with the specified key;

the second sequence generating module is used for generating a fused chaotic sequence by utilizing a synthetic key and a chaotic sequence iterative formula, wherein the fused chaotic sequence comprises a scrambling sequence and a diffusion sequence;

a target image scrambling module for extracting pixel components from the lower three-bit image by using a scrambling sequence and synthesizing 256 × 256 scrambled images; recording the position of each pixel component in the lower three-bit image to form an in-situ matrix;

The method comprises the following steps:

as shown in fig. 5, a random watermark is embedded by using a random 256-bit key for different digital images, then the watermark is extracted by using a correct key and a key modified by one bit randomly for each target image, and the resulting pixel change rate (NPCR) (it is easy to verify that the calculated value of the average change intensity (UACI) of the black and white image is equal to the pixel change rate and thus is not calculated) and the Normalized Correlation Coefficient (NCC) are compared, as shown in table 1.

TABLE 1

The normalized correlation coefficient is calculated by the following formula:

the watermark corresponding to the key which obviously randomly modifies one bit is not distinguishable by naked eyes and is obviously different from the watermark corresponding to the correct key, but the difference between the two is calculated to be only about 50 percent.

Statistical analysis and spike signal-to-noise ratio

The peak signal-to-noise ratio (PSNR), the pixel change rate (NPCR), the average intensity of change (UACI) and the Normalized Correlation Coefficient (NCC) were used to measure the similarity of the images before and after the watermark embedding (14 random images) using the method described in the example of the present invention, see table 2 for details.

TABLE 2

PSNR	NPCR	UACI	NCC
				46.2549760769052	0.375169805724455	0.00166081697892465	0.996448936630176
46.7909399075125	0.339024841437632	0.00147511538089513	0.997328398414791
				47.8293701125205	0.269194206446348	0.00114753348639878	0.999589621145703
47.1223101305230	0.291514510859120	0.00131098732105780	1.000000000000000
				42.1902594016716	0.595532081377152	0.00356581123146529	0.999968262476373
46.9554648357438	0.327810923258464	0.00141849060723465	0.998086363064243
				46.2046073318285	0.342553009575923	0.00158406866936241	0.999650844405241
46.4783441957147	0.363970504009164	0.00159162118455630	0.999593709517195
				50.5080979959813	0.132867476851852	0.000577021176268861	0.999898552463648
46.6055109765268	0.351727552816901	0.00153755688748504	0.997607603113948
				46.7244634281032	0.338530149096187	0.00148303318336615	0.998682708666844
42.9051649484471	0.656303833623421	0.00345873862752779	0.998518765390953
				47.5700763175056	0.288635812672176	0.00123099515655665	0.996125386743179
43.2376445443606	0.624047222222222	0.00321769789397240	0.986824038867765

The average value of PSNR before and after embedding the watermark is 46.2412307288103, indicating a high degree of similarity; the average of the remaining values is 0.378348709283644, 0.00180424912750514, 0.997737370778576 once; this means that the number of distinct pixels may be very large (possibly over 60%), but the difference in pixel values is usually small.

Linear correlation analysis

For random images (14 sheets in total), the image after embedding the watermark by using the method of the embodiment of the invention is similar to the original image in linear correlation (Pearson correlation coefficient); but the linear correlation of the pixel value difference distribution of both should be low. The statistical results of the experiment are shown in the following table.

TABLE 3

The difference in the linear correlation between the original image and the target image is small, and the linear correlation of the pixel value difference distribution is low. This means that by comparing the two, the probability of deriving the regularity of the embedded watermark is low.

Tamper attack

The method is mainly used for detecting the tampering of the image embedded with the watermark. Embedding a watermark into an original image to obtain a target image, then modifying the target image to different degrees, comparing the watermark extracted before modification with the watermark extracted after modification, and observing the influence of modification on the quality of the watermark extracted from the target image. Because the method of the embodiment of the invention does not modify the upper five bits of the pixel value of the original image and uses the SHA256 hash value as a part of the key, any modification (called semantic modification) to the upper five-bit matrix of the target image theoretically can result in that the watermark which can be identified by naked eyes cannot be extracted. The following experimental results are all measured by the degree of identification by naked eyes. Table 4 below is a preliminary experimental result with several modifications.

TABLE 4

It can be seen that the modification of the upper five bits is fatal to watermark extraction. Most modifications to the image content modify the upper five bits of at least one pixel, so the algorithm is absolutely resistant to such tampering.

Efficiency of operation

To verify the efficiency of the operation of the method described in the present example, in a basic environment: a CPU: intel i7-10700K, 3.8 GHz; memory: 32 GB; win 1064-bit operating system; a 64-bit algorithm program;

running the watermark embedding algorithm (automatically generating the key) according to the embodiment of the invention;

a Debug mode: the watermark is embedded 50 times in 14 random images (both in batch processing), each time taking 7660.16000000000 milliseconds on average and each image taking 547.154285714286 milliseconds on average. The table is time consuming for the past.

TABLE 5

7741	7635	7638	7633	7662
					7675	7660	7652	7686	7668
7688	7658	7659	7669	7670
					7649	7637	7654	7661	7680
7683	7653	7654	7658	7659
					7693	7656	7642	7661	7667
7665	7632	7636	7649	7653
					7671	7645	7634	7673	7645
7656	7635	7661	7666	7697
					7655	7648	7664	7648	7674

Release mode: the watermark is embedded 50 times in 14 random images (both in batch processing), each time taking 1860.10000000000 milliseconds on average and each image taking 132.864285714286 milliseconds on average. Table 6 is the time spent for the histories.

TABLE 6

1984	1860	1865	1847	1845
					1878	1860	1857	1847	2095
1878	1861	1866	1846	1838
					1858	1859	1848	1835	1850
1862	1856	1841	1840	1848
					1879	1848	1843	1845	1844
1862	1857	1859	1842	1847
					1856	1848	1851	1843	1853
1868	1849	1832	1837	1842
					1865	1864	1868	1829	1850

Running the watermark extraction algorithm (automatically generating a key) according to the embodiment of the invention;

a Debug mode: the watermark is extracted 50 times in succession on 14 random images (both in batch processing), each taking on average 10122.0200000000 milliseconds and each taking on average 723.001428571429 milliseconds. Table 7 is the time spent for the histories.

TABLE 7

Release mode: the watermark is extracted 50 times in succession on 14 images (both in batch processing), each taking on average 1856.72000000000 milliseconds and 132.622857142857 milliseconds on average. Table 8 is the time spent for the histories.

TABLE 8

1974	1847	1825	1844	1833
					1866	1839	1840	1835	1856
1845	1837	1828	1828	1836
					1840	1859	1834	1842	1837
1844	1856	1834	1841	1833
					1854	1834	1819	1838	1840
1840	1847	1842	1839	2575
					1840	1834	1836	1825	1830
1846	1848	1836	1830	1829
					1849	1841	1855	1827	1829

As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It is understood that the same or similar parts in the above embodiments may be mutually referred to, and the same or similar contents in other embodiments may be referred to for the contents which are not described in detail in some embodiments.

Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and alternate implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present invention.

Claims

1. A digital image encryption watermark embedding method based on a hybrid chaotic system and closed loop diffusion is characterized by comprising the following steps:

2. The method according to claim 1, wherein the fused chaotic sequence is generated by the steps of:

the chaotic sequence iterative formula comprises a 5D-HCCS and a 3D-LASM chaotic iterative formula, wherein the 3D-LASM iterative formula is obtained by performing three-dimensional expansion on a 2D-LASM iterative formula;

taking out the element components of the 5D-HCCS chaotic sequence according to the random index value ind (c), and sequentially adding the element components to a pseudo-random number sequence with N elements, wherein each element comprises M components to obtain a fused chaotic sequence;

wherein c represents the element component of the chaotic sequence, m is a modulus, n is a constant, and the value is 10.

3. The method according to claim 2, wherein when the fused chaotic sequence is a scrambled sequence, N-256 x 256+ 512; m ═ 12; keys for generating the initial value of the fused chaotic sequence are H1-H16 and K17-K32;

4. The method of claim 3, wherein the generation formula for generating 8 double-precision floating point numbers using the synthetic key is as follows:

b_j∈{-224.0,-244.0,-236.0,-216.0,-222.0,1.0,1.4,0.7}

c_j∈{0,1.5,0,-1.5,0,0,0.0037,0.0012}

5. The method according to claim 1, wherein the specific process of image scrambling is as follows:

B＝b1*2⁶+b2*2³+b3

G＝b4*2⁶+b5*2³+b6

Selecting an element c in the scrambling sequence in sequence, taking a random index value s2 of the sum of the last 6 components c7-c12 of c, taking a low 2-bit value b4 of an element (q1, q2) in the (s2+1) th channel of the image to be embedded with the watermark, and taking a low 3-bit value b5 of an element (q3, q4) in the ((s2+1) mod3+1) th channel of the image to be embedded with the watermark; taking a low 3-bit value b6 of an element with a position of (q5, q6) in the ((s2+2) mod3+1) th channel of the image to be embedded with the watermark; and recording (q1, q2), (q3, q4) and (q5, q6) to the in-situ matrix;

when calculating the random index value, the modulus m is 3;

6. The method of claim 1, wherein the image diffusion is performed as follows:

7. A digital image encryption watermark embedding device based on a hybrid chaotic system and closed loop diffusion is characterized by comprising:

the first sequence generation module generates a fused chaotic sequence comprising a scrambling sequence and a diffusion sequence by utilizing a synthesis key and a chaotic sequence iterative formula;

an image scrambling module which extracts pixel components from the lower three-bit image by using a scrambling sequence and synthesizes 256 × 256 scrambled images; recording the position of each pixel component in the lower three-bit image to form an in-situ matrix;

8. A digital image encryption watermark extraction method based on a mixed chaotic system and closed loop diffusion is characterized by being used for extracting watermarks of a digital image to be subjected to watermark extraction, wherein the watermarks in the digital image to be subjected to watermark extraction are embedded by adopting the digital image encryption watermark embedding method based on the mixed chaotic system and closed loop diffusion according to any one of claims 1 to 6;

the extraction method comprises the following steps:

and (3) key generation: calculating the hash value of the high five-bit image through a hash algorithm, and generating a synthetic key with a specified key;

Closed-loop back diffusion: carrying out closed-loop back diffusion on the 256 × 256 scrambled images embedded with the watermarks by using a diffusion sequence to form a back-diffused scrambled image matrix;

9. The method of claim 8, wherein the image back-diffusion is performed as follows:

10. A digital image encryption watermark extraction device based on a mixed chaotic system and closed loop diffusion is characterized by being used for extracting watermarks of a digital image to be subjected to watermark extraction, wherein the watermarks in the digital image to be subjected to watermark extraction are embedded by adopting the digital image encryption watermark embedding method based on the mixed chaotic system and closed loop diffusion according to any one of claims 1 to 6;

The extraction device comprises: