CN108365947B

CN108365947B - A kind of image encryption method based on Feistel network Yu dynamic DNA encoding

Info

Publication number: CN108365947B
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: 2019-05-24
Anticipated expiration: 2038-03-05
Also published as: CN108365947A

Abstract

The invention proposes a kind of image encryption method based on Feistel network Yu dynamic DNA encoding, for the cryptographic Hash for using Keccak algorithm to calculate original plaintext image as the initial value of Hyperchaotic Chen System, the chaos sequence generation Xi Er scrambled matrix generated using Hyperchaotic Chen System replaces the pixel of original image；Use DNA encoding operation as Feistel networkFFunction, key of the DNA sequence dna library as Feistel networkKRealize 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 transformation-DNA decoding ", the diffusion of the scramble transformation and pixel value of image pixel positions is realized, multiple scramble reduces the wheel number of encryption with DNA encoding, decoding.The present invention can effectively encrypt image, have plaintext sensibility strong, can be reasonably resistant to plaintext attack, differential attack and statistical attack.

Description

A kind of image encryption method based on Feistel network Yu dynamic DNA encoding

Technical field

The present invention relates to the technical fields of image encryption, more particularly to one kind is based on Feistel network and dynamic DNA encoding Image encryption method.

Background technique

Information security issue has become influence national security, social stability, economic development and personal the great of property and asks Topic, it is necessary to take measures to guarantee the integrality of information resources, availability, confidentiality and reliability.Digital picture has intuitive easy Identification, lively, High redundancy, the features such as large data capacity are one of common information interchange modes of people.Due to digital picture Have the characteristics that data volume is big, redundancy is high, existing classics encryption method DES, AES, Feistel and RSA etc. are because of it The reasons such as encryption efficiency is low, and safety is not high, have been unable to meet the needs of image encryption.

With deepening continuously for DNA molecular computing technique and biotechnology research.Scientists discovery nucleic acid sequence has Natural quaternary combination, this is formed by binary class seemingly with semiconductor on-off.It therefore, can with the permutation and combination of nucleotide To carry out information storage and calculating.Ultra-large concurrency, the storage density of ultra-high capacity possessed by DNA and ultralow energy Amount consumption just developed by people for fields such as molecular computing, data storage and cryptographies, and the research of this respect has can The birth of novel computer, new types of data memory and novel cipher system can be eventually led to, a new information revolution is caused. 1999, Gehani etc. proposed a kind of one-time pad mechanism based on DNA, gave method of substitution and two kinds of exclusive or method one time one Close cryptography scheme.2003, Chen etc. constructed a kind of cryptosystem based on DNA molecular sequence；2005, the benefits such as Kazuo Solves key-distribution problem with DNA；2006, Lu Mingxin etc. utilized DNA synthetic technology, DNA clone technology, DNA cloning skill Art and DNA chip technology, and a kind of encryption method based on DNA is proposed in conjunction with theory of computational complexity.2009, Mousa etc. designs a kind of Information hiding scheme,, will under the premise of not changing nucleic acid function using that can compare mapping techniques The arbitrary portion of cipher-text information insertion nucleic acid sequence.In short, the high computation capability and mass data storage capability of DNA, existing There is the limitation of biotechnology and computing technique to provide maltilevel security guarantee for existing DNA encryption method.But these DNA Encryption Algorithm is chiefly used in encryption text information and image information is directly encrypted extremely difficult.In recent years, in conjunction with DNA points The double dominant of son and conventional cipher, 2014, Xu Guangxian etc. proposed a kind of DNA image encryption calculation based on chaotic maps Method.2015, Wang etc. gave a kind of image encryption technology based on 2-Dlogistic mapping and DNA operation.2016, Zhou little An gives a kind of resume image based on DNA random ordering coding and chaotic maps.Chai in 2017 etc. combines DNA to grasp Make, gives a kind of resume image based on chaos.These algorithms only carry out displacement and gray scale to the position of image pixel Value is changed.But bit position change is less, is that could not achieve the purpose that really to spread.

Summary of the invention

Change less, the technical issues of real diffusion could not be reached for conventional images encryption method bit position, this Invention proposes a kind of image encryption method based on Feistel network Yu dynamic DNA encoding, by the two Feistel network and DNA The characteristic of coding organically combines, and constructs Xi Er scrambled matrix to figure by using the hyperchaos series that hyperchaotic system generates As being replaced, scramble and diffusion are carried out to image using chaos index sequence, Feistel network and dynamic DNA encoding technology, And by Cipher Feedback further enhance algorithm obscure and diffusion property.

In order to achieve the above object, the technical scheme of the present invention is realized as follows: it is a kind of based on Feistel network and dynamic The image encryption method of state DNA encoding, its step are as follows:

Step 1: at size being the two-dimensional image array I of m × n by greyscale image transitions that size is m × n₁；

Step 2: image array I is calculated using the Keccak algorithm of hash function₁Hashed value K1, pass through hashed value K1 The initial value of chaotic Chen system is obtained, brings initial value into Hyperchaotic Chen System generation comprising the sequence of L=m × n element B₁、B₂、B₃And B₄；

Step 3: the sequence B generated using Hyperchaotic Chen System₄ConstructionA Xi Er scrambled matrix KM₁、 KM₂、…、KM_T1；

Step 4: to image array I₁According to every one group of 4 pixels, encryption is carried out by the Xi Er scrambled matrix of construction and is set It changes, obtains image array I₂；

Step 5: ID number is downloaded from GenBank database are as follows: the DNA sequence dna of NZ_LOZQ01000042, from the S alkali Ji Chu starts 6mn base sequence of interception and is named as DNA sequence dna SQ；

Step 6: the sequence B generated according to Hyperchaotic Chen System₁, pass through position scramble scramble image array I₂In picture Plain position, the image array I after obtaining scramble₃；

Step 7: by image array I₃Dynamic DNA encoding, Feistel transformation and DNA is carried out to decode and revert to rectangular Formula obtains image array I₄, complete first round scramble and transformation；

Step 8: the sequence B generated according to Hyperchaotic Chen System₂, by position scramble to image array I₄Carry out scramble Obtain image array I₅；To image array I₅Dynamic DNA encoding, Feistel transformation and DNA is carried out to decode and revert to rectangular Formula obtains image array I₆, complete the second wheel scramble and transformation.

Step 9: the sequence B generated according to Hyperchaotic Chen System₃, by position scramble to image array I₆Carry out scramble Obtain image array I₇；To image array I₇Dynamic DNA encoding, Feistel transformation and DNA is carried out to decode and revert to matrix and obtain To image array I₈, complete third round scramble and transformation.

Step 10: according to ciphertext diffusion technique, to image array I₈In each pixel and previous pixel ciphertext into Row XOR operation obtains final image matrix I₉。

The sequence B₁、B₂、B₃And B₄Generation method are as follows: the equation of Hyperchaotic Chen System are as follows:

Wherein, x, y, z and w are the state variable of system；A, b, c, d and r are the control parameter of system, in a=35, b= 3, c=12, d=7 and when 0.085≤r≤0.798, system shows as hyperchaos movement；

Using the Keccak algorithm of hash function to image array I₁512 hashed value K1 are generated, are classified as 64 groups, often 8 bits of group, remember K1={ k₁, k₂, k₃..., k₆₄}；The initial value x of Hyperchaotic Chen System is calculated according to following formula₀、y₀、 z₀And w₀:

Wherein, v=6 (u-1), u=1,2,3,4,Indicate XOR operation；x′₀、y′₀、z′₀、w′₀It is initial for given parameters Value；round(h_u) it is round function；

In the case where Hyperchaotic Chen System is in hyperchaos state, by the initial value x of chaos system₀, y₀, z₀, w₀Bring hyperchaos into Starting end data is cast out by iteration in Chen system, L=m × n unduplicated values is taken out, obtains 4 discrete real numbers It is worth Hyperchaotic Sequence A₁: { a₁₁, a₁₂..., a_1L}、A₂: { a₂₁, a₂₂..., a_2L}、A₃: { a₃₁, a₃₂..., a_3LAnd A₄: { a₄₁, a₄₂..., a_4L}；Hyperchaotic Sequence A₁、A₂、A₃And A₄For the codomain of unified sequence of real numbers, the fractional part of 4 sequences is only taken, is obtained It is respectively B to new sequence₁: { b₁₁, b₁₂..., b_1L}、B₂: { b₂₁, b₂₂..., b_2L}、B₃: { b₃₁, b₃₂..., b_3LAnd B₄: {b₄₁, b₄₂..., b_4L, it may be assumed that

Wherein, [A_i] indicate to take Hyperchaotic Sequence A_iInteger part, mod () be complementation operation.

The sequence B generated in step 3 using Hyperchaotic Chen System₄Construct T1=[m*n/4] a Xi Er scrambled matrix KM₁、KM₂、...、KM_T1Method are as follows: matrix M is divided into four parts by given one 4 × 4 empty matrix M:

Wherein,

(1) Hyperchaotic Chen System generates Hyperchaotic Sequence as pseudorandom number generator, successively from Hyperchaotic Sequence B₄ 4 elements of middle selection fill M₁₁；

(2) submatrix M₁₂=I-M₁₁；

(3) submatrix M₂₂=-M₁₁；

(4) submatrix M₂₁=I+M₁₁；

(5) by four submatrix M of generation₁₁、M₁₂、M₂₂、M₂₁Merging obtains reversible Xi Er scrambled matrix M, by its assignment To KM₁；

(6) (1)~(5) step is repeated, Xi Er scrambled matrix KM is obtained₂、…、KM_T1。

The method of keyed permutation in the step 4 are as follows: by image array I to be encrypted₁Every 4 pixels are one group, will be every Group pixel is converted into 4 × 1 matrix I_4*1, by the reversible Xi Er scrambled matrix KM of construction 4 × 4, every group of image is wished You encrypt, and encryption formula is as follows:

Wherein, E is the matrix of consequence of Xi Er encryption, E_11~41Pixel, I for matrix E_11~41For one group of pixel to be encrypted, m_11-44For the element of Xi Er scrambled matrix KM；

Use the multiplication inverse matrix KM of Xi Er scrambled matrix KM^-1Ciphertext is decrypted:

I_4*1=(KM^-1* E) mod256=(KM*E) mod256.

The method of the position scramble are as follows: according to ascending order collating sequence B₁Or B₂Or B₃Permutation index sequence X is obtained, will be set It changes index sequence X to be filled to obtain permutation matrix according to m value of every row, with permutation matrix scramble image array I₂、I₄Or I₆。

The dynamic DNA encoding, Feistel transformation and the decoded implementation method of DNA are as follows: press image array to be processed It is grouped according to every 8 one group, dynamic DNA encoding is carried out to each group of pixel；After coding, every group includes 32 bases, is divided into L Feistel transformation, the F function for selecting DNA XOR operation to convert as Feistel are carried out with R Liang Ge group, DNA sequence dna SQ makees For the key K of Feistel transformation；Selection DNA encoding rule carries out DNA decoding after Feistel transformation.

The method of the Feistel transformation are as follows: clear packets P is divided into left and right two parts: P=(L₀, R₀), for adding The each round λ of close process, λ=1,2 ..., η, new left-half and right half part calculate generation according to the following rules here:

Wherein,Indicate step-by-step XOR operation, F is round function, K_λIt is the sub-key of λ wheel；Sub-key is derived from key K, and follow specific cipher key schedule algorithm.

The dynamic DNA encoding be according to pixel to be encoded in image array position in a matrix determine selection coding One kind of rule, to pixel I_i,jSelected DNA encoding rule R_i,jIt calculates as follows:

R_i,j+ 1 (7)=Mod ((i-1) * n+j, 8)

Wherein, i ∈ { 1,2 ..., m }, j ∈ { 1,2 ..., n }.

The implementation method of the ciphertext diffusion are as follows: by image array I₈It is m × n according to the length that is sequentially converted into of row major One-dimensional sequence S={ s₁,s₂,s₃,…s_m×n, if the sequence after ciphertext diffusion is SE={ se₁,se₂,se₃,…se_m×m, it is close The formula of text diffusion is as follows:

Wherein, element se (0)=127, l=1 is initialized, 2 ... m*n.

The coding rule of the dynamic DNA encoding are as follows: according to A → 00, C → 01, G → 10, T → 11 carry out corresponding coding, Then complement digital matchesAndWith the complementary pairing of base-pairAndIt coincide, shares 8 kinds in this way Coded combination meets complementary pairing rule, 8 kinds of coding rules are as follows:

Rule

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

；

Operation rule in dynamic DNA encoding are as follows: according to complementary pairing rule, for A → 00, C → 01, G → 10, T → 11 encode, the XOR operation rule between base are as follows:

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

；Addition rule between base are as follows:

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

；Subtraction rule between base are as follows:

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

。

Beneficial effects of the present invention: " displacement-diffusion-scramble " is used based on Feistel network and dynamic DNA encoding technology Structure realize；It uses Keccak algorithm to calculate initial value of the cryptographic Hash of original plaintext image as hyperchaotic system first, adopts The chaos sequence generated with hyperchaotic system generates Xi Er scrambled matrix and replaces to the pixel of original image；Next uses DNA F function of the encoding operation as Feistel network, key K of the DNA sequence dna library as Feistel network, by means of Feistel The diffusion of network implementations image pixel value；It is further spread finally by Cipher Feedback.The present invention passes through three-wheel " Chaotic Scrambling-DNA The cipher mode of coding-Feistel transformation-DNA decoding " keeps ciphertext randomness and attack tolerant stronger, it is ensured that encrypted Ciphertext is safer；Setting for image pixel positions is realized by Xi Er displacement, Feistel transformation, Chaotic Scrambling and dynamic DNA encoding The disorderly diffusion of transformation and pixel value；The F function that DNA sequence dna operation is converted as Feistel, by multiple scramble and DNA encoding, Decoding, to reduce the wheel number of encryption, to achieve the effect that more to take turns encryption.The experimental results showed that the present invention can carry out image The outstanding features such as effectively encryption has plaintext sensibility strong, and key space is big, and ciphertext statistical property is excellent；The Feistel of three-wheel Transformation, scramble and DNA encoding decoding can be reasonably resistant to plaintext attack, differential attack and statistical attack, have safety well Property and application potential.

Detailed description of the invention

In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with It obtains other drawings based on these drawings.

Fig. 1 is encryption flow figure of the invention.

Fig. 2 is the structure chart of Feistel network.

Fig. 3 is original image of the present invention and encrypted image；(a) it is original image, (b) is encrypted image, it is (c) close for mistake Decrypted image under key (d) changes the encrypted image after key.

Fig. 4 is the grey level histogram before and after Lena image encryption of the present invention；(a) grey level histogram before Lena is encrypted, (b) Grey level histogram after Lena encryption.

Fig. 5 compares for horizontal, vertical and diagonal direction adjacent pixel correlation；(a) it is original graph horizontal direction, (b) is Figure horizontal direction is encrypted, (c) is original graph vertical direction, is (d) encryption figure vertical direction, (e) is original graph diagonal direction, It (f) is encryption figure diagonal direction.

Specific embodiment

Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art are obtained every other under that premise of not paying creative labor Embodiment shall fall within the protection scope of the present invention.

As shown in Figure 1, a kind of image encryption method based on Feistel network Yu dynamic DNA encoding, its step are as follows:

Step 1: at size being the two-dimensional image array I of m × n by greyscale image transitions that size is m × n₁。

Step 2: image array I is calculated using the Keccak algorithm of hash function₁Hashed value K1, pass through hashed value K1 The initial value of chaos system is obtained, initial value is brought into Hyperchaotic Chen System and generates the sequence B comprising L element₁、B2、B₃And B₄。

As one kind of hash function, Keccak algorithm based on sponge structure be module most basic in contemporary cryptology it One, using the message value of random length as input, generate the HASH value of regular length.But the compression of hash function is not Traditional compression, hash function are a kind of irreversible compressions, once by Hash operation, obtained result be will be unable to It is reduced to original text.The key generated by cryptographic Hash, even if original image has extremely small variation, the cryptographic Hash for encrypting generation all will Entirely different, encryption key also will be entirely different.Original image information is combined with key, anti-brute force attack is 2⁵¹², therefore this Kind encryption method can effectively resist known-plaintext, chosen -plain attact and brute force attack.

Chaos has good pseudo-randomness, the unpredictability of track, to initial as a kind of peculiar non-linear phenomena A series of good characteristics such as not repeated of state and the extreme sensitivity of structural parameters, iteration, it is logical to be applied to secrecy extensively Letter.Compared with Low-dimensional Chaotic Systems, higher-dimension hyperchaotic system has more positivity Li Ya former times promise husbands to give advice, more complicated and be difficult to pre- The kinetic characteristics of survey, can effectively solve Low-dimensional Chaotic Systems kinetic characteristics degenerate problem, strong security, and algorithm realizes letter Single, key space is big.2005, Lee et al. constructed Hyperchaotic Chen System, equation by STATE FEEDBACK CONTROL are as follows:

Wherein, x, y, z and w are the state variable of system；A, b, c, d and r are the control parameter of system, in a=35, b= 3, c=12, d=7 and when 0.085≤r≤0.798, system shows as hyperchaos movement.

Using the Keccak algorithm of hash function to image array I₁512 hashed value K1 are generated, are classified as 64 groups, often 8 bits of group, remember K1={ k₁, k₂, k₃..., k₆₄}；The initial value x of Hyperchaotic Chen System is calculated according to following formula₀、y₀、 z₀、w₀:

Wherein, v=6 (u-1), u=1,2,3,4,Indicate XOR operation；x′₀、y′₀、z′₀、w′₀It is initial for given parameters Value；round(h_u) it is round function.

In the case where Hyperchaotic Chen System is in hyperchaos state, by the initial value x of chaos system₀, y₀, z₀, w₀Bring hyperchaos into Starting end data is cast out by iteration in Chen system, therefrom successively takes out L=m × n unduplicated values, available 4 Discrete real number value Hyperchaotic Sequence A₁: { a₁₁, a₁₂..., a_1L}、A₂: { a₂₁, a₂₂..., a_2L}、A₃: { a₃₁, a₃₂..., a_3LAnd A₄: { a₄₁, a₄₂,…,a_4L}；Hyperchaotic Sequence A₁、A₂、A₃And A₄For the codomain of unified sequence of real numbers, the decimal of 4 sequences is only taken Part, available new sequence is respectively B₁:{b₁₁,b₁₂,…,b_1L}、B₂:{b₂₁,b₂₂,…,b_2L}、B₃: { b₃₁,b₃₂,…, b_3LAnd B₄: { b₄₁,b₄₂,…,b_4L, it may be assumed that

Wherein, [A_i] indicate to take Hyperchaotic Sequence A_iInteger part, mod (x, y) be complementation operation, be in integer arithmetic In ask an integer x divided by the operation of the remainder of another integer y.

Step 3: the sequence B generated using Hyperchaotic Chen System₄ConstructionA Xi Er scrambled matrix KM₁、 KM₂、…、KM_T1。

Xi Er encryption (Hill) is the substitution ciphers that principle is discussed with fundamental matrix, by Lester S.Hill in nineteen twenty-nine Invention.Hill password is a kind of substitution password, and advantage has and can hide plaintext letter frequency, indicates succinct, is easy to computer reality It is existing, invertible matrix encrypting and decrypting etc. can be used, it can be applied to image encryption.The key of hill cipher is scrambled matrix, If scrambled matrix is irreversible, ciphertext will be unable to be reduced into plain text.In order to avoid strong correlation between scrambled matrix element, this hair It is bright to construct self-converse scrambled matrix using Hyperchaotic Sequence, to reduce the correlation between scrambled matrix, so that ciphertext be made to be difficult to brokenly Solution.

The Xi Er scrambled matrix M of self-converse is divided into four parts:

Wherein,

(1) Hyperchaotic Chen System generates Hyperchaotic Sequence as pseudorandom number generator, successively from Hyperchaotic Sequence B₄ 4 elements of middle selection fill M₁₁。

(2) submatrix M₁₂=I-M₁₁。

(3) submatrix M₂₂=-M₁₁。

(4) submatrix M₂₁=I+M₁₁。

(5) by four submatrix M of generation₁₁、M₁₂、M₂₂、M₂₁Merging obtains reversible Xi Er scrambled matrix M, by its assignment Give Xi Er scrambled matrix KM₁。

The Xi Er scrambled matrix M generated by chaology has good randomness according to chaotic characteristic each element, cannot Inherent regularity is simply found out, encryption intensity is high, is based on matrix in block form M11 in this way, and the cipher key matrix of generation has more Shandong Stick.What is generated in this way removes solution inverse matrix from as encryption system for key from inverse matrix.

Step 4: to image array I₁According to every one group of 4 pixels, encryption is carried out by the Xi Er scrambled matrix of construction and is set It changes, obtains image array I₂。

By image array I to be encrypted₁Every 4 pixels are one group, and every group of pixel is converted into 4 × 1 matrix I_4*1, lead to The reversible Xi Er scrambled matrix KM for crossing construction 4 × 4 carries out Xi Er encryption to every group of image.It is as follows to encrypt formula:

Wherein, E is the matrix of consequence of Xi Er encryption, E_11~41Pixel, I for matrix E_11~41For one group of pixel to be encrypted, k_11-44For the element of Xi Er scrambled matrix KM；Use the multiplication inverse matrix KM of Xi Er scrambled matrix KM^-1Ciphertext is decrypted: I_4*1=(KM^-1* E) mod256=(KM*E) mod256.

Step 5: ID number is downloaded from GenBank database are as follows: the DNA sequence dna of NZ_LOZQ01000042, from the S alkali Ji Chu starts 6mn base sequence of interception and is named as DNA sequence dna SQ.

Sequence SQ is used for the key K of Feistel transformation.

Step 6: the sequence B generated according to Hyperchaotic Chen System₁, it arranges to obtain permutation index sequence X according to ascending order, Permutation index sequence X is filled according to m value of every row can be obtained permutation matrix, with permutation matrix scramble image array I₂In Location of pixels, the image array I after obtaining scramble₃。

Step 7: by image array I₃It is grouped according to every 8 one group, dynamic DNA encoding is carried out to each group of pixel； After coding, every group include 32 bases, be divided into L and R Liang Ge group carry out Feistel transformation, select DNA XOR operation as The F function of Feistel transformation, the key K that DNA sequence dna SQ is converted as Feistel；Selection DNA encoding rule after Feistel transformation DNA decoding is then carried out, and reverts to matrix form and obtains image array I₄, complete first round scramble and transformation.

Luby and Rackoff is put forward for the first time using Feistel network the method for constructing pseudo-random permutation within 1988, it is logical It crosses and two basic operations of replacement and displacement is used alternatingly, realize sufficiently spreading and obscure to encryption data, have and preferably pacify Full property and encryption efficiency.Feistel cryptography architecture is for one of block cipher symmetrical structure.Traditional many groupings are close Code all uses the structure of Feistel, including DES, FEAL, RC5 etc..Feistel structure is a kind of typical iteration knot The cryptographic transformation of structure and a kind of product form can sufficiently realize diffusion and chaotic, the composition very high cryptographic system of intensity.

For Feistel network structure as shown in Fig. 2, in Feistel transformation, clear packets P is divided into left and right two Point, P=(L₀, R₀): for each round λ of ciphering process, λ=1,2 ..., η, new left-half and right half part are pressed here Following rule, which calculates, to be generated:

Wherein,Indicate step-by-step XOR operation, F is round function, K_λIt is the sub-key of λ wheel.Sub-key is derived from key K, and follow specific cipher key schedule algorithm.

For Feistel network structure, the effect of the round function F in encryption system is that the bit of input is diffused into output In, so that it may cleartext information is diffused into all groupings.Information each time is all diffused into other subgroups, when adding When close wheel number is η, all information all be will diffuse into subgroup.Therefore, the core encrypted is the selected of F function, no Same F function is exactly the different Encryption Algorithm for following Feistel structure, and a good F function is for cipher round results to Guan Chong It wants, under normal circumstances, F function needs to meet the following: 1. not requiring reversible: F function not being asked to have inverse function, it is 2. non-thread Property；3. confusion；4. diffusivity；5. avalanche: i.e. as wheel number increases the enhancing of its cipher round results avalanche type；6. bit is independent Property: the encrypted result of a bit is independent of other bit.The present invention using DNA calculate in DNA sequence dna operation as encryption become The round function changed meets the requirement of F function, and mainly it has good Cryptographic Properties.

DNA molecular is made of four kinds of deoxynucleotides, is respectively: adenine (A), cytimidine (C), guanine (G), thymus gland Pyrimidine (T).For two single strand dnas, a stable DNA molecular can be formed by the hydrogen bond between nucleotide.Alkali The chemical structure of base has determined the principle of base pair complementarity, also referred to as Watson-Crick basepairing rule, i.e. A and T it Between by two hydrogen bond formations, pass through three hydrogen bond formations between G and C.This natural quaternary combination, just with semiconductor On-off is formed by binary class seemingly.Therefore, the storage and calculating of information can be carried out with the permutation and combination of base.Nucleic acid number It is a data bank of all known nucleic acid information aggregates according to library, it includes the nucleotide sequence of nucleic acid, and mononucleotide is more The contents such as state property, structure, property and associated description.Database file can pass through computer network from Biological Information Resources center Network obtains.The ID number of sequence in the database is referred to as sequence code, it is with uniqueness and permanently.With sequencing technologies Fast development, the scale of nucleic acid database exponentially increase, average that one times was increased by less than 9 months.1998 1 Month, the sequence of 15500 species is included in EMBL, sequence number is more than 1,000,000, wherein 50% that the above are modes is raw The sequence of object.Up to the present the DNA sequence dna obtained can be disclosed and already exceed 1.63 hundred million.The data of such huge size Library is equivalent to a natural code book.A completely new thinking and solution is provided for image encryption technology.

In resume image, for achieve the purpose that pixel obscure with diffusion, be defined as follows rule: if according to A → 00, C → 01, G → 10, T → 11 carry out corresponding coding, then complement digital matchesAndIt is complementary with base-pair PairingAndIt coincide.8 kinds of coded combinations are shared in this way meets complementary pairing rule.For gray level image, often The gray value of a pixel can be indicated with 8 bits, if using DNA encoding, it is only necessary to encode 4 base sequences Column.It is converted into after DNA sequence dna, so that it may use the transformation rule of DNA sequence dna in image procossing.In encrypted image, it is Achieve the purpose that pixel value is upset, while defining following base operation rule.

1.8 kinds of coding rules of table

Rule

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

According to complementary pairing rule, for A → 00, C → 01, G → 10, T → 11 is encoded, and is provided between a kind of base here Operation rule be shown in Table 2- table 4, for other coding, equally can establish similar operation rule.

Table 2. XOR operation rule

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

3. addition rule of table

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 rule

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 where the local pixel value of image is the same, for example very much " 00 " is had, is using conventional DNA encoding rule When will appear many " A ", such a disadvantage becomes apparent from natural image especially medical image.If made It is encoded with 1 pair of medical image of rule in table 1, " A " base is most in the DNA sequence dna of conversion.In image encryption In the process using fixed DNA encoding, that is to say, that do not upset the bit distribution of plaintext.

Dynamic DNA encoding technology be according to pixel to be encoded in image array position in a matrix determine selection table 1 One kind of coding rule, namely to pixel I_i,jSelected DNA encoding rule R_i,jIt calculates as follows:

R_i,j+ 1 (7)=Mod ((i-1) * n+j, 8)

Wherein, i ∈ { 1,2 ..., m }, j ∈ { 1,2 ..., n }.

Since each pixel value can be encoded as 4 bases by 8 binary representations, each pixel, therefore after coding Sequence length be 4mn.If the 37th row of original image, the pixel values of 54 column are 108, with being represented in binary as [01101100], according to dynamic coding technology, rule should be selected for R_37,54=7, it is encoded, is somebody's turn to do with DNA encoding rule 7 The DNA sequence dna of pixel is [CGAT].

Step 8: the sequence B generated according to Hyperchaotic Chen System₂, step 6 is similar to image array I₄Carry out scramble Obtain image array I₅；To image array I₅Dynamic DNA encoding, Feistel transformation and DNA solution are carried out according to the method for step 7 Code simultaneously reverts to matrix form and obtains image array I₆, complete the second wheel scramble and transformation.

Step 9: the sequence B generated according to Hyperchaotic Chen System₃, step 6 is similar to image array I₆Carry out scramble Obtain image array I₇；To image array I₇Dynamic DNA encoding, Feistel transformation and DNA solution are carried out according to the method for step 7 Code simultaneously reverts to matrix and obtains image array I₈, complete third round scramble and transformation.

Ciphertext dispersion operation makes the minor change of plaintext can be spread to entire ciphertext, to upset plaintext image and ciphertext The relationship of image can be effective against the cryptographies attack means such as selection plaintext, realize ciphertext diffusion.By image array I₈According to Row major is sequentially converted into the one-dimensional sequence S={ s that length is m × n₁,s₂,s₃,…s_m×n, if the sequence after ciphertext diffusion is SE={ se₁,se₂,se₃,…se_m×m, the formula of ciphertext diffusion is as follows:

Wherein, element se (0)=127, l=1 is initialized, 2 ... m*n.

Decipherment algorithm is the inverse process of the above process.It will not be described here.This algorithm is also applied for the encryption of color image, Only the value of pixel need to be subjected to RGB resolution process.

The present invention specifically includes that first, Xi Er matrix permutation using the structure of " scramble-diffusion " of three-wheel, by means of super The sequence construct Xi Er scrambled matrix that chaotic Chen system generates replaces image array；Second, location of pixels scramble, benefit Image pixel positions are carried out scramble variation by the permutation index that the chaos sequence generated with Hyperchaotic Chen System is constituted；Third, Dynamic DNA encoding and Feistel are converted, and are carried out dynamic coding to image pixel, are converted into DNA sequence dna；Using DNA sequence dna operation As F function, the sequence in DNA sequence dna library realizes grouping Feistel transformation to the DNA sequence dna after conversion as key K.Most Afterwards, it is diffused by Cipher Feedback.

For the present invention, the feasibility to verify it is realized using Matlab software programming.Using the 256*256 of standard For lena gray level image as original image, key includes given value x '₀=y '₀=z '₀=w '₀=0.00000005；Nucleic acid data DNA sequence dna the ID number NZ_LOZQ01000042, initial position S=1 in library.Image is encrypted using the present invention, original image With encrypted image respectively as Fig. 3 (a) and 3 (b) is shown.

If computational accuracy is 10^-14, the space of key can reach 10¹⁰⁰, it is seen that the present invention comes with enough spaces Resist exhaustive attack.For the sensitivity of test key, Hyperchaotic Chen System is mapped, by initial value x '₀Value increase 0.00000001, in the case that other keys are constant.Encrypted image, obtained decryption knot are decrypted using modified key Shown in fruit such as Fig. 3 (c).From in Fig. 3 (c) as can be seen that all fail to decrypt correctly out original image after carrying out small change to key Picture.Furthermore using modified key pair image re-encrypted, obtain carrying out shown in encrypted image such as Fig. 3 (d) with Fig. 3 (b) Comparison is it is found that the different rates of corresponding pixel points are 99.62% or more between two ciphertext images, it is seen that the present invention has stronger Key sensitivity, and brute force attack can be resisted, there is good key safety.

Can the statistical information of image can expose the regularity of distribution of original image gray scale to a certain extent, change The statistical distribution of original image is also vital index in image encryption.The algorithm grasps the operation of image pixel gray level value Work is to resist attacker and carrying out gray-scale statistical attack.As shown in figure 4, it can be concluded that, exclusive or handles and displacement from experimental result Operation keeps gained encrypted image intensity profile highly uniform, this illustrates that the algorithm has and resists statistical analysis ability well, Make attacker that can not analyze original gray value distribution.

Further, the variance of histogram is introduced to measure the uniform situation of the pixel distribution of ciphertext image.Variance yields is lower Pixels illustrated distributing homogeneity is higher.It is encrypted using different keys come same plaintext image, and calculates corresponding two ciphertexts The variance yields of image.If the value of the corresponding variance of the two ciphertexts is close, mean when cipher key change, ciphertext image tool There is higher uniform histogram.The calculating of histogram variances is as follows:

Wherein, Z is image histogram value vector Z={ z₀,z₁,…,z₂₅₆, z_iAnd z_jIt is the pixel number that gray value is i and j Amount, n=256.

The histogram variances of plaintext image are 39851.33, using the key that front gives, the histogram side of encrypted image Difference is 283.7109, as the initial value x ' for changing chaos system₀, then variance is 231.7422, and it is close to illustrate that present invention encryption obtains Literary pixel distribution is uniform.

Related coefficient calculates as follows:

Wherein,

5. adjacent pixel correlation of table compares

The correlation of phase pixel is bigger in general original image, to prevent statistical analysis, it is necessary to reduce adjacent pixel Correlation.Encrypted image and each 2500 pairs of pixels pair of original image are randomly selected respectively using formula (9), and it is horizontal, vertical to test it With the pixel interdependence of diagonal direction, the results are shown in Table 5.As can be seen from Table 5, between image pixel before encrypting have compared with Big correlation, after encryption, correlation greatly reduces between image pixel.This shows its adjacent pixel not phase substantially It closes, the statistical nature of original image has been diffused into random ciphertext image.By calculating, original image and encrypted image phase relation Number is -0.00822.Compared with table 5 and Fig. 5 give the correlation between original image and encrypted image adjacent pixel pair.

Differential attack makes subtle change to original image, then the image to original image and after changing encrypts respectively. Contacting between original image and encrypted image is obtained by comparing image of two width after encrypted.Change usually using number of pixels Can whether variability (NPCR) and average change rate of strength (UACI) two standards, which resist difference measuring encryption method, is attacked It hits^[25-26]。

Wherein, m and n respectively represents the length and width of image, and C and a C ' expression two only pixels have differences Plaintext image corresponding to ciphertext image.For the pixel of (i, j), if C (i, j) ≠ C ' (i, j), D (i, j)=1, no Then D (i, j)=0.For Lena image, NPCR and UACI value of the invention is 99.6185% and 28.7344%.Therefore, this hair It is bright that there is good resisting differential attacking ability.

Comentropy is a kind of probabilistic index of test, and calculation formula is as follows:

Here, p (ε_i) indicate information ε_iThe probability of appearance.For gray level image, information ε has 256 kinds of states, minimum Value 0, maximum value 255.Then according to above formula it is found that showing that information is completely random when comentropy is 8.That is, close Literary comentropy is bigger, and information is safer.The comentropy that the present invention encrypts the ciphertext image that Lena image obtains is 7.989, this table The information leakage of bright ciphertext is minimum, further demonstrates safety of the invention.

In general it is assumed that attacker knows used encryption system, according to attacker's information state obtained, general allusion quotation The attack of type includes four kinds of attack types: attack with known plaintext, known plain text attack, chosen -plain attact and chosen ciphertext attacks.

It is above-mentioned four kinds attack type strengths be it is incremental in order, attack with known plaintext is most weak, chosen ciphertext attacks It is a kind of strongest attack, if a kind of cryptographic system can resist chosen ciphertext attacks, it is considered that he can also support Resist its excess-three kind attack pattern.The present invention is very sensitive to initial parameter and initial value, once one in them is changed, then The sequence B of generation₁、B₂、B₃And B₄Etc. sequences be always different, further, Feistel displacement and ciphertext diffusion phase, encryption Value is not only related to plaintext, also related to the ciphertext of previous pixel.It means that the present invention can resist selection plaintext or cipher text Attack.

The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.

Claims

1. a kind of image encryption method based on Feistel network Yu dynamic DNA encoding, which is characterized in that its step are as follows:

Step 2: image array I is calculated using the Keccak algorithm of hash function₁Hashed value K1, mixed by hashed value K1 The initial value of ignorant Chen system brings initial value into Hyperchaotic Chen System generation comprising the sequence B of L=m × n element₁、B₂、B₃ And B₄；

Step 4: to image array I₁According to every one group of 4 pixels, keyed permutation is carried out by the Xi Er scrambled matrix of construction, is obtained To image array I₂；

Step 5: ID number is downloaded from GenBank database are as follows: the DNA sequence dna of NZ_LOZQ01000042, from the S base Start 6mn base sequence of interception and is named as DNA sequence dna SQ；

Step 6: the sequence B generated according to Hyperchaotic Chen System₁, pass through position scramble scramble image array I₂In pixel position It sets, the image array I after obtaining scramble₃；

Step 7: by image array I₃Dynamic DNA encoding, Feistel transformation and DNA is carried out to decode and revert to matrix form and obtain To image array I₄, complete first round scramble and transformation；

Step 8: the sequence B generated according to Hyperchaotic Chen System₂, by position scramble to image array I₄Scramble is carried out to obtain Image array I₅；To image array I₅Dynamic DNA encoding, Feistel transformation and DNA is carried out to decode and revert to matrix form and obtain To image array I₆, complete the second wheel scramble and transformation；

Step 9: the sequence B generated according to Hyperchaotic Chen System₃, by position scramble to image array I₆Scramble is carried out to obtain Image array I₇；To image array I₇Dynamic DNA encoding, Feistel transformation and DNA is carried out to decode and revert to matrix and obtain figure As matrix I₈, complete third round scramble and transformation；

Step 10: according to ciphertext diffusion technique, to image array I₈In each pixel and previous pixel ciphertext carry out exclusive or Operation obtains final image matrix I₉。

2. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In the sequence B₁、B₂、B₃And B₄Generation method are as follows: the equation of Hyperchaotic Chen System are as follows:

Wherein, x, y, z and w are the state variable of system；A, b, c, d and r are the control parameter of system, in a=35, b=3, c= 12, when d=7 and 0.085≤r≤0.798, system shows as hyperchaos movement；

Using the Keccak algorithm of hash function to image array I₁512 hashed value K1 are generated, are classified as 64 groups, every group 8 Bit remembers K1={ k₁,k₂,k₃,…,k₆₄}；The initial value x of Hyperchaotic Chen System is calculated according to following formula₀、y₀、z₀And w₀:

Wherein, v=6 (u-1), u=1,2,3,4,Indicate XOR operation；x′₀、y′₀、z′₀、w′₀For given parameters initial value； round(h_u) it is round function；

In the case where Hyperchaotic Chen System is in hyperchaos state, by the initial value x of chaos system₀,y₀,z₀,w₀Bring hyperchaos Chen into Starting end data is cast out by iteration in system, L=m × n unduplicated values is taken out, it is super to obtain 4 discrete real number values Chaos sequence A₁:{a₁₁,a₁₂,…,a_1L}、A₂:{a₂₁,a₂₂,…,a_2L}、A₃:{a₃₁,a₃₂,…,a_3LAnd A₄:{a₄₁,a₄₂,…, a_4L}；Hyperchaotic Sequence A₁、A₂、A₃And A₄For the codomain of unified sequence of real numbers, the fractional part of 4 sequences is only taken, is obtained new Sequence is respectively B₁:{b₁₁,b₁₂,…,b_1L}、B₂:{b₂₁,b₂₂,…,b_2L}、B₃: { b₃₁,b₃₂,…,b_3LAnd B₄: { b₄₁,b₄₂,…, b_4L, it may be assumed that

3. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In the sequence B generated in step 3 using Hyperchaotic Chen System₄ConstructionA Xi Er scrambled matrix KM₁、 KM₂、…、KM_T1Method are as follows: matrix M is divided into four parts by given one 4 × 4 empty matrix M:

Wherein,

(1) Hyperchaotic Chen System generates Hyperchaotic Sequence as pseudorandom number generator, successively from Hyperchaotic Sequence B₄Middle selection 4 elements fill M₁₁；

(2) submatrix M₁₂=I-M₁₁；

(3) submatrix M₂₂=-M₁₁；

(4) submatrix M₂₁=I+M₁₁；

(5) by four submatrix M of generation₁₁、M₁₂、M₂₂、M₂₁Merging obtains reversible Xi Er scrambled matrix M, is assigned to KM₁；

4. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In the method for keyed permutation in the step 4 are as follows: by image array I to be encrypted₁Every 4 pixels are one group, by every group of picture Element is converted into 4 × 1 matrix I_4*1, by the reversible Xi Er scrambled matrix KM of construction 4 × 4, Xi Erjia is carried out to every group of pixel Close, encryption formula is as follows:

Wherein, E is the matrix of consequence of Xi Er encryption, E_11~41Pixel, I for matrix E_11~41For one group of pixel, m to be encrypted_11-44 For the element of Xi Er scrambled matrix KM；

I_4*1=(KM^-1* E) mod256=(KM*E) mod256.

5. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In the method for the position scramble are as follows: according to ascending order collating sequence B₁Or B₂Or B₃Permutation index sequence X is obtained, by permutation index Sequence X is filled to obtain permutation matrix according to m value of every row, with permutation matrix scramble image array I₂, image array I₄Or figure As matrix I₆。

6. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In the dynamic DNA encoding, Feistel transformation and the decoded implementation method of DNA are as follows: by image array to be processed according to every 8 A one group is grouped, and carries out dynamic DNA encoding to each group of pixel；After coding, every group includes 32 bases, is divided into L and R two A group carries out Feistel transformation, the F function for selecting DNA XOR operation to convert as Feistel, DNA sequence dna SQ conduct The key K of Feistel transformation；Selection DNA encoding rule carries out DNA decoding after Feistel transformation.

7. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In the method for the Feistel transformation are as follows: clear packets P is divided into left and right two parts: P=(L₀, R₀), for ciphering process Each round λ, λ=1,2 ..., η, new left-half and right half part calculate generation according to the following rules here:

Wherein,Indicate step-by-step XOR operation, F is round function, K_λIt is the sub-key of λ wheel；Sub-key is derived from key K, and abides by Follow specific cipher key schedule algorithm.

8. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In, the dynamic DNA encoding be according to pixel to be encoded in image array position in a matrix determine selection coding rule One kind, to pixel I_i,jSelected DNA encoding rule R_i,jIt calculates as follows:

R_i,j+ 1 (7)=Mod ((i-1) * n+j, 8)

Wherein, i ∈ { 1,2 ..., m }, j ∈ { 1,2 ..., n }.

9. the image encryption method according to claim 1 based on Feistel network Yu dynamic DNA encoding, feature exist In the implementation method of the ciphertext diffusion are as follows: by image array I₈Length is sequentially converted into according to row major as the one of m × n Tie up sequence S={ s₁,s₂,s₃,…s_m×n, if the sequence after ciphertext diffusion is SE={ se₁,se₂,se₃,…se_m×m, ciphertext expands Scattered formula is as follows:

Wherein, element se (0)=127, l=1 is initialized, 2 ... m*n.

10. the image encryption method based on Feistel network Yu dynamic DNA encoding according to claim 8 or claim 9, special Sign is, the coding rule of the dynamic DNA encoding are as follows: according to A → 00, C → 01, G → 10, T → 11 carry out corresponding coding, then Complement digital pairingAndWith the complementary pairing of base-pairAndIt coincide, shares 8 kinds of volumes in this way Code character conjunction meets complementary pairing rule, 8 kinds of coding rules are as follows:

Rule 1 2 3 4 5 6 7 8 00 A A C G C G T T 01 C G A A T T C G 10 G C T T A A G C 11 T T G C G C A A

；

Operation rule in dynamic DNA encoding are as follows: according to complementary pairing rule, for A → 00, C → 01, G → 10, T → 11 is compiled Yard, the XOR operation rule between base are as follows:

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

；Addition rule between base are as follows:

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

；Subtraction rule between base are as follows:

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

。