CN108365947A

CN108365947A - A kind of image encryption method based on Feistel networks Yu dynamic DNA encoding

Info

Publication number: CN108365947A
Application number: CN201810179620.4A
Authority: CN
Inventors: 牛莹; 张勋才; 刘磊; 朱向前; 周航宇
Original assignee: Zhengzhou University of Light Industry
Current assignee: Zhengzhou University of Light Industry
Priority date: 2018-03-05
Filing date: 2018-03-05
Publication date: 2018-08-03
Anticipated expiration: 2038-03-05
Also published as: CN108365947B

Abstract

The present invention proposes a kind of image encryption method based on Feistel networks Yu dynamic DNA encoding, the cryptographic Hash that original plaintext image is calculated using Keccak algorithms is used as the initial value of Hyperchaotic Chen System, and the chaos sequence generation Xi Er scrambled matrixs generated using Hyperchaotic Chen System are to the pixel of original image into line replacement；Use DNA encoding operation as Feistel networksFFunction, key of the DNA sequence dna library as Feistel networksKRealize image pixel value diffusion；It is further spread by Cipher Feedback.The present invention keeps ciphertext randomness and attack tolerant stronger by three-wheel " Chaotic Scrambling DNA encoding Feistel converts DNA decodings ", the diffusion of the scramble transformation and pixel value of image pixel positions is realized, multiple scramble reduces encrypted wheel number with DNA encoding, decoding.The present invention can effectively encrypt image, has plaintext sensibility strong, can be reasonably resistant to plaintext attack, differential attack and statistical attack.

Description

Image encryption method based on Feistel network and dynamic DNA coding

Technical Field

The invention relates to the technical field of image encryption, in particular to an image encryption method based on a Feistel network and dynamic DNA coding.

Background

Information security has become a significant problem affecting national security, social stability, economic development and personal property, and measures must be taken to ensure the integrity, availability, confidentiality and reliability of information resources. The digital image has the characteristics of intuition, easy identification, vividness, high redundancy, large data capacity and the like, and is one of the common information communication modes of people. Because digital images have the characteristics of large data volume, high redundancy and the like, the conventional classical encryption methods such as DES, AES, Feistel, RSA and the like cannot meet the requirements of image encryption due to low encryption efficiency, low security and the like.

With the continuous and intensive research on DNA molecular computing technology and biotechnology. Scientists have found that nucleic acid sequences have a natural quaternary combination, similar to the binary formed by semiconductor switching. Thus, information storage and calculation can be performed using the permutation and combination of nucleotides. The ultra-large-scale parallelism, ultra-high-capacity storage density and ultra-low energy consumption of DNA are being developed for the fields of molecular computing, data storage and cryptography, and the research in this field may eventually lead to the birth of new computers, new data storage and new cryptographic systems, leading to a new information revolution. In 1999, Gehani et al proposed a DNA-based one-time pad cipher scheme, giving two alternative and exclusive-OR one-time pad cipher schemes. In 2003, Chen et al constructed a coding system based on DNA molecular sequences; in 2005, Kazuo et al solved the key assignment problem with DNA; in 2006, lucumaxin and the like propose a DNA-based encryption method by using a DNA synthesis technology, a DNA cloning technology, a DNA amplification technology and a DNA chip technology and combining a computational complexity theory. In 2009, Mousa and the like designed an information hiding scheme, and ciphertext information was embedded into any part of an accounting sequence by using a comparable mapping technology without changing the function of nucleic acid. In a word, the high parallel computing capability and mass data storage capability of the DNA and the limitations of the existing biological technology and computing technology provide multiple safety guarantees for the existing DNA encryption method. However, these DNA encryption algorithms are often used for encrypting character information, and it is difficult to directly encrypt image information. In recent years, a chaos mapping-based DNA image encryption algorithm was proposed in 2014 by combining the dual advantages of DNA molecules and traditional passwords. In 2015, Wang et al presented an image encryption technique based on 2-D logistic mapping and DNA manipulation. In 2016, an image encryption algorithm based on DNA out-of-order coding and chaotic mapping is given by Zhou-Xiao' an. Chai and the like in 2017 combine with DNA operation to provide an image encryption algorithm based on chaos. These algorithms only permute the positions of the image pixels and change the grey values. But the bit position changes less and the true diffusion cannot be achieved.

Disclosure of Invention

Aiming at the technical problems that the bit position of the existing image encryption method is changed less and the true diffusion cannot be achieved, the invention provides an image encryption method based on a Feistel network and dynamic DNA coding, the Feistel network and the DNA coding are organically combined, a Hill encryption matrix is constructed by adopting a hyperchaotic series generated by a hyperchaotic system to replace an image, the chaos index sequence, the Feistel network and the dynamic DNA coding technology are utilized to scramble and diffuse the image, and the scrambling and diffusion characteristics of the algorithm are further enhanced through ciphertext feedback.

In order to achieve the purpose, the technical scheme of the invention is realized as follows: an image encryption method based on a Feistel network and dynamic DNA coding comprises the following steps:

the method comprises the following steps: converting a grayscale image of size m × n into a two-dimensional image matrix I of size m × n₁；

Step two: image matrix I is calculated by Keccak algorithm adopting hash function₁Obtaining an initial value of the chaotic Chen system through the hash value K, and bringing the initial value into the hyperchaotic Chen system to generate sequences B which respectively contain L-m multiplied by n elements₁、B₂、 B₃And B₄；

Step three: sequence B generated by hyperchaotic Chen system₄The structure T [ [ m ] n/4 ]]A Hill encryption matrix KM₁、KM₂、…、 KM_T；

Step four: for image matrix I₁Carrying out encryption replacement through the constructed Hill encryption matrix according to every 4 pixels to obtain an image matrix I₂；

Step five: downloading ID numbers from GenBank database as: the DNA sequence of NZ _ LOZQ01000042 is named DNA sequence SQ by cutting 6mn base sequences from the S base;

step six: sequence B generated according to hyperchaotic Chen system₁By scrambling the image matrix I by position₂To obtain a scrambled image matrix I₃；

Step seven: image matrix I₃Dynamic DNA coding, Feistel transformation and DNA decoding are carried out and restored to a matrix form to obtain an image matrix I₄Completing the first round of scrambling and transformation;

step eight: sequence B generated according to hyperchaotic Chen system₂Through a position scrambling pair image matrix I₄Scrambling to obtain an image matrix P₅(ii) a For image matrix P₅Dynamic DNA coding, Feistel transformation and DNA decoding are carried out and restored to a matrix form to obtain an image matrix P₆And finishing the second round of scrambling and transformation.

Step nine: sequence B generated according to hyperchaotic Chen system₃Through a position scrambling pair image matrix I₆Scrambling to obtain an image matrix P₇(ii) a For image matrix P₇Dynamic DNA coding, Feistel transformation and DNA decoding are carried out and restored into a matrix to obtain an image matrix P₈And completing the third round of scrambling and transforming.

Step ten: according to the ciphertext diffusion technique, the image matrix P is subjected to₈Performing XOR operation on each pixel in the image matrix P and the ciphertext of the previous pixel to obtain a final image matrix P₉。

The sequence B₁、B₂、B₃And B₄The generation method comprises the following steps: the hyperchaotic Chen system has the following equation:

wherein x, y, z and w are state variables of the system; a. b, c, d and r are control parameters of the system, and when a is 35, b is 3, c is 12, d is 7 and r is more than or equal to 0.085 and less than or equal to 0.798, the system shows hyper-chaotic motion;

image matrix I adopting Keccak algorithm of hash function₁Generating 512-bit hash value K, dividing the hash value into 64 groups of 8 bits, and recording K ═ K { (K) }₁,k₂,k3,…,k₆₄}; calculating an initial value x of the hyperchaotic Chen system according to the following formula₀、y₀、z₀And w₀：

Wherein, v is 6(i-1), u is 1,2, 3, 4,representing an exclusive or operation; x'₀、y′₀、z′₀、w′₀Setting an initial value of a given parameter; round (h)_i) Rounding to an integer function;

when the hyperchaotic Chen system is in a hyperchaotic state, the initial value x of the chaotic system is set₀,y₀,z₀,w₀The method comprises the steps of leading in a hyperchaotic Chen system, discarding initial end data through iteration, taking out L as m multiplied by n non-repetitive values from the initial end data, and obtaining 4 discrete real value hyperchaotic sequences A₁:{a₁₁,a₁₂,…,a_1L}、A₂:{a₂₁,a₂₂,…,a_2L}、A₃:{a₃₁,a₃₂,…,a_3LAnd A₄:{a₄₁,a₄₂,…,a_4L}; hyper-chaotic sequence A₁、A₂、A₃And A₄For unifying the value range of real number sequence, only taking the fractional part of 4 sequences to obtain new sequences respectively B₁:{b₁₁,b₁₂,…,b_1L}、B₂:{b₂₁,b₂₂,…,b_2L}、B₃：{b₃₁,b₃₂,…,b_3LAnd B₄：{b₄₁,b₄₂,…, b_4LAnd i.e.:

wherein [ A ]_i]Representing the hyperchaotic sequence A_iThe integer part of (d), mod (,) is the remainder operation.

Sequence B generated by hyperchaotic Chen system in step three₄The structure T [ [ m ] n/4 ]]A Hill encryption matrix KM₁、KM₂、…、KM_TThe method comprises the following steps: given a 4 x 4 empty matrix M, the matrix M is divided into four parts:

wherein,

(1) the hyperchaotic Chen system is used as a pseudo-random number generator to generate a hyperchaotic sequence, and a hyperchaotic sequence B is sequentially generated from the hyperchaotic sequence₄Select 4 elements in, fill M₁₁；

(2) Sub-matrix M₁₂＝I-M₁₁；

(3) Sub-matrix M₂₂＝-M₁₁；

(4) Sub-matrix M₂₁＝I+M₁₁；

(5) Four sub-matrices M to be generated₁₁、M₁₂、M₂₂、M₂₁Combining to obtain reversible Hill encryption matrix M, and assigning it to KM₁；

(6) Repeating the steps (1) to (5) to obtain the Hill encryption matrix KM₂、…、KM_T。

The method for encryption and replacement in the fourth step comprises the following steps: image matrix I to be encrypted₁One group of every 4 pixels, each group of pixels being converted into a 4 x 1 matrix I_4*1And constructing a reversible Hill encryption matrix KM of 4 multiplied by 4, and performing Hill encryption on each group of images, wherein the encryption formula is as follows:

wherein E is a result matrix of Hill encryption, E_11～41Is a pixel of matrix E, I_11～41For a group of pixels, m, to be encrypted_11-44Is an element of the hill encryption matrix KM;

multiplicative inverse matrix KM using Hill-encryption matrix KM^-1And (3) decrypting the ciphertext:

I＝(KM^-1*E)mod256＝(KM*E)mod256。

the position scrambling method comprises the following steps: sequence B in ascending order₁Or B₂Or B₃Obtaining a replacement index sequence X, filling the replacement index sequence X according to m values of each row to obtain a replacement matrix, and scrambling an image matrix I by using the replacement matrix₂、I₄Or I₆。

The implementation method of dynamic DNA coding, Feistel transformation and DNA decoding comprises the following steps: grouping the image matrixes to be processed according to 8 groups, and carrying out dynamic DNA coding on each group of pixels; after encoding, each group comprises 32 bases, the groups are divided into two groups of L and R to carry out Feistel transformation, DNA exclusive OR operation is selected as an F function of the Feistel transformation, and a DNA sequence SQ is used as a secret key K of the Feistel transformation; and selecting a DNA coding rule for DNA decoding after Feistel transformation.

The Feistel transformation method comprises the following steps: the plaintext block P is divided into two parts: p ═ L₀，R₀) For each round λ of the encryption process, thislet λ 1, 2.,. eta, the new left and right halves are calculated as follows:

wherein,representing a bitwise XOR operation, F is a round function, K_λIs a subkey of the lambda round; the subkey is derived from the key K and follows a specific key scheduling algorithm.

The dynamic DNA coding is one of the coding rules determined according to the position of the pixel to be coded in the image matrix, and is used for pixel I_i,jThe selected DNA coding rule R_i,jThe calculation is as follows:

R_i,j＝Mod((i-1)*n+j,8)+1 (7)

wherein i belongs to {1,2, …, m }, and j belongs to {1,2, …, n }.

The ciphertext diffusion implementation method comprises the following steps: image matrix P₈Converting into one-dimensional sequence S with length of m × n in line priority order₁,s₂,s₃,…s_m×nAnd the sequence after the ciphertext diffusion is set as SE ═ SE₁,se₂,se₃,…se_m×mThe formula of ciphertext diffusion is as follows:

the initialization element se (0) is 127, l is 1,2, … m n.

The coding rule of the dynamic DNA code is as follows: coded correspondingly according to A → 00, C → 01, G → 10, T → 11, the complementary numbers are pairedAndcomplementary pairing with base pairingAndin agreement, so that the total of 8 coding combinations satisfy the complementary pairing rules, the 8 coding rules are:

the operational rules in dynamic DNA coding are: the rule of exclusive or operation between bases for a → 00, C → 01, G → 10, T → 11 codes according to the complementary pairing rule is:

XOR	A	C	G	T
					A	A	C	G	T
C	C	A	T	G
					G	G	T	A	C
T	T	G	C	A

the rules of addition between bases are:

ADD	A	C	G	T
					A	A	C	G	T
C	C	G	T	A
					G	G	T	A	C
T	T	A	C	G

the rules of subtraction between bases are:

the invention has the beneficial effects that: based on a Feistel network and a dynamic DNA coding technology, the method is realized by adopting a structure of 'displacement-diffusion-scrambling'; firstly, calculating a hash value of an original plaintext image by using a Keccak algorithm to serve as an initial value of a hyper-chaotic system, and generating a Hill encryption matrix by using a chaotic sequence generated by the hyper-chaotic system to replace pixels of the original image; secondly, using DNA coding operation as an F function of the Feistel network, using a DNA sequence library as a key K of the Feistel network, and realizing image pixel value diffusion by means of the Feistel network; and finally, further diffusing through ciphertext feedback. The invention makes the ciphertext more random and anti-attack through three rounds of chaos scrambling-DNA coding-Feistel transformation-DNA decoding encryption modes, and ensures that the encrypted ciphertext is safer; realizing scrambling transformation of image pixel positions and diffusion of pixel values through Hill replacement, Feistel transformation, chaotic scrambling and dynamic DNA coding; the DNA sequence operation is used as an F function of Feistel transformation, and the encryption round number is reduced through multiple scrambling and DNA encoding and decoding, so that the effect of multiple rounds of encryption is achieved. The experimental result shows that the method can effectively encrypt the image and has the outstanding characteristics of strong plaintext sensitivity, large key space, excellent ciphertext statistical property and the like; three rounds of Feistel transformation, scrambling and DNA coding and decoding can effectively resist plaintext attack, differential attack and statistical attack, and have good safety and application potential.

Drawings

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

Fig. 1 is an encryption flow diagram of the present invention.

Fig. 2 is a structural diagram of a Feistel network.

FIG. 3 is a diagram of an original image and an encrypted image according to the present invention; (a) the original image, (b) the encrypted image, (c) the decrypted image under the wrong key, and (d) the encrypted image after the key is changed.

FIG. 4 is a gray level histogram of a Lena image of the present invention before and after encryption; (a) lena pre-encryption gray level histogram, and (b) Lena post-encryption gray level histogram.

FIG. 5 is a comparison of horizontal, vertical and diagonal neighboring pixel correlation; (a) the horizontal direction of the original image, (b) the horizontal direction of the encrypted image, (c) the vertical direction of the original image, (d) the vertical direction of the encrypted image, (e) the diagonal direction of the original image, and (f) the diagonal direction of the encrypted image.

Detailed Description

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

As shown in fig. 1, an image encryption method based on Feistel network and dynamic DNA encoding includes the following steps:

the method comprises the following steps: converting a grayscale image of size m × n into a two-dimensional image matrix I of size m × n₁。

Step two: image matrix I is calculated by Keccak algorithm adopting hash function₁Obtaining an initial value of the chaotic system through the hash value K, and bringing the initial value into the hyperchaotic Chen system to generate a sequence B containing L elements₁、B₂、B₃And B₄。

As one of the HASH functions, the Keccak algorithm is one of the most basic modules in modern cryptography based on a sponge structure, and generates a HASH value of a fixed length with a message value of an arbitrary length as an input. However, the compression of the hash function is not the traditional compression, the hash function is an irreversible compression, and once the hash function is subjected to hash operation, the obtained result cannot be restored to the original text. The key generated by the hash value is completely different from the original image even if the original image has very slight change, and the encryption key is completely different. Combines the original image information with the key, and has brute force attack resistance of 2⁵¹²Therefore, the encryption method can effectively resist known plaintext, chosen plaintext attack and brute force attack.

Chaos is a unique nonlinear phenomenon, has a series of excellent characteristics such as good pseudo-randomness, unpredictability of tracks, extreme sensitivity to initial state and structural parameters, non-repeatability of iteration and the like, and is widely applied to secret communication. Compared with a low-dimensional chaotic system, the high-dimensional hyper-chaotic system has more positive Lyapunov teaching, more complex and unpredictable dynamic characteristics, can effectively solve the problem of dynamic characteristic degradation of the low-dimensional chaotic system, and has strong confidentiality, simple algorithm implementation and large key space. In 2005, lie et al constructed a hyperchaotic Chen system by state feedback control, the equation of which is:

wherein x, y, z and w are state variables of the system; a. b, c, d and r are control parameters of the system, and when a is 35, b is 3, c is 12, d is 7 and r is more than or equal to 0.085 and less than or equal to 0.798, the system shows hyper-chaotic motion.

Image matrix I adopting Keccak algorithm of hash function₁Generating 512-bit hash value K, dividing the hash value into 64 groups of 8 bits, and recording K ═ K { (K) }₁,k₂,k3,…,k₆₄}; calculating an initial value x of the hyperchaotic Chen system according to the following formula₀、y₀、z₀、w₀：

Wherein, v is 6(i-1), u is 1,2, 3, 4,representing an exclusive or operation; x'₀、y′₀、z′₀、w′₀Setting an initial value of a given parameter; round (h)_i) Rounding to an integer function.

When the hyperchaotic Chen system is in a hyperchaotic state, the initial value x of the chaotic system is set₀,y₀,z₀,w₀The method comprises the steps of leading in a hyperchaotic Chen system, discarding initial end data through iteration, sequentially taking out L (m) multiplied by n non-repetitive values from the initial end data, and obtaining 4 discrete real value hyperchaotic sequences A₁:{a₁₁,a₁₂,…,a_1L}、A₂:{a₂₁,a₂₂,…,a_2L}、A₃:{a₃₁,a₃₂,…,a_3LAnd A₄:{a₄₁, a₄₂,…,a_4L}; hyper-chaotic sequence A₁、A₂、A₃And A₄For unifying the value range of real number sequence, only taking the fractional part of 4 sequences to obtain new sequences B₁:{b₁₁,b₁₂,…,b_1L}、B₂:{b₂₁,b₂₂,…,b_2L}、B₃：{b₃₁,b₃₂,…,b_3LAnd B₄：{b₄₁,b₄₂,…,b_4LAnd i.e.:

wherein [ A ]_i]Representing the hyperchaotic sequence A_iMod (x, y) is a remainder operation, which is an operation of dividing one integer x by another integer y in an integer operation.

Step three: sequence B generated by hyperchaotic Chen system₄Constructing T-m n/4 Hill encryption matrixes KM₁、KM₂、…、KM_T。

Hill encryption (Hill) is an alternative cipher that uses the principles of the fundamental matrix theory, invented by Lester s. Hill passwords are a class of substitute passwords, and have the advantages of being capable of hiding plaintext letter frequency, concise in representation, easy to realize by a computer, capable of using reversible matrix encryption and decryption and the like, and capable of being applied to image encryption. The key of the Hill cipher is the encryption matrix, and if the encryption matrix is not reversible, the cipher text cannot be restored into the plaintext. In order to avoid strong correlation among the elements of the encryption matrix, the invention uses the hyperchaotic sequence to construct the self-inverting encryption matrix to reduce the correlation among the encryption matrices, thereby making the ciphertext difficult to crack.

Dividing a self-inversed Hill encryption matrix M into four parts:

wherein,

(1) the hyperchaotic Chen system is used as a pseudo-random number generator to generate a hyperchaotic sequence, and a hyperchaotic sequence B is sequentially generated from the hyperchaotic sequence₄Select 4 elements in, fill M₁₁。

(2) Sub-matrix M₁₂＝I-M₁₁。

(3) Sub-matrix M₂₂＝-M₁₁。

(4) Sub-matrix M₂₁＝I+M₁₁。

(5) Four sub-matrices M to be generated₁₁、M₁₂、M₂₂、M₂₁Combining to obtain reversible Hill encryption matrix M, and assigning it to Hill encryption matrix KM₁。

The Hill encryption matrix M generated by the chaos theory has good randomness according to each element of the chaos characteristic, cannot simply calculate the intrinsic regularity, and has high encryption strength, so that the generated key matrix has more robustness based on the block matrix M11. The so generated self-inverse matrix is used for the key as an encryption system to avoid solving the inverse matrix.

Step four: for image matrix I₁Carrying out encryption replacement through the constructed Hill encryption matrix according to every 4 pixels to obtain an image matrix I₂。

Image matrix I to be encrypted₁One group of every 4 pixels, each group of pixels being converted into a 4 x 1 matrix I_4*1Each set of images is hilt encrypted by constructing a 4 x 4 reversible hilt encryption matrix KM. The encryption formula is as follows:

wherein E is a result matrix of Hill encryption, E_11～41Is a pixel of matrix E, I_11～41For a group of pixels, k, to be encrypted_11-44Is an element of the hill encryption matrix KM; multiplicative inverse matrix KM using Hill-encryption matrix KM^-1And (3) decrypting the ciphertext: i ═ KM^-1*E)mod256＝(KM*E)mod256。

Step five: downloading ID numbers from GenBank database as: the DNA sequence of NZ _ LOZQ01000042 was named DNA sequence SQ by cutting 6mn bases from the S-th base.

Sequence SQ is used for Feistel transformed key K.

Step six: sequence B generated according to hyperchaotic Chen system₁Obtaining a permutation index sequence X according to ascending order, filling the permutation index sequence X according to m values of each row to obtain a permutation matrix, and scrambling an image matrix I by using the permutation matrix₂To obtain a scrambled image matrix I₃。

Step seven: image matrix I₃Grouping every 8 groups, and carrying out dynamic DNA coding on each group of pixels; after the encoding, the image data is processed,each group comprises 32 bases, and is divided into two groups of L and R for Feistel transformation, DNA exclusive OR operation is selected as an F function of the Feistel transformation, and a DNA sequence SQ is used as a secret key K of the Feistel transformation; selecting a DNA coding rule to perform DNA decoding after Feistel transformation, and recovering the DNA coding rule into a matrix form to obtain an image matrix I₄And finishing the first round of scrambling and transformation.

Luby and Rackoff in 1988 firstly proposed a method for constructing pseudo-random permutation by using a Feistel network, which realizes sufficient diffusion and confusion of encrypted data by alternately using two basic operations of substitution and permutation and has better security and encryption efficiency. The Feistel cipher structure is a symmetric structure used in block ciphers. Many conventional block ciphers employ the Feistel structure, including DES, FEAL, RC5, etc. The Feistel structure is a typical iterative structure and is also a cipher transformation in a product form, diffusion and chaos can be fully realized, and a high-strength cipher system is formed.

Fig. 2 shows a structure diagram of a Feistel network, where a plaintext block P is divided into left and right blocks in a Feistel transform, where P is (L)₀， R₀) for each round of the encryption process λ, where λ is 1,2, η, the new left and right halves are generated as follows:

wherein,representing a bitwise XOR operation, F is a round function, K_λIs the subkey of the lambda-th round. The subkey is derived from the key K and follows a specific key scheduling algorithm.

for Feistel network structure, the round function F in encryption system is used for diffusing input bit into output, then the plaintext information can be diffused into all the groups, every information can be diffused into other subgroups, when the number of encryption rounds is η, all the information can be diffused into subgroups.

The DNA molecule consists of four deoxynucleotides, respectively: adenine (A), cytosine (C), guanine (G), thymine (T). For two single-stranded DNA molecules, a stable DNA molecule can be formed by hydrogen bonding between nucleotides. The chemical structure of the bases determines the principle of base complementary pairing, also known as Watson-Crick base pairing, i.e., A and T are paired by two hydrogen bonds and G and C are paired by three hydrogen bonds. This natural quaternary combination is just like the binary formed by switching semiconductors. Therefore, information can be stored and calculated using the base sequence combinations. A nucleic acid database is a database of all known nucleic acid information sets, and includes nucleotide sequences, single nucleotide polymorphisms, structures, properties, and related descriptions of nucleic acids. The database file may be obtained from a bioinformatic resource center over a computer network. The ID number of a sequence in a database is called a sequence code, and it has uniqueness and permanence. With the rapid development of sequencing technologies, the size of nucleic acid databases is growing exponentially, doubling on average less than 9 months. 15500 species of sequences are included in EMBL in 1 month 1998, the number of the sequences exceeds one million, and more than 50% of the sequences are sequences of model organisms. The number of publicly available DNA sequences has been over 1.63 hundred million by far. Such a huge database is equivalent to a natural codebook. Provides a brand new idea and solution for the image encryption technology.

In an image encryption algorithm, in order to achieve the purpose of pixel aliasing and diffusion, the following rules are defined: complementary digit pairings if the corresponding coding is performed according to A → 00, C → 01, G → 10, T → 11Andcomplementary pairing with base pairingAndand (5) performing anastomosis. Thus, there are 8 coding combinations that satisfy the complementary pairing rules. For grayscale images, the grayscale value of each pixel can be represented by an 8-bit binary number, if DNA coding is used, only 4 base sequences need to be encoded. After conversion into a DNA sequence, the conversion rules for the DNA sequence can be applied to image processing. In the encrypted image, the following base operation rule is defined for the purpose of disturbing the pixel values.

TABLE 1.8 coding rules

Rules

1

2

3

4

5

6

7

8

00

A

C

G

C

G

T

01

C

G

A

T

C

G

10

G

C

T

A

G

C

11

T

G

C

G

C

A

The algorithm rules between bases are given in tables 2-4 for the A → 00, C → 01, G → 10, T → 11 codes according to the complementary pairing rules, and similar algorithm rules can be established for other codes as well.

TABLE 2 XOR algorithm

XOR	A	C	G	T
					A	A	C	G	T
C	C	A	T	G
					G	G	T	A	C
T	T	G	C	A

TABLE 3 addition rule

ADD	A	C	G	T
					A	A	C	G	T
C	C	G	T	A
					G	G	T	A	C
T	T	A	C	G

TABLE 4 Subtraction rules

Sub	A	C	G	T
					A	A	T	G	C
C	C	A	T	G
					G	G	C	A	T
T	T	G	C	A

In the case of local pixel values of the image being the same, for example, there are many "00", and many "a" occur when the conventional DNA coding rule is used, such a disadvantage becomes very obvious in natural images, especially medical images. If the medical image is encoded using rule 1 in Table 1, the "A" base is the most abundant in the converted DNA sequence. Fixed DNA coding is used in the image encryption process, that is, the bit distribution of the plaintext is not disturbed.

The dynamic DNA coding technique is to select one of the coding rules in Table 1 according to the position of the pixel to be coded in the image matrix, i.e. to the pixel I_i,jThe selected DNA coding rule R_i,jThe calculation is as follows:

R_i,j＝Mod((i-1)*n+j,8)+1 (7)

wherein i belongs to {1,2, …, m }, and j belongs to {1,2, …, n }.

Since each pixel value can be represented by an 8-bit binary, each pixel is encoded as 4 bases, and thus the length of the encoded sequence is 4 mn. Such as the original imageIs 108, represented in binary [01101100 ]]According to the dynamic coding technique, the rule should be chosen to be R_37,54The coding was performed according to DNA coding rule 7, and the DNA sequence of the pixel was obtained as [ CGAT ═ 7]。

Step eight: sequence B generated according to hyperchaotic Chen system₂Similar to the step six pairs of image matrices I₄Scrambling to obtain an image matrix P₅(ii) a For image matrix P₅Performing dynamic DNA encoding, Feistel transformation and DNA decoding according to the method of the seventh step and recovering the dynamic DNA encoding, Feistel transformation and DNA decoding into a matrix form to obtain an image matrix P₆And finishing the second round of scrambling and transformation.

Step nine: sequence B generated according to hyperchaotic Chen system₃Similar to the step six pairs of image matrices I₆Scrambling to obtain an image matrix P₇(ii) a For image matrix P₇Performing dynamic DNA encoding, Feistel transformation and DNA decoding according to the method of the seventh step and recovering the dynamic DNA encoding, the Feistel transformation and the DNA decoding into a matrix to obtain an image matrix P₈And completing the third round of scrambling and transforming.

The ciphertext diffusion operation enables tiny changes of the plaintext to be diffused to the whole ciphertext, so that the relation between the plaintext image and the ciphertext image is disturbed, the cryptology attack means such as plaintext selection can be effectively resisted, and the ciphertext diffusion is realized. Image matrix P₈Converting into one-dimensional sequence S with length of m × n in line priority order₁,s₂,s₃,…s_m×nAnd the sequence after the ciphertext diffusion is set as SE ═ SE₁,se₂, se₃,…se_m×mThe formula of ciphertext diffusion is as follows:

the initialization element se (0) is 127, l is 1,2, … m n.

The decryption algorithm is the inverse of the above process. And will not be further described herein. The algorithm is also suitable for the encryption of color images, and only the RGB decomposition processing is needed to be carried out on the pixel values.

The invention adopts a three-wheel scrambling-diffusing structure, which mainly comprises: firstly, performing Hill matrix permutation, namely constructing a Hill encryption matrix by means of a sequence generated by a hyperchaotic Chen system to permute an image matrix; secondly, pixel position scrambling, namely scrambling and changing the pixel position of the image by using a replacement index formed by a chaos sequence generated by a hyperchaotic Chen system; thirdly, dynamic DNA coding and Feistel transformation are carried out, image pixels are dynamically coded and converted into DNA sequences; and adopting DNA sequence operation as an F function, and taking a sequence in a DNA sequence library as a key K to realize grouping Feistel transformation on the converted DNA sequence. And finally, performing diffusion through ciphertext feedback.

For the present invention, the feasibility of the invention was verified using Matlab software programming. Taking a standard 256 x 256 lena grey scale image as the original image, the key comprises the given value x'₀＝y′₀＝z′₀＝w′₀0.00000005; DNA sequence ID No. NZ _ LOZQ01000042 of nucleic acid database, start position S ═ 1. The image is encrypted by the present invention, and the original image and the encrypted image are shown in fig. 3(a) and 3(b), respectively.

If the calculation accuracy is 10^-14The space of the key can reach 10¹⁰⁰It can be seen that the present invention has sufficient room to resist exhaustive attacks. To test the sensitivity of the key, the primary value x 'is mapped to the hyperchaotic Chen System'₀The value of (d) is increased by 0.00000001, and the other keys are unchanged. The encrypted image is decrypted using the modified key, and the resulting decryption result is shown in fig. 3 (c). As can be seen from fig. 3(c), the original image cannot be correctly decrypted even when the key is slightly changed. Thirdly, the image is re-encrypted by using the modified key to obtain an encrypted image as shown in the figure3(d), as can be seen from comparison with fig. 3(b), the difference rate of corresponding pixel points between two ciphertext images is above 99.62%, and it can be seen that the present invention has strong key sensitivity, can resist violent attack, and has good key security.

The statistical information of the image can expose the distribution rule of the gray value of the original image to a certain extent, and whether the statistical distribution of the original image can be changed is also a crucial index in image encryption. The arithmetic operation of the algorithm on the gray value of the image pixel is to resist the attack of an attacker on gray statistics. As shown in fig. 4, it can be obtained from the experimental results that the xor processing and the permutation operation make the gray distribution of the obtained encrypted image very uniform, which shows that the algorithm has a very good capability of resisting statistical analysis, so that an attacker cannot analyze the original gray value distribution range.

Further, the variance of the histogram is introduced to measure the uniformity of the pixel distribution of the ciphertext image. A lower variance value indicates a higher uniformity of the pixel distribution. And encrypting the same plaintext image by using different keys, and calculating the variance value of the two corresponding ciphertext images. If the variance values of the two ciphertexts are close, it means that the cipher text image has a higher uniform histogram when the key is changed. The histogram variance is calculated as follows:

where Z is an image histogram value vector Z ═ Z₀,z₁,…,z₂₅₆}，z_iAnd z_jIs the number of pixels having gray values i and j, and n is 256.

The histogram variance of the plaintext image is 39851.33, the above-given key is applied, the histogram variance of the encrypted image is 283.7109, and the initial value x 'of the chaotic system is changed'₀The variance is 231.7422, which indicates that the ciphertext pixels obtained by the encryption method of the present invention are uniformly distributed.

The correlation coefficient is calculated as follows:

wherein,

TABLE 5 neighboring Pixel correlation comparison

Generally, the correlation of pixels in the original image is relatively large, and in order to prevent statistical analysis, the correlation of adjacent pixels must be reduced. 2500 pairs of pixels of the encrypted image and the original image were randomly selected using equation (9), respectively, and the correlation between the pixels in the horizontal, vertical, and diagonal directions was measured, and the results are shown in table 5. As can be seen from table 5, there is a large correlation between the image pixels before encryption, and the correlation between the image pixels after encryption is greatly reduced. This indicates that its neighboring pixels have been substantially uncorrelated and that the statistical features of the original image have been diffused into the random ciphertext image. The correlation coefficient between the original image and the encrypted image is-0.00822 by calculation. Table 5 and fig. 5 show the correlation comparison between adjacent pairs of pixels of the original image and the encrypted image.

The differential attack is to slightly change the original image and then encrypt the original image and the changed image. The association between the original image and the encrypted image is obtained by comparing the two encrypted images. Two criteria, the rate of change of the Number of Pixels (NPCR) and the rate of average intensity change (UACI), are typically used to measure whether an encryption method can withstand differential attacks.

Wherein m and n represent the length and width of the image respectively, and C' represent two ciphertext images corresponding to plaintext images with only one pixel point having difference. For the pixel of (i, j), if C (i, j) ≠ C' (i, j), D (i, j) is 1, otherwise D (i, j) is 0. For Lena images, the NPCR and UACI values of the present invention are 99.6185% and 28.7344%. Therefore, the invention has good differential attack resistance.

The information entropy is an index of testing uncertainty, and the calculation formula is as follows:

here, p (i) represents the probability of occurrence of the information i. For a grayscale image, there are 256 states of information, a minimum value of 0 and a maximum value of 255. Then, according to the above formula, when the information entropy is 8, it indicates that the information is completely random. That is, the larger the ciphertext information entropy, the more secure the information. The information entropy of the ciphertext image obtained by encrypting the Lena image is 7.989, which shows that the information leakage of the ciphertext is extremely small, and further proves the safety of the method.

In general, assuming that the attacker knows the cryptographic system used, a typical attack in general comprises four attack types, depending on the information obtained by the attacker: ciphertext-only attacks, known-plaintext attacks, select-plaintext attacks, and select-ciphertext attacks.

The strength of the four attack types is increased in sequence, only the ciphertext attack is the weakest, the selective ciphertext attack is the strongest attack, if a cryptosystem can resist the selective ciphertext attack, the cryptosystem can be considered to resist the selective ciphertext attackThe remaining three attack modes can be resisted. The invention is very sensitive to the initial parameters and values, the sequence B being generated once one of them is changed₁、B₂、B₃And B₄The sequences are always different, further, in the Feistel permutation and ciphertext diffusion stage, the encrypted value is not only related to the plaintext, but also related to the ciphertext of the previous pixel. This means that the present invention is resistant to chosen plaintext or ciphertext attacks.

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

Claims

1. An image encryption method based on a Feistel network and dynamic DNA coding is characterized by comprising the following steps:

Step two: image matrix I is calculated by Keccak algorithm adopting hash function₁Obtaining an initial value of the chaotic Chen system through the hash value K, and bringing the initial value into the hyperchaotic Chen system to generate sequences B which respectively contain L-m multiplied by n elements₁、B₂、B₃And B₄；

Step three: sequence B generated by hyperchaotic Chen system₄Structure of the deviceA Hill encryption matrix KM₁、KM₂、…、KM_T；

2. The Feistel network and dynamic DNA coding based image encryption method according to claim 1, wherein the sequence B is₁、B₂、B₃And B₄The generation method comprises the following steps: the hyperchaotic Chen system has the following equation:

when the hyperchaotic Chen system is in a hyperchaotic state, the initial value x of the chaotic system is set₀,y₀,z₀,w₀The initial end data is omitted by iteration in the hyperchaotic Chen system,taking out the non-repeated values of L-m x n to obtain the hyperchaotic sequences A of 4 discrete real values₁:{a₁₁,a₁₂,…,a_1L}、A₂:{a₂₁,a₂₂,…,a_2L}、A₃:{a₃₁,a₃₂,…,a_3LAnd A₄:{a₄₁,a₄₂,…,a_4L}; hyper-chaotic sequence A₁、A₂、A₃And A₄For unifying the value range of real number sequence, only taking the fractional part of 4 sequences to obtain new sequences respectively B₁:{b₁₁,b₁₂,…,b_1L}、B₂:{b₂₁,b₂₂,…,b_2L}、B₃：{b₃₁,b₃₂,…,b_3LAnd B₄：{b₄₁,b₄₂,…,b_4LAnd i.e.:

3. The Feistel network and dynamic DNA coding-based image encryption method according to claim 1, characterized in that in the third step, a sequence B generated by a hyperchaotic Chen system is adopted₄Structure of the deviceA Hill encryption matrix KM₁、KM₂、…、KM_TThe method comprises the following steps: given a 4 x 4 empty matrix M, the matrix M is divided into four parts:

wherein,

(2) Sub-matrix M₁₂＝I-M₁₁；

(3) Sub-matrix M₂₂＝-M₁₁；

(4) Sub-matrix M₂₁＝I+M₁₁；

4. The Feistel network and dynamic DNA coding based image encryption method according to claim 1, wherein the encryption replacement method in step four is: image matrix I to be encrypted₁One group of every 4 pixels, each group of pixels being converted into a 4 x 1 matrix I_4*1And constructing a reversible Hill encryption matrix KM of 4 multiplied by 4, and performing Hill encryption on each group of images, wherein the encryption formula is as follows:

I＝(KM^-1*E)mod256＝(KM*E)mod256。

5. the Feistel network and dynamic DNA coding based image encryption method of claim 1, wherein the position scrambling is performedThe method comprises the following steps: sequence B in ascending order₁Or B₂Or B₃Obtaining a replacement index sequence X, filling the replacement index sequence X according to m values of each row to obtain a replacement matrix, and scrambling an image matrix I by using the replacement matrix₂、I₄Or I₆。

6. The Feistel network and dynamic DNA coding-based image encryption method according to claim 1, wherein the dynamic DNA coding, Feistel transformation and DNA decoding are implemented by: grouping the image matrixes to be processed according to 8 groups, and carrying out dynamic DNA coding on each group of pixels; after encoding, each group comprises 32 bases, the groups are divided into two groups of L and R to carry out Feistel transformation, DNA exclusive OR operation is selected as an F function of the Feistel transformation, and a DNA sequence SQ is used as a secret key K of the Feistel transformation; and selecting a DNA coding rule for DNA decoding after Feistel transformation.

7. The Feistel network and dynamic DNA coding based image encryption method according to claim 1, wherein the Feistel transformation method is: the plaintext block P is divided into two parts: p ═ L₀，R₀) for each round of the encryption process λ, where λ is 1, 2.. eta., η, the new left and right halves are generated as follows:

8. The Feistel network and dynamic DNA coding based image encryption method of claim 1, which is characterized in thatCharacterized in that the dynamic DNA coding is one of the selection coding rules determined according to the position of the pixel to be coded in the image matrix, and is used for pixel I_i,jThe selected DNA coding rule R_i,jThe calculation is as follows:

R_i,j＝Mod((i-1)*n+j,8)+1 (7)

wherein i belongs to {1,2, …, m }, and j belongs to {1,2, …, n }.

9. The Feistel network and dynamic DNA coding-based image encryption method according to claim 1, wherein the ciphertext diffusion is implemented by: image matrix P₈Converting into one-dimensional sequence S with length of m × n in line priority order₁,s₂,s₃,…s_m×nAnd the sequence after the ciphertext diffusion is set as SE ═ SE₁,se₂,se₃,…se_m×mThe formula of ciphertext diffusion is as follows:

the initialization element se (0) is 127, l is 1,2, … m n.

10. The Feistel network and dynamic DNA coding-based image encryption method according to claim 8 or 9, wherein the coding rule of the dynamic DNA coding is: coded correspondingly according to A → 00, C → 01, G → 10, T → 11, the complementary numbers are pairedAndcomplementary pairing with base pairingAndin agreement, so that the total of 8 coding combinations satisfy the complementary pairing rules, the 8 coding rules are:

XOR A C G T A A C G T C C A T G G G T A C T T G C A

the rules of addition between bases are:

ADD A C G T A A C G T C C G T A G G T A C T T A C G

the rules of subtraction between bases are: