A bit-level image encryption algorithm bad on spatiotemporal chaotic system and lf-adaptive
Lin Teng,Xingyuan Wang n
Faculty of Electronic Information and Electrical Engineering,Dalian University of Technology,Dalian1160
24,China
a r t i c l e i n f o
Article history:
Received5April2012
Received in revid form
3June2012
Accepted4June2012
Available online27June2012
Keywords:
Chaos encryption
Bit-level encryption
Self-adaptive
a b s t r a c t
This paper propos a bit-level image encryption algorithm bad on spatiotemporal chaotic system
which is lf-adaptive.We u a bit-level encryption scheme to reduce the volume of data during
encryption and decryption in order to reduce the execution time.We also u the adaptive encryption
scheme to make the ciphered image dependent on the plain image to improve performance.Simulation
results show that the performance and curity of the propod encryption algorithm can encrypt
plaintext effectively and resist various typical attacks.
&2012Elvier B.V.All rights rerved.
1.Introduction
With the rapid development of computer network technology,
a lot of nsitive information is transmitted over the network;
information curity becomes more and more important.Image
information transmission has incread rapidly and image
encryption technology has drawn more attention.Nowadays,
会计电算化就业前景
image encryption schemes include two process:substitution
and diffusion[1].The substitution stage permutes all the pixels as
a whole,without changing their values.In the diffusion stage,the
pixel values are modified quentially so that a tiny change in a
pixel spreads to as many pixels in the cipher-image as possible.
The two process can achieve a satisfactory level of curity.
Image encryption is different from text encryption due to some
inherent features such as bulk data capacity and high correlation
among pixels.Therefore,traditional cryptographic techniques such as
DES,IDES and RSA are no longer suitable for image encryption.The
properties of chaotic maps such as nsitivity to initial conditions and
random-like behavior have attracted attention to develop image
encryption algorithms.
In recent years,some chaos-bad image encryption algorithms
have been developed[2–5].Xiang et al.[6]propod a lective
image encryption using a spatiotemporal chaotic system.Liao et al.
[7]propod a novel image encryption algorithm bad on lf-
adaptive wave transmission.In Refs.[8–10],CML-bad spatiotem-
northkorea
poral chaos systems were ud in image encryption.
In this paper,we u a bit-level encryption scheme to reduce
the volume of data during encryption and decryption in order to
reduce the execution time.We also u the adaptive encryption
scheme to make the ciphered image dependent on the plain
image to improve performance,so the algorithm propod in this
paper can resist various typical attacks.
The rest of this paper is organized as follows.Section2briefly
reviews preliminary concepts in bit-level imaging,lf-adaptive
encryption and coupled map lattice.Section3describes the
propod encryption algorithm.The curity of the scheme is
evaluated in Section4.Section5concludes the paper.
2.Preliminary
2.1.Bit-level image
In a gray-level image,the brightness between black and white
is quantized into an integer number of levels ranging from0to
255.The value of the pixel at coordinate(x,y)is denoted as f(x,y).
Each pixel can transform to an8bit binary value,given by
fðx,yÞ¼pð8Þpð7Þpð6Þpð5Þpð4Þpð3Þpð2Þpð1Þð1Þ
So,the image can be divided into8binary images according to
the bit locations within a pixel.Select the sample image Lena of
size256Â256and with256Gy levels(Fig.1),divide it into
8binary images(Fig.2)according to the bit locations within a
pixel.In Fig.2,Pic i reprents the binary image obtained by
collecting the i th bits of all the plain-image pixels.
A bit can contain different amounts of information depending
on its position in the pixel.For example,‘‘1’’at the8th bit of a
Contents lists available at SciVer ScienceDirect
journal homepage:/locate/optcom
Optics Communications
huanjian
0030-4018/$-e front matter&2012Elvier B.V.All rights rerved.
dx.doi/10.1016/j.optcom.2012.06.004
n Corresponding author.
E-mail address:tenglin@mail.dlut.edu(L.Teng),
wangxy@dlut.edu(X.Wang).
Optics Communications285(2012)4048–4054
pixel reprents 128(27),but it only reprents 1(21)at the first bit.The higher 4bits (8th,7th,6th and 5th)carry 94.125%of the total information of the image.On the other hand,the lower 4bits (4th,3rd,2nd and 1st)carry less than 6%of the image informa-tion,according to Eq.(2).The percentage of the pixel information is shown in Table 1.p ði Þ¼2i
P i ¼0
2ð2Þ
In order to reduce the computation cost,we permute the higher 4bits binary images independently and the binary images of the lower 4bits are permuted as a whole to reduce the execution time.
2.2.Self-adaptive encryption
The basic idea of lf-adaptive is to divide an image into two parts equally,and the information of one part is ud to encrypt the other part.In this paper,we divide an image into two binary parts equally,that is the higher 4bits binary images part (Pic 5–Pic 8)and the lower 4bits binary images part (Pic 1–Pic 4).We u the information of the lower 4bits binary images part to encrypt the higher 4bits binary images part.2.3.Coupled map lattice
A coupled map lattice (CML)is ud as a spatiotemporal chaos system here,which is a dynamic system with discrete-time,discrete-space and continuous states.It consists of nonlinear maps located on the lattice sites,named as local maps.Each local map is coupled with other local maps in terms of certain coupling rules.Becau of the intrinsic nonlinear dynamics of each
local
Fig.1.Plain Lena image of size 256Â
教师爱岗敬业256.
Fig.2.Image encryption experimental results.(a)Pic 1,(b)Pic 2,(c)Pic 3,(d)Pic 4,(e)Pic 5,(f)Pic 6,(g)Pic 7and (h)Pic 8.
Table 1
Percentage of pixel information contributed by different bits.
Bit position (i þ1)in the pixel Percentage p (i )of the pixel information 10.392220.78433 1.56864 3.1375 6.275612.55725.108
50.20
L.Teng,X.Wang /Optics Communications 285(2012)4048–40544049
map and the diffusion due to the spatial coupling among the local maps,a CML can exhibit spatiotemporal chaos.CML was intro-duced by Kaneko [11],and can be described as x n þ1ði Þ¼ð1Àe Þf ðx n ði ÞÞþ
e
2
ðf ðx n ði À1ÞÞþf ðx n ði þ1ÞÞÞð3Þ
where n is the time index,i (i ¼1,2,y ,L )is the lattice site index,e A (0,1)is a coupling constant;x n (i )reprents the state variable for the i th site at time n (n ¼1,2,y ).The periodic boundary condition x n (0)¼x n (L )is assumed.
The local mapping function f (x )is chon to be the logistic map:
x n þ1¼ax n ð1Àx n Þ
ð4Þ
with parameter a A (3.5699456,4),and x n A (0,1),the system is in chaotic state.
3.The propod algorithm
3.1.Higher 4bits binary images permutation algorithm by the CML system
Here we u the information of the lower 4bits binary images part to permute the higher 4bits binary images independently.
Step 1:Without loss of generality,we assume that the size of the plain-image P is M ÂN ,convert P into its binary image Pic 1–Pic 8;the size of each image is M ÂN .We divide binary images into two parts equally,that is the higher 4bits binary images part (Pic 5–Pic 8)and the lower 4bits binary images part (Pic 1–Pic 4).Converting Pic 1–Pic 8to vectors P i ,each vector has a length of M ÂN .
Step 2:Calculate four values’sum (n )(n ¼1,2,3,4)by summa-tion of all the binary values within each lower 4bits binary image Pic n .Let g (i ,j )be the binary value at row i ,column j in the binary image,then the value of sum (n )got in image Pic n can be obtained as follows:
sum ðn Þ¼X
ði ,j ÞA Pic
n
g ði ,j Þ:Step 3:The number of CML lattices L is t to 4which is equal to the number of higher 4bits binary images.Initialize the system with the parameters a ,e and value quences x 0ðn Þ¼1=ððsum ðn Þþ1ÞÂn Þðn ¼1,2,3,4Þto iterate the chaotic system m þMN times,discard the former m values to avoid harmful effects.Each lattice generates MN values x i (n )(i ¼1,2,y ,MN ),so the chaotic system generates 4MN values totally.
Sort each x i (n )value {x m þ1(n ),x m þ2(n ),y ,x m þMN (n )}in ascending order and get x i ðn Þ¼x m þ1ðn Þ,x m þ2ðn Þ,...,x m þMN ðn Þ.Find the position of values x i ðn Þin x i (n )and mark down the transform positions TN n ¼{t 1(n ),t 2(n ),y ,t MN (n )}(n ¼1,2,3,4).
Step 4:Rearrange the elements of each higher vector P i (i ¼5,6,7,8)according to TN n ,that is,move the t 1(n )element of vector P n þ4to the first element,t 2(n )element of vector P n þ4to the cond element,etc.,until all the elements of each vector have been permutated and get 4vectors P 0i ði ¼5,6,7,8Þ.3.2.Higher 4bits binary images diffusion
Step 1:U the logistic map (Eq.(4))to generate the chaotic quence,t the initial parameter a 1and initial value y 0to iterate the chaotic system m 1þ4MN times and discard the former m 1values to avoid harmful effects.The chaotic quence has 4MN elements y (i )¼{y 1,y 2,y ,y 4MN }.Select MN elements z (j )(1r j r MN )from y (i ),u the following formula to convert z (j )to integer quence z 1(j ),
z 1ðj Þ¼f loor ðz ðj ÞÂð1014ÞÞmod 256,
where floor (i )is the biggest integer which is not bigger than i .The elements in z 1(j )range from 0to 255.Covert z 1(j )to binary quence z 01ðj Þ,lect the higher 4bits of z 01ðj Þand form 4vectors z i
(i ¼5,6,7,8),each vector having a length of MN .
Step 2:U the information of the lower 4bits binary images part to diffu the permuted higher 4vectors P i 0according to the following formula:
C i ¼ðP i 0þP i À4þz i Þmod 2ði ¼5,6,7,8Þ,
ð5Þ
where C i is ciphered higher 4vector,P i À4are 4lower vectors transformed from 4lower binary images.Covert C i to 4binary images and get ciphered higher 4binary images Pic 0i ði ¼5,6,7,8Þ.
3.3.Lower 4bits binary images permutation
Combine Pic 1–Pic 4horizontally and get matrix P combine with 4N rows and 4N columns.Covert P combine to vector P lower ,which has a length of 4MN .
Sort y (i )¼{y 1,y 2,y ,y 4MN }in ascending order and get y 1,y 2,...,y 4MN .Next,find the position of values y 1,y 2,...,y 4MN in y (i )and mark down the transform position TM ¼{t 1,t 2,y ,t 4MN }.
Rearrange the elements of vector P lower according to TM ,and get permuted vector P 0lower .Covert P 0lower to matrix P 0combine with 4N rows and 4N columns,partition P 0combine into 4matrices Pic 0i ði ¼1,2,3,4Þfrom left to right;the size of each matrix is M ÂN .Pic 0i ði ¼1,2,3,4,5,6,7,8Þare the ciphered binary images,com-bine them to get a integer image (Eq.(1))according to the bit locations within a pixel.So,we can get the encrypted image C pic .
3.4.Image decryption
The decryption procedure is similar to that of the encryption
process but in reverd order.
Set the initial parameters and initial values as same as tho in the encryption process and u same methods to obtain TM ,TN i ,and z i .Convert C pic into its binary images Pic 0i ði ¼1,2,3,4,5,6,7,8Þ;the size of each image is M ÂN .We divide binary images into two parts equally,that is the higher 4bits binary images part (Pic 05–Pic 08)and the lower 4bits binary images part (Pic 01–Pic 04).Covert Pic 01–Pic 08to vectors C i ;each vector has a length of M ÂN .
Combine Pic 01–Pic 04horizontally and get matrix P 0combine ,convert P 0combine to get vector P 0
lower .Rever permute P 0lower according to TM and get the reverd permutation P lower .So,we can get Pic 1–Pic 4.Covert Pic 1–Pic 4to vectors P i (i ¼1,2,3,4).
U the following formula to diffu C i (i ¼5,6,7,8)reverly,where P i 0is the decrypted diffu value of higher 4binary images 0vectors:
P i 0¼ðC i ÀP i À4Àz i Þmod2ði ¼5,6,7,8Þ
ð6Þ
Rever permute P i 0ði ¼5,6,7,8Þaccording to TN i and get the reverd permutation vectors P i (i ¼5,6,7,8).So,we can get Pic 5–Pic 8.Transform Pic 1–Pic 8into the plain image.
4.Experimental results 4.1.Encryption results
The plain-image Lena with size 256Â256is ud for encryption.The initial parameters and initial values are a ¼4.0,e ¼0,1a 1¼3.99and y 0¼0.12345678912345,and m ¼m 1¼500.Fig.2(a)shows the plain-image.Fig.2(b)shows the encrypted image.
L.Teng,X.Wang /Optics Communications 285(2012)4048–4054
4050
4.2.Security analysis
A good encryption algorithm should resist all kinds of known attacks,such as exhaustive attack,statistical attack and chon-plaintext/cipher text attack.In this ction,we will discuss the curity analysis of the propod encryption scheme.
4.2.1.Key space analysis
A good encryption scheme should be nsitive to the cret keys,and the key space should be large enough to make brute-force attacks infeasible.In this algorithm,the initial conditions and parameters a ,a 1and e ,y 0can be ud as keys as well as the initial iteration numbers m and m 1.If the precision is 10À14,the
key space size can reach to 1056;it is bigger than 2128.So,the key space is large enough to resist the brute-force attacks.
dressup
4.2.2.Key nsitivity analysis
Several key nsitivity tests are performed.Fig.3(a)shows the encrypted image of Lena with the correct encryption key.And Fig.3(b),(c),(d),and (e)show the encrypted image of Lena with the wrong encryption key a ¼3.99999999999999,e ¼0.10000000000001a 1¼3.99000000000001,and y 0¼0.1234567898764respectively.So it can be concluded that the propod algorithm is nsitive to the key,a small change of the key will generate a completely different decryption result and cannot get the correct
plain-image.
Fig.3.Key nsitivity analysis.(a)Decrypted image with correct initial parameters;(b)decrypted image with different initial value a ¼3:99999999999999;(c)decrypted image with different initial value e ¼0:10000000000001;(d)decrypted image with different initial value a 1¼3:99000000000001and (e)decrypted image with different initial value y 0¼0:
1234567898764.
Fig.4.Histograms.(a)Histograms of plain-image and (b)histograms of ciphered-image.
L.Teng,X.Wang /Optics Communications 285(2012)4048–40544051
Fig.5.Correlation of adjacent pixels.(a)horizontally adjacent pixels in the plain image;(b)horizontally adjacent pixels in the ciphered image;(c)vertically adjacent pixels in the plain image;(d)vertically adjacent pixels in the ciphered image;(e)diagonally adjacent pixels in the plain image and (f)diagonally adjacent pixels in the ciphered image.
L.Teng,X.Wang /Optics Communications 285(2012)4048–4054
4052
4.2.3.Histogram analysis
The frequency of each gray level can be en from the histogram,it leads to the leakage of image information.Simula-tion results are shown in Fig.4,from thefigures,we can e that histogram of the cipher-image is fairly uniform and is signifi-cantly different from that of the original image.
4.2.4.Correlation analysis
In order to protect against statistical attack,we must decrea the correlation of two adjacent pixels in the ciphered image[12]. Calculate the correction coefficient of each pair by using the following formulas:
r xy¼
covðx,yÞ
ffiffiffiffiffiffiffiffiffi
DðxÞ
pffiffiffiffiffiffiffiffiffiffi
DðyÞ
p,ð7Þ
where
DðxÞ¼1
N
英语在线朗读
X N
广州出国留学机构i¼1
ðx iÀEðxÞÞ2,covðx,yÞ¼
1
draconianN
X N
i¼1
ðx iÀEðxÞÞðy iÀEðyÞÞ,
EðxÞ¼1
N
X N
i¼1
x i,
here,x and y are gray-scale values of two adjacent pixels in the image.
We randomly lect2000pairs of two adjacent pixels from a plain image Fig.1(a)and a ciphered image Fig.1(b)to calculate the correction coefficient.Fig.5shows the correlation of two images in horizontal,vertical and diagonal directions.Then the correlation coefficient of the two pixel pairs is calculated in Table2.From Table2we can e that the correlation coefficient of the ciphered image is much smaller than that of the plain image,so the chaotic encryption algorithm satisfies zero co-correlation.
4.2.
5.Information entropy analysis
Information theory is a mathematical theory of data communica-tion and storage found by Shannon in1949[13].An important theory in information theory is entropy.The entropy H(m)of a message source m can be calculated as
HðmÞ¼X
2NÀ1
i¼0
韩国语翻译
pðm iÞlog
1
i
ð8Þ
where p(m i)reprents the probability of symbol m i and the entropy is expresd in bits.Actually,given that a real information source ldom transmits random messages,in general,the entropy value of source is smaller than the ideal one.However,when the messages are encrypted,their ideal entropy should be8.If the output of such a cipher emits symbols with entropy of less than8,then,there would be a possibility of predictability which threatens its curity.The value obtained is very clo to the theoretical value of8.This means that information leakage in the encryption process is negligible and the encryption system is cure against the entropy attack.Using the above-mentioned formula,we have got the entropy H(m)¼7.997450.
4.2.6.NPCR and UACI analysis.
NPCR stands for the number of pixels change rate while one pixel of plain image is changed.The clor NPCR gets to100%,the more nsitive the cryptosystem is to the changing of plain image, and the more effective it is in resisting plaintext attack.UACI stands for the average intensity of differences between the plain image and ciphered image.The bigger the UACI is,the more effective is the cryptosystem in resisting differential attack.Here are the formulae to calculate NPCR and UACI:
NPCR¼
P
ij
Dði,jÞ
WÂH
Â100%,ð9ÞUACI¼
1
WÂH
X
i,j
C1ði,jÞÀC2ði,jÞ
255
2
4
3
banggo5Â100%,ð10Þ
where W and H reprent the width and height of the image respectively,and C1and C2are respectively the ciphered images before and after one pixel of the plain image is changed.
Two plain-images are ud in the tests.Thefirst image is the original plain-image,and the other is obtained by changing the first pixel from‘173’to‘174’.Then the two images are encrypted with the same key to generate the corresponding cipher-images C1and C2.The results according to the propod algorithm of NPCR and UACI are NPCR¼93.6768%and UACI¼33.3364%.The results show that the propod cryptosystem could resist plain-text attack and differential attack effectively.
4.2.7.Classical types of attacks
When cryptanalyzing a cryptosystem,the general assumption made is that the cryptanalyst knows exactly the design and working of the cryptosystem under study;he knows everything about the cryptosystem except the cret key.This is an evident requirement in today0s cure communications networks,usually referred to as Kerckhoff’s principle[14].There are four classical types of attacks:
1.Ciphertext only:the opponent posss a string of ciphertext.
2.Known plaintext:the opponent posss a string of plaintext,
and the corresponding ciphertext.
3.Chon plaintext:the opponent has obtained temporary access
to the encryption machinery.Hence he can choo a plaintext string,and construct the corresponding ciphertext string.
4.Chon ciphertext:the opponent has obtained temporary
access to the decryption machinery.Hence he can choo a ciphertext string,and construct the corresponding plaintext string.
Obviously,chon plaintext attack is the most powerful attack. If a cryptosystem can resist this attack,it can resist other types of attack.
In this paper,we u the lf-adaptive scheme to encrypt the higher4binary images,that is,u the information of the lower 4bits binary images part to encrypt the higher4bits binary images part.So,different ciphered images have different plain lower4binary images value,the opponent would not be able to u one plaintext and corresponding ciphertext to decrypt the other ciphered image.The propod algorithm can resist the chon plaintext/ciphertext attack.
5.Conclusions
In this paper,we propod a bit-level image encryption algorithm bad on spatiotemporal chaotic and lf-adaptive Table2
Correlation coefficient of two adjacent pixels in plain-image and ciphered-image. Correlation coefficient Plain-image Ciphered-image Horizontal0.9217490.024178 Vertical0.971100À0.019425 Diagonal0.9227490.024322
L.Teng,X.Wang/Optics Communications285(2012)4048–40544053
