An Image Encryption Scheme Based on Hybrid Orbit of Hyper-chaotic Systems

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1 I. J. Computer Network and Informaton Securty Publshed Onlne Aprl 5 n MECS ( DOI:.585/jcns An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems Junmng Ma and Rusong Ye* Department of Mathematcs Shantou Unversty Shantou Guangdong 5563 P. R. Chna * Correspondng author Emal: rsye@stu.edu.cn Abstract hs paper puts forward a novel mage encrypton scheme based on ordnary dfferental equaton system. Frstly a hyper-chaotc dfferental equaton system s used to generate two hyper-chaotc orbt sequences. Introducng the dea of hybrd orbt two orbts are mxed to generate a hybrd hyper-chaotc sequence whch s used to be the ntal chaotc key stream. Secondly the fnal encrypton key stream s generated through two rounds of dffuson operaton whch s related to the ntal chaotc key stream and plan-mage. herefore the algorthm s key stream not only depends on the cpher keys but also depends on plan-mage. Last but not least the securty and performance analyss have been performed ncludng key space analyss hstogram analyss correlaton analyss nformaton entropy analyss peak sgnal-to-nose rato analyss key senstvty analyss dfferental analyss etc. All the expermental results show that the proposed mage encrypton scheme s secure and sutable for practcal mage and vdeo encrypton. Index erms Hyper-chaotc system hybrd hyperchaotc sequence mage encrypton dffuson operaton. I. INRODUCION Wth the rapd developments of multmeda processng and network technques n the last decades dgtal multmeda data lke mages vdeos audos s beng stored on dfferent meda ncreasngly shared and communcated over the Internet and wreless networks. Protecton of dgtal nformaton aganst llegal usage becomes extremely urgent. Image encrypton s a drect and effcent way to protect mage nformaton from unauthorzed eavesdroppng. Dgtal mages possess some ntrnsc features such as bulk data capacty hgh correlaton among adjacent pxels and human vsual propertes. As a consequence tradtonal encrypton algorthms such as DES RSA [] are there not sutable for practcal dgtal mage encrypton due to the weakness of low-level effcency whle encryptng mages. Chaotc system has been popularzed n most aspects of scence such as mathematcs physcs bology computer fnance and even arts. In partcular chaotc system has been successfully ntroduced to modern cryptography thanks to ts fantastc features such as topologcal transtvty orbt nscrutablty senstvty to ntal condtons and control parameters pseudorandomness etc. whch meet the fundamental requrements such as mxng and dffuson n the sense of cryptography. hese propertes make chaotc system a potental canddate for constructng cryptosystems [-5]. As a consequence many chaos-based mage cryptosystems have been proposed. However most of the exstng chaos-based mage cryptosystems adopted low dmensonal chaotc systems wth permutaton-dffuson archtecture. he permutaton dffuson chaos-based mage encrypton scheme s frstly proposed Frdrch n 998 []. he proposed archtecture s usually composed of two processes: chaotc confuson of pxel postons permutaton process and dffuson of pxel gray values dffuson process where the former permutes the plan-mage pxel postons governed a D chaotc map whle the latter changes the pxel gray values sequentally controlled a D chaotc map so that a tny change for one pxel can spread out to almost all pxels n the whole mage. he Frdrch archtecture has become the most popular structure adopted n a great number of chaos-based mage encrypton algorthms subsequently proposed [-8 -]. However some mage encrypton schemes based on low dmensonal chaotc systems wth permutaton dffuson archtecture are broken recently [6-]. he common drawbacks of permutaton dffuson based mage encrypton algorthms are outlned as follows. Frstly the key stream n the dffuson step only depends on the cpher key. he key streams used to encrypt dfferent plan-mages are the same f the cpher key keeps unchanged. he attacker can obtan the key stream known-plantext attack and chosen-plantext attack. Secondly the two processes wll become ndependent f the plan-mage s a homogeneous one wth dentcal pxel gray value []. hrdly the cryptosystems based on low dmensonal chaotc systems have some weakness such as small key space short perodcty and weak securty. Such a knd of encrypton algorthms can be generally attacked the followng steps: () a homogeneous mage wth dentcal pxel gray values s adopted to elmnate the confuson effect; () the key-stream of the dffuson process s obtaned va known-plantext or chosen plantext attacks; () the remanng cpher-mage can be regarded as the output of a knd of permutaton-only cpher whch has been shown nsecure and can be cryptanalyzed known-plantext or chosen plantext attacks [ 3].

2 6 An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems It has been ponted out that the permutaton process s not necessary n an mage encrypton scheme. Usually omttng the permutaton process wll mprove the executng tme and make the proposed scheme more smple and easy to mplement. For example the two stages of permutaton and dffuson were combned and were executng at the same tme at the pxel level or bt level [7]. Regardng the securty ssue hyper-chaotc systems can be employed to mprove the securty of the cryptosystem proposed [7 4]. Hgher dmensonal chaotc systems wth hgher dmensonal attractors shall have good chaotc features. he adoptng of hgher dmensonal chaotc systems whch own more than one postve Lyapunov exponents clearly mproves the securty of encrypton scheme generatng more complex dynamcal behavor or hgh randomness. It s more dffcult to predct the chaotc sequences generated hgher dmensonal chaotc systems. herefore some hgh dmensonal chaotc systems are used n mage encrypton. In ths paper we propose an mage encrypton scheme based on hybrd orbt of hyper-chaotc system and dffuson-only mechansm. As far as we know mage encrypton scheme based on hybrd orbt of hyper-chaotc system only wth dffuson operaton has not been reported. he adoptng of hybrd orbt of hyper-chaotc system can enlarge the key space effcently and therefore enhance the securty. Gven two sets of ntal states the fourth order Ronge-Kutta method s used to generate two orbts of the hyper-chaotc system consstng of four ordnary dfferental equatons. ent map s appled to generate one pseudo-random sequence to determne the hybrd orbt ponts from whch of the two yelded orbts. Based on the mproved hyper-chaotc sequences derved the hybrd orbt we desgn an mage encrypton scheme wth plan-mage dependent key stream. he proposed scheme apples dfferent key streams when encryptng dfferent plan-mages (even wth the same hybrd hyper-chaotc sequences). o make the proposed scheme resst dfferental analyss attack we perform one dffuson process wth two rounds of dffuson operaton whch depends on both the cpher keys and the planmage. he dffuson process can modfy the pxel values and break the correlatons between adjacent pxels of an mage smultaneously. he securty and performance analyss of the proposed mage encrypton are carred out usng the hstograms correlaton coeffcents nformaton entropy key senstvty analyss dfferental analyss key space analyss etc. All the expermental results show that the proposed mage encrypton scheme s hghly secure and excellent performance whch makes t sutable for practcal applcaton. he rest of the paper s organzed as follows. In Secton II we brefly ntroduce the hyper-chaotc system and dscuss ts chaotc natures. he mproved hybrd sequence from hyper-chaotc sequences s outlned as well. Secton III devotes to desgnng the mage encrypton scheme. One dffuson functon s presented to encrypt mages. In Secton IV we present the results of securty and performance analyss of the proposed mage encrypton scheme usng the hstograms correlaton coeffcents nformaton entropy key senstvty analyss dfferental analyss key space analyss encrypton rate analyss etc. Secton V concludes the paper. II. HE HYPER-CHAOIC SYSEM AND IS HYBRID ORBIS A. he hyper-chaotc system he notaton of hyper-chaotc system s frstly put forward Rössler n 979 [5]. Hyper-chaotc system s a hgh order ordnary dfferental equaton whch s wdely appled n cryptography and crcut desgn. Hyperchaotc system presents more than one postve Lyapunov exponents and therefore generates more complex dynamcal behavor or hgh randomness. he hyperchaotc sequences generated surely mprove the securty of encrypton scheme. In ths paper a hyper-chaotc system s used n key schemng and modeled x a( y x) yz y cx y xz w z xy bz dw xz w where a b c and d are system parameters. When a 35 b 8/ 3 c 55 d.3 the Lyapunov exponents of system () are mplyng that system () exhbts a hyper-chaotc behavor. For the ntal condton ( x y z w ) one can obtan four hyper-chaotc sequences { x y z w : 3 } the fourth order Runge Kutta algorthm. hese hyper-chaotc sequences are non-perodcty and very senstve dependence on ntal condtons ( x y z w ). Settng the ntal condtons ( x 5 y z 5 w ) and ntegraton step h=. we solve system () and get the frst 5 real values of each sequence. he correspondng sequence pars are depcted n Fgure. (a) x y projecton ()

3 An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems 7 { x y z w : 3 L / 4}. hen we process the four hyper-chaotc sequences to be four 8-bt gray value sequences s fx s fx( s )) ) () * 4 mod( ( - 56 (b) x z projecton where fx ( x) rounds the elements of x to the nearest ntegers towards zero mod( xy ) represents the remander of x dvded y. We then get four hyper- chaotc sequences { xs ys zs ws... L / 4}. We ntegrate the four sequences to be one mxed sequence S { k... L} k43 xs k4 ys k4 zs. (3) k ws... L / 4. 4 (c) x w projecton (d) y z projecton Set the ntal condton to be ( x y z w ) dfferent from ( x y z w ) one can smlarly obtan another ntegrated sequence S { k... L}. C. Generaton of hybrd hyper-chaotc sequences he tent map s used to generate one random sequence { t n... L} whch s quantzed to be one n two-value sequence { ln n... L}. l n s used to determne l n k n to form one hybrd sequence { k l n n L}. he chaotc tent map s defned n t t q q t t n t qt -q (4) (e) y w projecton (f) z w projecton Fg.. he phase dagrams of hyper-chaotc sequence pars. B. Generaton of hyper-chaotc sequences Assume that we need one hyper-chaotc sequence wth length L. Set the ntal condton to be ( x y z w ) one can solve system () the fourth order Runge Kutta algorthm to obtan four hyper-chaotc sequences where q s the control parameter t s the state varable t s the ntal value. he tent map shows good chaotc nature ncludng ergodcty pseudo-randomness hgh senstvty to control parameters and ntal values etc. Set the control parameter and ntal value q.3 t.4 we terate the system (4) to get chaotc sequence { tn n... L} and yeld the choce sequence l floor ( t ) L. (5) o mprove the computaton effcency we ntroduce two counter varables () () whch are used to count the number of ponts selected from the k th hyper-chaotc k sequence S. () () are ntalzed to be zero. As the k th hyper-chaotc sequence k s k S s chosen ncreased. When the hybrd hyper-chaotc sequence wth length L s fnally generated () L. We denote

4 8 An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems the hybrd hyper-chaotc sequence wth length L to be { mk... L} yelded l mk.... k ( l ) L (6) III. HE PROPOSED IMAGE ENCRYPION SCHEME We assume that the plan-mage s a 8-bt gray-scale mage of sze L M N t s an nteger matrx of M rows and N columns n whch the values range from to 55. he D pxel gray value matrx can be convert to a D vector P { p p... p L } where p denotes the gray level of the mage pxel n the row floor( / N ) and column mod ( N ) where floor( x ) rounds x to the nearest nteger less than or equal to x. he hyper-chaotc system () s used to generate the ntal chaotc key stream. he mage encrypton scheme s based on the fnal secret key stream whch s not only related on the orgnal chaotc key stream but also the plan-mage. he mage encrypton scheme ncludes generatng ntal chaotc key stream and two rounds of dffuson operaton. A. he generaton of ntal chaotc key stream Step. Input the ntal condtons ( x y z w ) and ( x y z w ) set the step h and nteger N 5 the control parameter and ntal condton qt nteger C 55. Step. Solve the hyper-chaotc system () wth the ntal condtons ( x y z w ) and ( x y z w ) respectvely. Dscard the frst N ponts of the orbts to overcome the transent effect. Set the N th ponts ( x y z w ) and ( x y z w ) to the new N N N N N N N N ntal condtons. Step 3. Iterate the tent map (4) for N L tmes and dscard the frst N transent ponts and preserve the remander whch s stll denoted as { t... L} and then generate the two-value orbt choce sequence Ln ( l l... l L ). Step 4. o reduce the workload we count the number of and n Ln ( l l... l L ). It s then easy to calculate needed orbt pont numbers and of the two hyperchaotc orbt derved from the new ntal condtons ( x y z w ) and ( x y z w ). N N N N N N N N We note that and should satsfy 4 ( ) L and can be calculated cel( sum( Ln j) / 4) j j where sum( x y) denotes the total number of x( ) y( ) L cel( x ) rounds x to the nearest nteger greater than or equal to x. Step 5. Solve the system () ntal condton ( x y z w ) and step h and get four hyper-chaotc N N N N sequences{ x y z w N... N ()}. We then generate the frst mproved hyper-chaotc sequence { k...4 } () and (3). Smlarly the second mproved hyper-chaotc sequence { k...4 } ether generated wth ntal condton ( x y z w ) N N N N and step h. Step 6. Combne the mproved hyper-chaotc sequences { k...4 } and { k...4 } to be one hybrd ntal key stream mk... L (6). B. wo rounds of dffuson operaton Assume that the D gray value matrx of the plan- P p p... pl mage s converted to be one vector and C c c c... L denotes the correspondng vector of the cpher-mage. One dffuson process s outlned as follows. Step. Set. Step. Compute the frst pxel gray value of the cpher-mage usng the frst pxel gray value of the plan-mage the nteger C and the frst ntal key stream element mk c btxor ( p btxor (mod( C mk 56) mk )) where btxor x y returns the result after btwse XOR operaton. Step 3. Let and calculate the next pxel gray value of the cpher-mage usng c the th pxel gray value of the plan-mage and the th ntal key stream element mk c btxor ( p btxor (mod( c mk 56) mk )) Step 4. Return to Step 3 untl L and fnally we get the cpher-mage vector C c c... cl after one round of dffuson. Step 5. Set. Step 6. Utlzed the frst pxel gray value c the last one c L and mk to get c c btxor ( c btxor (mod( c mk 56) mk )) L Step 7. Let then calculate c c btxor ( c btxor (mod( c mk 56) mk )) Step 8. Return to Step 7 untl L. he fnally yelded vector C c c... cl s the resulted cphermage after two rounds of dffuson operaton. s

5 An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems 9 IV. SECURIY AND PERFORMANCE ANALYSIS Accordng to the basc prncple of cryptology [] an deal encrypton cryptosystem requres senstvty to cpher keys.e. the cpher-text should have close correlaton wth the keys. Furthermore an deal encrypton scheme should have a large key space to make brute-force attack nfeasble; t should also well resst varous knds of attacks lke statstcal attack dfferental attack etc. Some securty analyss wll be performed on the proposed mage encrypton scheme ncludng the most mportant ones lke key senstvty test key space analyss statstcal analyss and dfferental attack analyss. he plan-mage s 56 gray-scale and of sze (ncludng Lena Boat Cameraman). In the smulaton experment we set two ntal condtons ( x 5 y z 5 w ) ( x y 5 z w 5) Shannon ponted out n hs masterpece [6] the possblty to solve many knds of cphers statstcal analyss. herefore passng the statstcal analyss on cpher-mage s of crucal mportance for a cryptosystem. Indeed an deal cryptosystem should be robust aganst any statstcal attack. In order to prove the securty of the proposed encrypton scheme the followng statstcal tests are performed. () Hstogram analyss. We encrypt the plan-mage Lena (Fgure (a)) and get the cpher-mage Fgure (b). We also plot the hstograms of plan-mage and cphermage as shown n Fgures (c)-(d). Fgure (d) shows that the hstograms of cpher-mage s farly unform and sgnfcantly dfferent from the hstogram of the orgnal plan-mage Fgure (c). Hence t does not provde any useful nformaton for the opponents to perform any statstcal analyss attack on the encrypted mage. (a) plan-mage Lena and step h. N C 3 q.3 t.4. All the analyss shows that the proposed mage encrypton scheme s hghly secure thanks to ts hgh senstvty of the control parameters and ntal condtons of the consdered chaotc systems large key space and satsfactory dffuson mechansm. A. Key space analyss Key space conssts of all the possble cpher keys. A good mage encrypton scheme needs to contan suffcently large key space for compensatng the degradaton dynamcs n PC. It should be also large enough to effectvely resst brute-force attack and prevent nvaders decryptng orgnal data even after they nvest large amounts of tme and resources. We can just set the two ntal condtons ( ) x y z w of x y z w the hyper-chaotc system the ntal condton t and the control parameter q of chaotc tent map to be the cpher keys. If they are represented as floatng number wth -4 4 precson then the number of x s herefore the total cpher keys wll be as many as ( ) whch s large enough to make brute-force attack nfeasble. B. Statstcal analyss (b) cpher-mage of Lena (c) Hstogram of Lena (d) hstogram of choer-mage of Lena Fg.. he hstogram analyss result.

6 3 An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems () Correlaton analyss of adjacent pxels. o test the correlaton between two adjacent pxels the followng performances are carred out. Frst we select pars of two adjacent pxels randomly from coeffcent of the selected pars usng the followng formulae: Cr cov xy D x D y x y x E x y E y cov E x x D x x E x where xyare the gray-scale values of two adjacent pxels n the mage and s the total pars of pxels randomly selected from the mage. he correlatons of two adjacent pxels n the plan-mage and n the cphermage are shown n able. It s clear from able that the proposed mage encrypton technque sgnfcantly reduces the correlaton between the adjacent pxels of the plan-mage. able. Correlaton between adjacent pxels of plan-mage and cpher-mage. horzontal vertcal dagonal Plan-mage Lena Cpher-mage of Lena Plan-mage Boat Cpher-mage of Boat Plan-mage Cameraman Cpher-mage of Cameraman () Correlaton between plan-mages and cphermages. We have also analyzed the correlaton between plan-mage and cpher-mage computng the two-dmensonal correlaton coeffcents between of plan-mage and cpher-mage. he D-correlaton coeffcents are calculated C AB H W ( A j A)( B j B) HW j H W H W ( A j A) ( B j B) H W j H W j H W H W A A B B H W H W j j j j where A represents one of the red green and blue channel of the plan mage B represents one of the red green and blue channel of the cpher mage A and B are the mean values of the elements of D matrces A and B respectvely; M and N are respectvely the heght and wdth of the plan/cpher mage. We have computed the correlaton coeffcents for the par of plan-mage Lena and ts correspondng cpher-mage. he results are shown n able. One can see from the results that the correlaton coeffcents between plan-mage and cphermage are very small (or practcally zero) hence the cpher-mage owns the characterstcs of a random mage. able. Correlaton between plan-mage and cpher mage. Image Encrypton CC entropy PSNR Decrypton CC Lena Boat Cameraman (v) Informaton entropy analyss. Informaton entropy s a measure of the uncertanty assocated wth a random varable and can be also a measure of dsorder and randomness. It quantfes the amount of nformaton contaned n data usually n bts/symbol. wo extremely cases are: a long sequence of repeatng characters and a truly random sequence. he former has entropy of snce every character s predctable and the latter has maxmum entropy snce there s no way to predct the next character n the sequence. Regardng mage t can be used to measure the unformty of mage hstograms. he entropy Hm ( ) of a message source m can be measured L H( m) p( m )log( p( m )) (bts) where L s the total number of symbols m pm ( ) represents the probablty of occurrence of symbol m and log denotes the base logarthm so that the entropy s expressed n bts. For a random source emttng 56 symbols ts entropy s Hm ( ) 8 bts. For a 8-bt gray mage the nformaton entropy s gven as 8 H( m) P( I )log (bts). PI ( )

7 An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems 3 We have calculated the nformaton entropes for planmages and ther correspondng cpher-mages. he results are shown n able. he value of nformaton entropy for the cpher-mage produced the proposed mage encrypton scheme s very-very close to the expected value of truly random mage.e. 8bts. Hence the proposed encrypton scheme s extremely robust aganst entropy attacks. (v) Peak sgnal-to-nose rato analyss. Another parameter to descrbe the encrypton qualty s the peak sgnal-to-nose rato (PSNR). hs term s descrbed based on that the mean squared error (MSE) s calculated. hs crteron provdes the error between nput mage and output mage. he MSE value s M N MSE IO j IE j M N j where O E I j s the pxel value of plan-mage I j s the pxel value of cpher-mage. hus the PSNR s descrbed log I max PSNR MSE where I max s the maxmum of pxel value of the mage. he PSNR should be a low value whch corresponds to great dfference between the orgnal mage and the encrypted mage. o determne the encrypton qualty the PSNR s computed for the encrypton of Lena Boat and Cameraman. In able the PSNR values are shown n the fourth column. he results show that these PSNR values are all very low. herefore the encrypton qualty s good n sense of PSNR. C. Senstvty Analyss o test the senstvty of cpher keys and plan-mage two measures NPCR (net pxel change rate) and UACI (unfed average changng ntensty) are usually used. NPCR measures the percentage of dfferent pxel numbers between the two encrypted mages. UACI measures the average ntensty of dfference between the two encrypted mages. hey can be calculated the followng formulae: / j ( ) NPCR D j % M N c ( j) - c ( j) UACI % M N j 55 where c and c are the two cpher-mages and D( j ) s defned c( j) c( j) D( j) otherwse. he NPCR for two random mages whch s an expected estmate for an deal mage cryptosystem s L gven NPCR ( ) % where L s the Expected number of bts used to represent all the gray values of the consdered mage. For a 8-bt gray scale mage L hence NPCR Expected %. he UACI for two random mages whch s an expected estmate for an deal mage cryptosystem s L ( ) gven UACI Expected %. For a 8- L L bt gray mage UACI Expected %. () Key senstvty analyss. A good mage encrypton scheme should be extremely senstve to cpher keys whch s an essental feature for any good cryptosystem n the sense that t can effectvely prevent nvaders decryptng orgnal data even after they nvest large amounts of tme and resources. Assume that we want to verfy the senstvty of cpher key K we encrypt the plan-mage A ( A( j)) M N wth K and K+ K respectvely whle keepng the other keys unchanged the correspondng encrypted mages are A A respectvely where K s the perturbng value. We then calculate the correspondng NPCRUACICC and PSNR. We set the perturbng value to be and get the results shown n able 3. All the expermental results show that the cpher keys are all strongly senstve. able 3. Key senstvty analyss Perturbng value NPCR UACI CC PSNR x y z w a t () Plan-mage senstvty analyss. he dfferental cryptanalyss of a block cpher s the study of how dfferences n a plantext can affect the resultant dfferences n the cphertext wth the same cpher key. It

8 3 An Image Encrypton Scheme Based on Hybrd Orbt of Hyper-chaotc Systems s usually done mplementng the chosen plantext attack but now there are extensons whch use known plantext as well as cphertext attacks also. As for mage cryptosystems attackers may generally make a slght change (e.g. modfy only one pxel) of the plan-mage and compare the two cpher-mages (obtaned applyng the same cpher key on two plan-mages havng one pxel dfference only) to fnd out some meanngful relatonshps between the plan-mage and the cphermage. If a meanngful relatonshp between plan-mage and cpher-mage can be found n such analyss whch may further facltate the opponents to determne the cpher key. If one mnor change n the plan-mage wll cause sgnfcant random and unpredctable changes n the cpher-mage then the encrypton scheme wll resst dfferental attack effcently. o test the robustness of mage cryptosystems aganst the dfferental cryptanalyss We have performed the dfferental analyss calculatng NPCR and UACI on plan-mage Lena. he analyss has been done randomly choosng pxels (one at a tme ncludng the very frst and very last pxels) n each plan-mage and changng ther all three color values one unt. he average values of NPCR and UACI thus obtaned for all three mages are gven n Fgure 3. It s clear that the NPCR and UACI values are very close to the expected values thus the proposed mage encrypton technque shows extreme senstvty on the plantext and hence not vulnerable to the dfferental attacks. he average of the NPCR values s % and the average of UACI s % they are both hghly close to ther expectaton values % and % respectvely. (a) NPCR values D. Resstance to known-plantext and chosen-plantext attacks It follows from the encrypton scheme that mk s related to the ntal cpher keys of the hyper-chaotc system and c depends on the pxel gray values of the plan-mage. Hence the pxel gray values of the planmage are employed to change the fnal encrypton keys except for the frst pxel n the frst round of dffuson operaton. Hence the fnal encrypton keys depend on not only the ntal state value of the hyper-chaotc system but also the plan-mage. When dfferent plan-mages are encrypted the correspondng key stream s not the same. he attacker cannot obtan useful nformaton encryptng some specal mages snce the resultant nformaton s related to those chosen-mages. herefore the attacks proposed n Refs. [6 ] become neffectve on ths new scheme. he proposed scheme can well resst the known-plantext and the chosen-plantext attacks. V. CONCLUSIONS In ths paper a novel plan-mage dependent encrypton scheme based on hybrd orbt of hyper-chaotc system s proposed. wo hyper-chaotc sequences are generate from one hyper-chaotc system and then are mproved and ntegrated nto one hybrd sequence to acheve better randomness and securty for mage encrypton. One dffuson procedure wth two rounds of dffuson operatons are performed whch makes the key stream depend on both the ntal hybrd hyper-chaotc sequence and plan-mage. herefore the key stream n the encrypton process depends on both the ntal keys and the plan-mage and the cpher-mage can resst the known-plantext and chosen-plantext attacks effcently. he key space s large enough to resst brute-force attacks as well. All the performance analyss shows that the scheme can well prevent the mage from statstcal attackng and that the scheme possesses hgh key senstvty and gets a good ablty to resst dfferental attack. Wth hgh-level securty t can be used n nternet applcatons such as network securty and secure mage communcatons. ACKNOWLEDGMEN hs research s supported Natonal Natural Scence Foundaton of Chna (No. 75 & No. 738). REFERENCES (b) UACI values Fg. 3. he dfferental analyss. [] B. Schener Appled Cryptography: Protocols Algorthms and Source Code n C John Wley and sons New York 996. [] F. Huang Z.-H. Guan A modfed method of a class of recently presented cryptosystems Chaos Soltons and Fractals 3(5) [3] G. J. Zhang Q. Lu A novel mage encrypton method based on total shufflng scheme Optcs Communcatons 84()

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