CN107563950A - A kind of safe and efficient digital image encryption method - Google Patents
A kind of safe and efficient digital image encryption method Download PDFInfo
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Abstract
The present invention relates to a kind of safe and efficient digital image encryption method, comprise the following steps：1) using the first~tri- group of required chaos state variable of three-dimensional Chen systems generation encryption；2) scrambling encryption is carried out to original text using first group of chaos state variable, upsets the position of pixel, produce scramble ciphertext；3) encryption is diffused to scramble ciphertext using the second~tri- group of chaos state variable, generates final ciphertext.Invention introduces Chen systems, Chen systems are three-dimensional chaotic systems, possess excellent chaotic characteristic, higher key sensitiveness and unpredictability, and bigger key space, by can effective lifting system encryption performance；The related parameter of original text is introduced to upset the generation process of Scrambling Matrix, introduces high intensity diffusion equation, the security of energy effective guarantee encryption system.
Description
Technical field
The present invention relates to a kind of digital image encryption field, specially a kind of safe and efficient digital image encryption method.
Background technology
It is the multimedia messages of representative because of it using digital picture along with the rapid development of computer and modern communication technology
It is directly perceived, lively, vivid to have the characteristics that, it has also become a kind of most commonly seen expression way in internet information, penetrate into bank,
The every aspect of the lives such as medical treatment, traffic, shopping, social activity.Incident with the importance that becomes increasingly conspicuous is severe all the more
Security threat, because image information often relates to the sensitive information of the various fields such as military, politics, finance, medical treatment, business, its
In opening and interconnecting transmission off the net and storage there is huge potential safety hazard, easily by unauthorized access, steal, distort, hinder
Cut and wait network security attacks.39th time《China Internet network state of development statistical report》It has been shown that, met with safe thing in 2016
User's accounting of part reaches the 70.5% of whole netizens, it is believed that user's ratio of online environment " less safe " and " very dangerous "
Up to 20.3%；The PC quantity that viral trojan horse program was infected in the whole nation is 2.47 hundred million, is monthly influenceed by viral trojan horse program
PC quantity at 40,000,000 between fifty-five million platform；According to another ASSOCIATE STATISTICS, 2015 because of disparate networks information security events
Caused by loss up to 91,500,000,000 yuan.In addition, as a kind of important strategic resource, information security is concerning national politics safety, warp
Ji safety, social safety, cultural security and national defense safety, turn into the important battlefield of 21 century international competition, the guarantor of information security
Barrier ability also turns into an important factor for weighing a national comprehensive strength.Encryption be ensure information safety it is most simple and most effective
Mode.The contemporary cryptology of current main-stream is characterized based on algorithm complexity theory more, and typical algorithm has DES (Data
Encryption Standard), AES (Advanced Encryption Standard) and IDEA (International
Data Encryption Algorithm).But compared with text message, image information has that data volume is huge, important information point
Dissipating, the features such as information redundance is high, above classics AES considers these particularity of image information, therefore not
It is suitable for image encryption.Academia adds image is carried out using such as DES, AES scheduling algorithm for being conventionally used to one-dimensional data encryption
It is close to be referred to as " naivety encryption " (Naive Encryption), it is believed that although this method can also protect the safety of image, source
In the internal characteristicses of digital picture, this method does not simultaneously have practical value.Since the 1980s, some scholar lands
Supervention is existing, and there is be closely connected between chaology and cryptography.Some essential characteristics of chaos system, such as ergodic
(Ergodicity), Combination (Mixing), certainty (Exactness), the sensitiveness to primary condition
(Sensitivity), can get up with chaotic (Confusion) in cryptography and the concept connection of diffusion (Diffusion),
Thus nearly Chaos Immune Algorithm during the last ten years has obtained extensive research.Specific in terms of New chaotic image encryption, the U.S. is learned within 1998
The elaboration of the characteristics of person's Fridrich combinations digital picture itself and Shannon on cryptography, it is proposed that have founder
The replacement of meaning-diffusion image Encryption Architecture, as shown in figure 1, causing industry extensive concern；Subsequent Lian et al. is developed
For classics scramble-diffusion framework, as shown in Fig. 2 in this framework scramble module upset pixel position but keep its pixel
It is worth constant, and spreads module and mask is then carried out to pixel value and spreads the difference of original text, attacked with strengthening system resistance known-plaintext
Hit the ability with chosen -plain attact.Researcher is based on this, it is proposed that a large amount of new and effective resume images,
Pixel-level Chaotic Technology, modified diffusion scheme, scramble diffusion integrated processes, original text related key parameter and bit-level figure
As scramble etc. has emerged a large amount of achievements.
It is corresponding to be, the security of Chaotic Image Encryption Algorithm with the sustainable development of cryptoanalysis and constantly by
To threat, substantial amounts of Chaotic Image Encryption Algorithm is cracked successively.In the resume image that these are cracked, three below
Safety defect often occurs.
First, in traditional Chaotic Image Encryption Algorithm, typically become using One Dimensional Chaotic Maps grey iterative generation chaos state
Amount, and further quantify produce encryption needed for key stream, but the general simple structure of One Dimensional Chaotic Maps, key space it is small, with
Machine performance is relatively poor, and these state variables are often moved back when being quantified as and encrypting required key stream with a certain degree of performance
Change, so that the randomness of caused key stream substantially reduces, and further influence the overall security performance of system；
Secondly, in traditional Chaotic Image Encryption Algorithm, required key stream (such as Scrambling Matrix or diffusion mask) is encrypted
Only determined by input key, and unrelated with encrypted original text, it is such the characteristics of system is produced when encrypting different original texts
Raw key stream is duplicate, so that attacker can obtain this by chosen -plain attact and known plain text attack
Key stream, in this, as equivalent key, and then crack whole system；
Again, existing achievement in research is it has been proved that the only encryption method of scramble (Permutation-only), no matter it is put
How complicated random process is, can not all resist chosen -plain attact and known plain text attack, so needing one after scramble
Module is spread, with the statistical nature of covering system and spreads original text difference simultaneously, but common diffusion equation is with password
The development of analytics and cracked successively.
The content of the invention
For the deficiency of existing Chaotic Image Encryption Algorithm, the problem to be solved in the present invention be to provide it is a kind of possess it is excellent
The safety of chaotic characteristic, higher key sensitiveness and unpredictability, bigger key space and safer diffusion property
Efficient digital image encryption method.
In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of safe and efficient digital image encryption method of the present invention, comprises the following steps：
1) using the first~tri- group of required chaos state variable of three-dimensional Chen systems generation encryption；
2) scrambling encryption is carried out to original text using first group of chaos state variable, upsets the position of pixel, produce scramble
Ciphertext；
3) encryption is diffused to scramble ciphertext using the second~tri- group of chaos state variable, generates final ciphertext.
In step 1), Chen system equations are as follows：
Wherein, a, b, c are the first~tri- control parameter, and x, y, z is the first~tri- system variable；Work as a=35, b=3, c ∈
When [20,28.4], system is in chaos state, the first~tri- system variable inputted when the 3rd control parameter c and first iteration
x0、y0、z0As system key, i.e. system key is (x0,y0,z0,c)；
If image to be encrypted is P, its size is the length and width of M × N, M and N difference representative image；Three-dimensional Chen
Chaos state variable needed for system generation encryption includes procedure below：
101) 3 arrays are established, are designated as X, Y and Z respectively, array length is M × N, and its element is set to X (i), Y (i)
With Z (i) (0≤i≤M × N-1), for storing the numerical value of x, y and z caused by chaos system iteration；
102) input system key (x0,y0,z0, c), iteration Chen systems are formula (1) N0It is secondary, make system well into mixed
Ignorant state；
103) continue iterative chaotic system M × n times, and x caused by iteration, y and z value are respectively put into array X, Y and Z
In, as the first~tri- group of chaos state variable.
N0For constant, N0≥300。
In step 2), using first group of chaos state variable, i.e. array X, scrambling encryption is carried out to original text, upsets pixel
Position, produce scramble ciphertext, original text and scramble ciphertext be regarded as one-dimensional sequence in scrambling process, P={ P are respectively adopted
(0), P (1) ..., P (M × N-1) }, C={ C (0), C (1) ..., C (M × N-1) } represents original text and the pixel of scramble ciphertext；
201) average pixel value of original text all pixels is calculated, i.e.,
G=mean (P), (2)
For wherein mean functions to take mean value function, g is the average value of original text pixel；
202) array X is quantified, produces scrambling sequence, quantifying equation is：
K1(i)=i+mod [(abs (X (i))-floor (abs (X (i)))) × g × 1015,MN-i)](0≤i≤M×N-
1) (3)
Wherein, abs (x) is takes absolute value function, and floor (x) returns to the nearest integer less than or equal to x, mod (x,
Y) it is to take the remainder function；
203) from front to back, i.e., terminate since i=0 to i=M × N-1, exchange P (i) and P (K1(i) numerical value), and
P (i) after exchange is entered as C (i), i.e.,：
Wherein, temp is the temporary variable set, is often once exchanged, and original text one point P (i) of disappearance, ciphertext increases
One point C (i), after end to be encrypted, original text all disappears, and ciphertext produces simultaneously.
In step 3), using the second~tri- group of chaos state variable, i.e. array Y and array Z, scramble ciphertext is diffused
Encryption, generates final ciphertext, including procedure below：
301) array Y and array Z are quantified, produces diffusion mask K2And K3, quantifying equation is：
Wherein, L is the grey level of image to be encrypted；
302) from front to back, i.e., terminate since i=0 to i=M × N-1, scramble ciphertext C (i) is diffused added successively
Close, diffusion equation is：
Wherein,Bit-level step-by-step XOR is represented, it is constant to set D (- 1)=seed, for encrypting first pixel.
Present invention additionally comprises step 4) according to demand for security, repeat step 1) -3), carry out more wheel encryptions.
The invention has the advantages that and advantage：
1. the present invention uses the more preferable chaos system of random performance：Invention introduces Chen systems, Chen systems are three
Chaos system is tieed up, possesses excellent chaotic characteristic, higher key sensitiveness and unpredictability, and bigger key sky
Between, by can effective lifting system encryption performance；
2. the present invention is using the related disorder method of original text：Invention introduces the related parameter of original text to upset scramble
The generation process of matrix, so that the Scrambling Matrix that system generates when encrypting different original texts is different, lifting system is supported
The ability of anti-chosen -plain attact and known plain text attack；
3. the present invention is using the higher diffusion equation of security performance：Invention introduces the expansion of the high intensity as shown in formula (5)
Equation is dissipated, the decryption complexity of the equation has been verified as 2n-2, very close 2nThe theoretical value of (n is the number of bits of pixel),
The security of energy effective guarantee encryption system.
Brief description of the drawings
Fig. 1 is the New chaotic image encryption Organization Chart that Fridrich is proposed in the prior art；
Fig. 2 is scramble-diffusion Encryption Architecture figure classical in the prior art；
Fig. 3 is encryption frame diagram of the present invention；
Fig. 4 is original document image used in example；
Fig. 5 is the ciphertext graph picture after scramble in example；
Fig. 6 is final encrypted cipher text image in example.
Embodiment
With reference to Figure of description, the present invention is further elaborated.
As shown in figure 3, the present invention is a kind of safe and efficient digital image encryption method, comprise the following steps：
1) using the first~tri- group of required chaos state variable of three-dimensional Chen systems generation encryption；
2) first group of chaos state variable is utilized, be i.e. array X, scrambling encryption is carried out to original text, upsets the position of pixel,
Produce scramble ciphertext；
3) the second~tri- group of chaos state variable, i.e. array Y and array Z are utilized, encryption is diffused to scramble ciphertext, it is raw
Into final encrypted cipher text.
In the present invention, original text and ciphertext are regarded as one-dimensional sequence, and P={ P (0), P (1) ..., P (M × N- is respectively adopted
1) }, C={ C (0), C (1) ..., C (M × N-1) }, D={ D (0), D (1) ..., D (M × N-1) } represent original text, scramble ciphertext
And final encrypted cipher text, L represent the number of greyscale levels of image to be encrypted.In the present embodiment, original text to be encrypted is shown in Fig. 4
Gray level image, size M=N=512, M and N distinguish the length and width of representative image, N0=300, number of greyscale levels L=256,
Key (x0,y0,z0, c)=(1.5839,2.4912,3.2013,28), constant seed=123；Encrypting step is as follows：
In step 1), Chen system equations are as follows：
Wherein, a, b, c are the first~tri- control parameter, and x, y, z is the first~tri- system variable；Work as a=35, b=3, c ∈
When [20,28.4], system is in chaos state, the first~tri- system variable inputted when the 3rd control parameter c and first iteration
x0,y0,z0As system key, i.e. system key is (x0,y0,z0,c)；
In step 1), if image to be encrypted is P, it is sized to M × N, and three-dimensional Chen systems generation is encrypted required
Chaos state variable includes procedure below：
101) 3 arrays are established, are designated as X, Y and Z respectively, array length is M × N, and its element is set to X (i), Y (i)
With Z (i) (0≤i≤M × N-1), for storing the numerical value of x, y and z caused by chaos system iteration；
102) input system key (x0,y0,z0, c), iteration Chen systems (formula 1) N0Secondary (N0For constant, N0>=300),
Make system well into chaos state；
103) continue iterative chaotic system M × n times, and x caused by iteration, y and z value are respectively put into array X, Y and Z
In, as the first~tri- group of chaos state variable.
In the present embodiment, step 101) establishes 3 arrays, and array length is M × N=262144, the element X of corresponding array
(i), Y (i), Z (i) (0≤i≤262143) are respectively used to store the value of x, y and z caused by chaos system iteration；
Step 102) input system key (1.5839,2.4912,3.2013,28), by the chaos system shown in formula (1)
Iteration 300 times, makes system well into chaos state；
Step 103) continues iterative chaotic system 262144 times, and x caused by iteration, y and z value are respectively put into array
In X, Y and Z, the array of generation is：X=27.3192836636065,27.394015208521 ... ,-
1.17506957145386, Y={ 31.6978918478302,31.5553258428948 ..., 1.15389486747088 },
Z=35.6037382011979,35.9826618322906 ..., 21.7926706779081 }；
Invention introduces Chen systems, the system is three-dimensional chaotic system, possesses excellent chaotic characteristic, higher close
Key sensitiveness and unpredictability, and bigger key space, by can effective lifting system encryption performance.
In step 2), using first group of chaos state variable, i.e. array X, scrambling encryption is carried out to original text, upsets pixel
Position, produce scramble ciphertext；
201) average pixel value of original text all pixels is calculated, i.e.,
G=mean (P), (2)
Wherein, for mean functions to take mean value function, g is the average value of original text pixel；
202) array X is quantified, produces scrambling sequence, quantifying equation is：
K1(i)=i+mod [(abs (X (i))-floor (abs (X (i)))) × g × 1015,MN-i)](0≤i≤M×N-
1)(3)
Wherein, abs (x) is takes absolute value function, and floor (x) returns to the nearest integer less than or equal to x, mod (x,
Y) it is to take the remainder function；
203) from front to back, i.e., terminate since i=0 to i=M × N-1, exchange P (i) and P (K1(i) numerical value), and
P (i) after exchange is entered as C (i), i.e.,：
Wherein, temp is the temporary variable set, is often once exchanged, and original text one point P (i) of disappearance, ciphertext increases
One point C (i), after end to be encrypted, original text all disappears, and ciphertext produces simultaneously.
In the present embodiment, scrambling encryption is carried out to original text, upsets the position of pixel, generation scramble ciphertext C={ C (0), C
(1),…,C(262143)}；
Step 201) calculates the average pixel value of original text all pixels, i.e.,
G=mean (P)=112.446754455566,
Step 202) quantifies to array X, quantifies shown in equation such as formula (3), caused scrambling sequence is K1=
{253784,70961,…,262143}；
Step 203) from front to back, i.e., terminates since i=0 to i=262143, exchanges P (i) and P (K1(i) number)
Value, with first point, namely P (0), exemplified by, ciphering process is：
The ciphertext ultimately generated is C={ 75,146 ..., 38 }, as shown in Figure 5.
Invention introduces the generation process that the related parameter g of original text upsets Scrambling Matrix, so that encrypting different originals
The Scrambling Matrix that system generates when literary changes, the ability of lifting system resistance chosen -plain attact and known plain text attack.
In step 3), using the second~tri- group of chaos state variable, i.e. array Y and array Z, scramble ciphertext is diffused
Encryption, generates final ciphertext, including procedure below：
301) array Y and array Z are quantified, produces diffusion mask K2And K3, quantifying equation is:
Wherein, L is the grey level of image to be encrypted；
302) from front to back, i.e., terminate since i=0 to i=M × N-1, scramble ciphertext C (i) is diffused added successively
Close, diffusion equation is：
Wherein,Bit-level step-by-step XOR is represented, D (- 1)=123 is set, for encrypting first pixel.
In the present embodiment, encryption is diffused to scramble ciphertext C, and generates final ciphertext D={ D (0), D (1) ..., D
(262143)}；
Step 301) is quantified with equation (4) to array Y and array Z, the mask needed for diffusion phase is produced, after quantization
Caused array is K2={ 154,164 ..., 30 }, K3=82,71 ..., 152 }；
Step 302) from front to back, i.e., terminates since i=0 to i=262143, and scramble ciphertext C (i) is added successively
It is close, shown in diffusion equation such as formula (5), with first point, namely exemplified by C (0)：
The ciphertext ultimately generated is D={ 16,130 ..., 157 }, as shown in Figure 6.
Invention introduces the high intensity diffusion equation as shown in formula (5), the decryption complexity of the equation has been verified as
2n-2, very close 2nThe theoretical value of (n is the number of bits of pixel), the security of energy effective guarantee encryption system.
Required present invention additionally comprises step 4) according to Cipher Strength, 1) -3), carry out more wheel encryptions.In the present invention, encryption is strong
Degree includes but is not limited to violence attacking ability, anti-known-plaintext/chosen -plain attact ability and resisting differential attacking ability.
Claims (6)
1. a kind of safe and efficient digital image encryption method, it is characterised in that comprise the following steps：
1) using the first~tri- group of required chaos state variable of three-dimensional Chen systems generation encryption；
2) scrambling encryption is carried out to original text using first group of chaos state variable, upsets the position of pixel, produce scramble ciphertext；
3) encryption is diffused to scramble ciphertext using the second~tri- group of chaos state variable, generates final ciphertext.
2. the safe and efficient digital image encryption method as described in claim 1, it is characterised in that：In step 1), Chen systems
Equation of uniting is as follows：
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Wherein, a, b, c are the first~tri- control parameter, and x, y, z is the first~tri- system variable；Work as a=35, b=3, c ∈ [20,
When 28.4], system is in chaos state, the first~tri- system variable x inputted when the 3rd control parameter c and first iteration0、y0、
z0As system key, i.e. system key is (x0,y0,z0,c)；
If image to be encrypted is P, its size is the length and width of M × N, M and N difference representative image；Three-dimensional Chen systems
Chaos state variable needed for generation encryption includes procedure below：
101) 3 arrays are established, are designated as X, Y and Z respectively, array length is M × N, and its element is set to X (i), Y (i) and Z
(i) (0≤i≤M × N-1), for storing the numerical value of x, y and z caused by chaos system iteration；
102) input system key (x0,y0,z0, c), iteration Chen systems are formula (1) N0It is secondary, make system well into chaos shape
State；
103) continue iterative chaotic system M × n times, and x caused by iteration, y and z value be respectively put into array X, Y and Z,
As the first~tri- group of chaos state variable.
3. the safe and efficient digital image encryption method as described in claim 2, it is characterised in that：N0For constant, N0≥300。
4. the safe and efficient digital image encryption method as described in claim 1, it is characterised in that：In step 2), is utilized
One group of chaos state variable, i.e. array X, scrambling encryption is carried out to original text, upsets the position of pixel, scramble ciphertext is produced, puts
Original text and scramble ciphertext are regarded as one-dimensional sequence during unrest, P={ P (0), P (1) ..., P (M × N-1) }, C is respectively adopted
=C (0), C (1) ..., and C (M × N-1) } represent original text and the pixel of scramble ciphertext；
201) average pixel value of original text all pixels is calculated, i.e.,
G=mean (P), (2)
For wherein mean functions to take mean value function, g is the average value of original text pixel；
202) array X is quantified, produces scrambling sequence, quantifying equation is：
K1(i)=i+mod [(abs (X (i))-floor (abs (X (i)))) × g × 1015,MN-i)](0≤i≤M×N-1)(3)
Wherein, abs (x) is the function that takes absolute value, and floor (x) returns to the nearest integer less than or equal to x, and mod (x, y) is
Take the remainder function；
203) from front to back, i.e., terminate since i=0 to i=M × N-1, exchange P (i) and P (K1(i) numerical value), and exchange
P (i) afterwards is entered as C (i), i.e.,：
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Wherein, temp is the temporary variable set, is often once exchanged, and original text one point P (i) of disappearance, ciphertext increases by one
Point C (i), after end to be encrypted, original text all disappears, and ciphertext produces simultaneously.
5. the safe and efficient digital image encryption method as described in claim 1, it is characterised in that：In step 3), is utilized
Two~tri- groups of chaos state variables, i.e. array Y and array Z, encryption is diffused to scramble ciphertext, generates final ciphertext, wrapped
Include procedure below：
301) array Y and array Z are quantified, produces diffusion mask K2And K3, quantifying equation is：
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</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>&times;</mo>
<msup>
<mn>10</mn>
<mn>15</mn>
</msup>
<mo>,</mo>
<mi>L</mi>
<mo>)</mo>
<mo>&rsqb;</mo>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>i</mi>
<mo>&le;</mo>
<mi>M</mi>
<mo>&times;</mo>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>K</mi>
<mn>3</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>mod</mi>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mi>a</mi>
<mi>b</mi>
<mi>s</mi>
<mo>(</mo>
<mi>Z</mi>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>f</mi>
<mi>l</mi>
<mi>o</mi>
<mi>o</mi>
<mi>r</mi>
<mo>(</mo>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>Z</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>)</mo>
<mo>&times;</mo>
<msup>
<mn>10</mn>
<mn>15</mn>
</msup>
<mo>,</mo>
<mi>L</mi>
<mo>&rsqb;</mo>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>i</mi>
<mo>&le;</mo>
<mi>M</mi>
<mo>&times;</mo>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>,</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, L is the grey level of image to be encrypted；
302) from front to back, i.e., terminate since i=0 to i=M × N-1, be diffused encryption to scramble ciphertext C (i) successively,
Diffusion equation is：
<mrow>
<mi>D</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>mod</mi>
<mo>&lsqb;</mo>
<msub>
<mi>K</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>K</mi>
<mn>3</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>L</mi>
<mo>&rsqb;</mo>
<mo>&CirclePlus;</mo>
<mi>mod</mi>
<mo>&lsqb;</mo>
<msub>
<mi>K</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>K</mi>
<mn>3</mn>
</msub>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>&CirclePlus;</mo>
<mi>C</mi>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>&CirclePlus;</mo>
<mi>D</mi>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>L</mi>
<mo>&rsqb;</mo>
<mo>,</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,Bit-level step-by-step XOR is represented, it is constant to set D (- 1)=seed, for encrypting first pixel.
6. the safe and efficient digital image encryption method as described in claim 1, it is characterised in that also including step 4) basis
Demand for security, repeat step 1) -3), carry out more wheel encryptions.
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