C25_ an Encryption Scheme for Images Based on the DWT and a Chaotic Cipher

1 E. E. D

2 C. E. D

3 E. E. D

A partialgoes throencryptedElknz algTwo othereduce enscramblinthat comp 1. Intro [7]. Sincimage ensecure asattacks [7Elknz [4]high leve encryptingain info‘house’. T change insequencemaps arefrom thegenerate consistinunpredictbitwise e[2],[3]. T the initiakey. Theorbits wi

26th

An E

Department

Departmen

Departmen

encryption syough a single-d by the Elkngorithm hops er chaotic mancryption to ong the rest of plete perceptu

oduction There are two

ce wavelet bancryption techs they are bas7],[8],[9]. The]. The schemeel of security bThe idea is to

ng this matrix ormation abouTherefore, theChaotic mapsn the value oe [1]. These pe used in the ge first three le

a stream ciphng of randomtable without exclusive-OR The random nu

The orbit of al condition. T

e offset is the ill at first over

h NATIONAMarch 17-19

Encryptio

Said El-K

t, Faculty of

t, Faculty of

t, Faculty of

ystem based o-level discretenz cipher. Thebetween eigh

aps are used tone quarter of

the image infual encryption

o basic ways sed compressniques based

se solely on rae encryption e aims at reduby scramblingo encrypt the a

alone will prout the image fre horizontal (cs are extremef the initial c

properties makgeneration of etters of the her a key is in

m numbers, eaknowledge o(XOR). In sy

umber generata given map i

The seeds, offsdifference be

rlap. To avoid

AL RADIO S9, 2009, Facul

on Schemand a

Khamy1, M.

of Engineerie-mail:

of Engineerie-mail: m.a

of Engineerie-mail: col

on the chaotic e 2-dimensionae other subbaht chaotic mapto produce rathe image infoformation. Thn is accomplish

to encrypt digsion appearedin the waveleandom permuscheme prese

ucing encryptiog the rest of thapproximationovide complerom the other ch), vertical (cely dynamic aondition in thke chaotic mathe stream ciauthors’ namnput into a ranach 8 bits loof the input kymmetric enctor used here iis the sequencsets and the oretween the seed overlapping

SCIENCE COlty of Enginee

26th NFuture Un

e for ImaChaotic C

Abou El-N

ing, Alexandelkhamy@

ing, AAST, Pabouelnasr@ing, AAST, Pllege4a@m

Abstract

stream cipheral wavelet tra

ands are scramps to generateandom map anformation. Yethe system is exhed in all subb

gital images: and was ado

et domain haveutations makinented here is bon time by on

he image. n matrix (ca) ate perceptual matrices, esp

cv), and diagoand extremelyhe order of 10aps ideal for ipher Elknz. (

mes.) Stream cndom number

ong. For a hikey. The key-cryption, the is the set of chce produced brbit hopping ced of two adjand insuffici

ONFERENCering, Future U

NATIONAL RADiversity, 5th Comp

ages BasedCipher

Nasr2, Amina

dria Univerieee.org P.O. Box [email protected]. Box M

mailcity.com

r Elknz is preansform (2-D Dmbled using the the scramblind orbit hoppt it provides a xplained in debands as well

in the specialopted in the Je been numerong them suscebased on the Dnly encrypting

as it holds moencryption, it

pecially in imanal (cd) matri

y sensitive to 0-9 will cause encryption. In

(Pronounced eciphers typicar generator. Tigh level of -stream is comsame key is haotic maps. y iterating x0,

codes are kept acent orbits. ent divergenc

CE (NRSC20Univ., Egypt

DIO SCIENCE Cpound, New Cair

d on the D

a El-Zein3

rsity, Alexan

Miami 1029, m

Miami 1029,

esented in this DWT), the lohe same basicing pattern. Eping patterns. high level of

etail and examas in the imag

l domain or inJPEG2000 staous. Howevereptible to knoDWT and the

g part of the im

ost of the imagt would be posages that haveices will be scchanges in tha deviation a

n this paper, el-kinz, the cially encrypt oThe generator security, the mbined with used for encr

, where x0 is tsecret, i.e. the

Since the offsce of the orbit

09) C25

CONFERENCE, Nro, Egypt, March

DWT

ndria 21544

Alexandria

Alexandria

paper. After west frequencc Elknz algor

Each map has The system security by su

mples are givege as a whole.

n the transformandard, sugger, many of thewn or chosene chaotic streamage, yet main

ge’s informatissible for an a

e a lot of edgecrambled. he initial condaway from thmany differen

ipher’s name ione byte at a produces a kkey-stream sthe plaintext ryption and d

the seed of they are derivedsets are very ts producing th

15

NSRC’2009 17-19, 2009

4, Egypt,

a, Egypt,

a, Egypt,

the image cy band is ithm. The 16 orbits. is able to

ufficiently n to show .

m domain estions for ese are not n-plaintext am cipher ntaining a

on. While attacker to es, such as

ditions. A he original nt chaotic is derived time. To

key-stream should be using the

decryption

e map i.e. d from the small, the he cipher,

they mussettle. Wbefore this greatertent map. 2. Chao map is alexpressed

logistic mproducin0.5), it ca

tent map as:

the map p 3. The K secure thparameteFirst, the464. Thishifted cyzeros arewith the 1. 2. 3. 4. 5. bits are torbits of hopping pthe seed,decimal p 4. Initia

transmittmap oncerightmosrepresent

26th

st be iterated We use a fixedhose of the quar than that of . The tent map

otic Maps

In this paper,lso used to ged as follows:

where xn is thmap parameteng the map hoan be expresse

where μQ is this used to pro

where μT is thproducing the

Key

The key is inhe algorithm sers. A few sime sum of the ks value will nyclically to th

e added on theshifted key us24 bits: the se24 bits: the se24 bits: the se16 bits: the of376 bits: dividEach sub-key

those of the orf the tent mappatterns of the then a decimpoint.

alization V

An initializatiter and sent toe. The resultint numbers arts the seed of


a number of d settle for alladratic map fothe logistic m

p has 43 orbits

we use a numenerate the ma

he nth value ir. For chaotic

opping patterned as follows:

he quadratic moduce the orbi

he tent map pe orbit hopping

n binary formashould not us

mple but dynamkey is calculaneed 9 bits tohe right sum te left. This prsing the XOR eed of the quaeed of the logieed of the tentffset of the tended into eight

y is 47 bits lonrbit hopping c

p generating te respective m

mal point. The

Vector

ion vector (IV the receiver wng number is

re then extracf the map pro


f times beforel maps. We hor the same inmaps. The orbs. Each orbit i

mber of logistap hopping pa

xn+1 = μL

in the sequenc behavior, μLn to be equal

xn+1 = μ

map parameteit hopping pat

xn+1 = 0

arameter. Forg patterns to b

at. It is of lengse a constant mic changes a

ated. Since theo express it. Ttimes. Next, 4roduces a seqoperator. The

adratic map pristic map prodt map producinnt map product sub-keys, onng, the first 24code. The orbthe orbit hoppmaps. Before ie offset needs

V) is generatedwith the encrytaken to an ac

cted. This nuoducing the m


26th NFuture Un

e being used thave found thanitial conditionbit hopping cois used to gene

tic and quadraattern. The log

L. xn (1 - xn),

nce, xn+1 is theshould be neto 3.991. The

μQ – 4.( xn)2,

er. For chaotictterns, it is def

.5 – μT. | xn|,

r chaotic behabe equal to 1.9

gth 464 bits (key [6], i.e. tare therefore me key is of lenTherefore, sum48 binary blo

quence of lenge result is dividoducing the IV

ducing the mapng the orbit hocing the orbit h

ne for each cip4 bits are the bit hopping coping patterns. it is used, two s to be much

d each time a ypted messageccuracy of fouumber is then

map hopping p



to produce that the orbits ons. For this reaode (OHC) coerate a unique

atic chaotic mgistic map is d

e value n+1 iar or equal toe quadratic m

c behavior, μQfined for the r

avior, μT shoul995.

(24 + 24 + 24the key shoulmade to the kngth 464 bits,m is always e

ocks of sum agth 48x9 + 32ded as followV. p hopping patopping patternhopping patte

pher generatingseed, the next

ode is a numbThese orbits zeros are addsmaller so fou

message is ene. The IV is furteen decimaln added to thpattern. This e



he cipher. Thiof the logisticason, the settlorresponds to e orbit hopping

aps to producdefined for the

in the same so 4 [5]. We hamap is defined

Q should be neregion (-0.5, 0

ld be near to 2

4 + 16 + 47x8d not corresp

key before ext, then the maxexpressed in 9are placed nex2 = 464. Thiss to provide th

ttern. ns.

erns. g map. t 16 bits are ther that will coare then use

ded to the left ur zeros are a

ncrypted. Thefound by iteratl places withohe number takensures a dyn

09) C25


is number is cc map begin te of the quadran orbit numg pattern.

ce the cipher. e region (0,1)

sequence, andave taken μL od over the reg

ear or equal to0.5), it can be

2. We have ta

8). For the syspond directly tracting the paximum value 9 bits. The kext to each oths sequence is he system para

he offset, and orrespond to oed to generateof the decima

added to its le

e IV is generating a chaotic

out rounding. ken from the

namic keystrea

25

NSRC’2009 17-19, 2009

called the to diverge ratic maps

mber in the

A logistic , it can be

(1)

d μL is the of the map gion (-0.5,

(2)

o 0.5. The expressed

(3)

aken μT of

stem to be to system arameters. of sum is

ey is then her and 32 combined ameters:

the last 7 one of the e the orbit al value of eft, then a

ated at the quadratic The eight

e key that am as the

keystreambe used t 5. Gene

generatioorbits. Beof the cipdue to thmore thatherefore is randomgeneratioproduce provides number iobtain a number ocorresponconstitute

1. corresponiterated S2. multiplieresulting each numcorrespon3. number oproduce t4. signs are

26th

m changes eacto generate the

erating the

An overview on of both theefore generatipher, the maphe fact that thean once in the the SA will cThe orbit hopm, the orbit on process a dsuch patternsa non-repetiti

in the orbit honumber greatof orbits in ending to one es an orbit hop

Key

The SA produBefore beginnding to the oS times, whereThe logistic m

ed by a numbnumber is rou

mber in the seqnd to one of thThen the tentof the orbit othe first five sThese numbe ignored. The


ch time a mese random scra

Scramblin

of the systeme cipher and thing the cipher hopping patte Elknz algorhe sequence. continue until pping patterns hopping patte

different numbs, the orbits ive orbit hoppopping patternter than one. ach map. Theof the 16 or

pping pattern.

KeyManipulation

uces the scramnning to prodorbit hopping e S is the settlemap producinber M. the puunded then diquence is founhe eight mapst map orbit cof the cipher g

samples. ers are taken toen, the decima


sage is encrypambling patter

ng Pattern

m can be seenhe scramblingwe must first

tern in the scrithm produceHowever thea unique sequare generated

erns are of uber of times. Tof the tent m

ping pattern. En, the numberThe producede remainder irbits in the re. Therefore, th

Eight Sub-Keys

O

Seed

Seed, Offset

Figure 1.

mbling patternduce the ciphcodes given i

e. ng the map hourpose of thisivided by 8, wnd. This will p.

orresponding tgenerating ma

o an accuracyal point is rem


26th NFuture Un

pted, even if thrn the IV ensu

n in Fig. 1. Tg algorithm, fot find the mapambling algors random num

e SA dependsuence of the bd from a tent munknown lengTherefore, varmap are only Each time an or is multipliedd number is ts then found.espective ciphhere are 43 dif

Cipher-GeneratMaps

Tent Map

Logistic Map

Map Pa

Orbit Hopping Code

Orbit Pa

Overview of

n as follows: her and the in the key, an

opping patterns is to obtainwhich is the nuproduce a num

to that map’s ap to be used

y of fourteen dmoved from ea



he same key ires that it too

There are eighour logistic, a and orbit hoprithm (SA) dombers, this mes on producinlock size B is

map with 43 ogths. Differenriable length o

iterated wheorbit of the tend by a numberthen rounded . This will prher generatinfferent orbit h

ingSequence

Hoppingattern

Hoppingattern

the system

scrambling pnd all the orbi

n is iterated on a sequence umber of mapmber ranging b

orbit hoppingfor sampling

decimal placesach number an



s used. As theis dynamic.

ht different chand four quadrpping patternsoes not have aeans that a givng a sequencgenerated.

orbits. Since thnt maps may orbit hopping pn called-on bnt map is iterar T, the reasonand divided b

roduce a numbg map. Each opping pattern

SequenceManipulation

pattern, the oits of the ciph

once. The numof numbers g

ps used in the between zero

g code is iteratg. This orbit i

s without rounnd the rightmo

09) C25


ese same maps

haotic maps usratic. Each m

s. Unlike the ina known lengtven number mce of unique

he map hoppinbe used in t

patterns are nby the algoritated to producn for this is thby 16, where

mber between orbit in the

ns.

n

Stream Ciph

orbits of the her generating

mber producedgreater than oSA. The remaand seven, wh

ted once to prs iterated five

nding and anyost eight digit

35

NSRC’2009 17-19, 2009

s will also

sed in the map has 16

n the case th. This is may occur

numbers,

ng pattern the cipher eeded. To thm. This ce an orbit he need to

16 is the 0 and 15, tent map

her

tent map maps are

d will be one. The ainder of hich will

rovide the e times to

y negative ts are then

taken. AnThe remapattern tois already5. pattern is 6. Syste approximexpressedcipher ththey willencryptiowill be dmatrices 1. 2. 3. in each m4. coefficienand blockthe rightm5. wavelet t length caSecondlyfaster, or 7. Exam From thethe orbitoffsets, aequal to stream is image hodetails. Tcombinedidentical after desc

26th

ny numbers leainder is then o ensure that ny in the sequenThis process

s a sequence o

em

The image fimation (ca), hod in the matri

he values of thl range from on the Elknz kivided by 100will be scramEach matrix iEach block haThe scramblin

matrix. Each pair of cnts C1 to C7 wk numbers stamost bottommThis is done iThe encryptetransform (IDWThe system c

an be used to y, the SA can r a smaller num

mples In the first ex

e key, the seedt hopping patand orbit hopp37591, and S a one time paThe scramblin

ouse. It can bThe effect of d effect of ento the origina

crambling.


ess than eight found. The re

no numbers arnce then it is dis repeated un

of numbers tha

irst goes throorizontal (ch)ix ca. The ca he Elknz key-

0 to 65,535key-stream wi0 to give the e

mbled using theis divided intoas B coefficienng pattern is d

coefficients rewill replace thart at the leftmmost corner. in each matrixd ca matrix aWT) to produan offer a varmake the sysuse a larger n

mber of block

xample the imad of the tent mtterns are 0.00ping codes forS is taken as 1ad, which meang algorithm

be seen in Figscrambling on

ncryption andal as can be s


digits are padesulting numbre repeated. Ifdiscarded. ntil the scrambat range from

ough the sing, vertical (cv)matrix will b

-stream will n. The ca matill be combinencrypted ca ce previously g

o N blocks of 8nts. divided into p

eplace each othe coefficientsmost topmost c

x until all the mand the scrambuce the encrypriable level of stem faster, ornumber of blo

ks can be used

age ‘house’, omap is equal to

09157322 andr all the other130 for the logans that its lenwill divide eagure 3 that enn ch, cv, and

d scrambling cseen in Figure


26th NFuture Un

dded on the rigbers are checkf the number i

bling sequenc1 to B/8.

le-level 2-D ), and diagonabe encrypted unot be either. trix will be med with the cacoefficients. Tgenerated scra8 pixels.

pairs. Each pa

ther. If the firss C9 to C16, ancorner of the m

matrices are sbled ch, cv, an

pted image. f security, firstr a longer cip

ocks, which wto increase th

of size 256 X o 0.00397126,d 0.00008271r maps (see Tagistic map, an

ngth is equal toach subband inncrypting cacd can be se

can be seen ie 6. In Figure



ght with zerosked one by oneis not already

e has reached

DWT resultinal (cd) matriceusing the ElknThe Elknz kemultiplied bya coefficients uThe horizontal ambling patter

ir represents a

st two numbernd C1 to C7 wmatrix and in

crambled. nd cd matrice

tly the length pher can be uswill use shorterhe level of scra

256, will go th and the seed

1 respectivelyable 1). In thind 150 for theo the number nto 32 blockshas the effec

een in Figure in Figure 5. Te 7 we can see



s. These numbe against any in the sequen

d the required

ng in four coes. The lowesnz cipher. Un

ey-stream willy 100 to remousing the XO(ch), vertical

rn as follows:

a pair of 8 coe

rs in the pattewill replace C9

crease along t

es then underg

of the cipher sed to increasr chaotic sequambling and t

hrough the aband offset of

y. The key alis example T ie quadratic anof coefficient

s. In Figure 2 ct of complete4 (a), (b), an

The recoverede the individu

09) C25


bers are dividenumbers alrea

nce it is added

length. The sc

oefficient matst frequency snlike the origil not be limiteove any fractR operation. T(cv), and diag

efficients in e

ern are 1 and 2to C16. The c

the row until

go 2-D invers

is variable, sose the level ofuences and thetherefore the s

bove mentionethe tent map p

lso provides tis equal to 92nd tent maps. ts to be encrypwe can see thely securing t

nd (c) respectid image is fouual coefficient

45

NSRC’2009 17-19, 2009

ed by B/8. ady in the

d to it, if it

crambling

trices; the ubband is inal Elknz ed to 256, tions. For The result gonal (cd)

each block

2, then the coefficient the end at

se discrete

o a shorter f security. erefore be security.

ed system. producing the seeds,

2743, M is The key-

pted. he original the image ively. The und to be t matrices

26th

Figu

(

Figure 4

Map #

0 1 2 3 4 5 6 7


re 2. Origina

(a)

4. For ‘house

Type

Logistic Logistic Logistic Logistic

Quadratic Quadratic Quadratic Quadratic


Parameters

al image ‘hou

’ (a) Scrambl

Map parameter

4.00 3.98 3.96 3.94 0.50 0.49 0.48 0.47


26th NFuture Un

Table 1

s Obtained fr

se’. F

(b)

led ch, (b) Sc

Seed

0.005239170.002010720.009073000.003611360.001582840.006512030.001182330.00326537



rom the Key

Figure 3. Afte

rambled cv, a

Offs

750 0.00009220 0.00006030 0.00003670 0.00002465 0.00002370 0.00008370 0.00003790 0.00003



er encrypting

(c

and (c) Scram

set Ohop

co92370 461335 93397722870 124295 287040 536734 339678 7

09) C25


g ca.

c)

mbled cd.

rbit pping ode 42 97 3 15

21 56 38 72

55

NSRC’2009 17-19, 2009

In the seccan be sethe coeffcoefficien

26th

Figure 5. E

(

Figure 7. Fo

cond exampleeen in Fig 8. Tficient matricent matrices ca

Figure


Encrypted an

(a)

or ‘house’ (a)

e we will use aThe combined es are sufficiean be seen.

e 8. Original i


nd scrambled

) Descramble

a larger imageeffect of encr

ently scrambl

image ‘Maria


26th NFuture Un

‘house’.

(b)

ed ch, (b) Des

e, ‘Mariam’ isryption and scled in (a), (b)

am’. Fi



Figure 6. Re

scrambled cv,

s 1024 X 768crambling can), and (c) of F

gure 9. Encry



ecovered ‘hou

(c

, and (c) Desc

pixels. The orn be seen in FiFig. 10. In Fi

ypted and scr

09) C25


use’.

c)

crambled cd.

riginal image ig. 9. It can beig. 11 the des

rambled ‘Ma

65

NSRC’2009 17-19, 2009

‘Mariam’ e seen that scrambled

ariam’.

F The systeThe IV neach time 8. Conc the lowescramblethem aredescriptioperceptua

Referen

1. T. Row1-4. 2. W. Sta3. S. El-K

26th

(a)

Figure 10.

(a)

Figure 11. Fo

The security em is also safenot only affece a message is

clusion

A partial encest frequency ed. Both the ee affected by on of the techal encryption

nces

wlands and D.

allings, CryptoKhamy, M. Lo


. For ‘Mariam

or ‘Mariam’ (

of the propose against know

cts the cipher, s encrypted.

ryption technband of the

encryption anthe IV ensu

hnique and hain the spatial

. Rowlands, “A

ography and notfy, and A. A


m’ (a) Scram

(a) Descramb

sed system reswn/chosen pla

it also affect

ique for imagimage, howed scrambling

uring that theyave shown thrand transform

A more resilie

network securAli, “The FBG


26th NFuture Un

(b)

mbled ch, (b) S

(b)

bled ch, (b) D

sides in the naintext attacksts the permuta

ges has been pever it is high

algorithms ary are dynamirough exampl

m domains.

ent approach t

rity, Prentice HG stream ciphe



Scrambled cv

escrambled c

number of poss as it uses an ation pattern.

presented in thhly secure as re based on mic and henceles the ability

to chaotic enc

Hall, New Jersr,” Proc. of U



v, and (c) Scra

cv, and (c) De

ssible combinaIV that changThis means th

his paper. Ththe rest of t

multiple chaoti secure. We

y of the system

ryption,” Proc

sey, 2006. URSI-NRSC, 20

09) C25


(c)

ambled cd.

(c)

escrambled cd

ations of permges with everyhat the pattern

e system onlythe other banic systems, anhave given am to provide

c. of ICITA, 2

007, pp. 1-8.

75

NSRC’2009 17-19, 2009

d.

mutations. y message. n changes

y encrypts ds are all

nd both of a detailed complete

002, pp.

4. A. El-ZEncryptio5. S. El-wireless 6. M. Sob2001, vol7. S. Li, GB. Furht 8. S. LianEncryptio372–3769. G. GicomparisMultimed

26th

Zein, S. El-Khon," URSI-GAKhamy, M. Gcommunicatiobhy and A. Shl. 2, pp. 1001-G. Chen, “Chand D. Kirovsn and Z. Wangon,” In Proc. , 2003. inesu, T. Onason between sdia Communi


hamy, and M.A'2008, ChicagGad, and S. Sons,” Proc. of hehata, “Meth-1004.

haos-Based Enski, CRC Presg, “ComparisoInt. Conferen

ali and D.D. simple techniqcations Confe


Abou El-Nasgo, USA, AugShaaban, “Apf EUROCON, hods of attacki

ncryption for Dss, 2004. on of several wnce on Comp

Giusto, “Effques for mobierence (MobiM


26th NFuture Un

sr, "The Chaotgust, 2008. pplications an2005, vol. 1, ping chaotic en

Digital Image

wavelet coeffiputer Network

ficient Scramile application

Media’06), 200



tic Stream Cip

d optimizatiopp. 433-436.

ncryption and

s and Videos,

ficients confusks and Mobil

mbling of Wavns,” Proceedin06.



pher "Elknz" f

on of chaotic

countermeasu

,” in Multimed

sion methods ale Computing

velet-based Cngs of the 2n

09) C25


for High Secu

maps in next

ures,” Proc. of

dia Security H

applied in mug (ICCNMC’2

Compressed Imnd Internation

85

NSRC’2009 17-19, 2009

urity Data

t-g secure

f ICASSP,

Handbook,

ltimedia 2003), pp.

mages, A al Mobile

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Said E

2 C. E. D3 E. E.

presen

dimen

encryp

same b

maps t

chaotic

system

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image

show t

well as

26th

An Encrypt

E. El-Kham

1 E. E. Depar

Department, FDepartment, F

A partial

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basic Elkn

to generat

c maps ar

m is able to

vides a hi

informati

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rtment, Facult

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encryption

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26th NFuture Un

ges Based on

Abou El-Na

ring, Alexandrl: elkhamy@ie

AST, P.O. BoxAST, P.O. Box

UMMAR

based on t

image goe

2-D DWT

The other

Elknz alg

pattern. E

random m

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ty by suff

explained

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n the DWT

sr2, Member

ria Universityeee.org

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the chaoti

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gorithm ho

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c stream c

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owest fre

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has 16 or

rbit hoppi

he image

scrambling

and examp

plished in

09) C25


aotic Ciphe

d Amina El

21544, Egypt,

bouelnasr@gmege4a@mailci

cipher "El

-level disc

quency b

mbled usi

een eight c

rbits. Two

ing pattern

informatio

g the rest

ples are g

all subba

95

NSRC’2009 17-19, 2009

er

-Zein3

,

mail.com ity.com

lknz" is

crete 2-

band is

ing the

chaotic

o other

ns. The

on. Yet

of the

given to

ands as

بالقفز "

ة القفز

س نظام

مستوى

بديل

لية من

26th

"الكنز"وارزم

ة لتوليد أنمطة

ضوي أيضا نفس

ث يحتوي أقل

التب م خوارزم

على درجة عال


يقوم خو ".نز

ضوية إضافية

لتبديل الفوض

ذبذبية، حيث

قط و يستخدم

مع الحفاظ ع


ي

الكنز" وضوية

م خرائط فوض

دم خوارزم ال

عدة مستويات

ذا المستوى فق

ير إلى الربع م


26th NFuture Un

لخص عربي

دم الشفرة الفو

تستخدم. عشر

يستخد .خرائط

صورة إلى عد

يتم تشفير هذ

م آمية التشفير



مل

لصور يستخد

راتها الستة ع

ن مدارات الخ

يتم تقسيم الص

لهذا السبب.

كذا يقلل النظام



فير الجزئي لل

وضوية و مدا

مطة القفز بين

.ا يجعله آمن

نات الصورة

هكذ .مستويات

09) C25


ث نظام للتشف

ان خرائط فو

أنم لخرائط و

في التوليد مما

ى معظم مكون

ي في باقي الم

105

NSRC’2009 17-19, 2009

يقدم البحث

ما بين ثما

فيما بين ا

ف" الكنز"

ذبذبة على

الفوضوي

. األمان

C25_ an Encryption Scheme for Images Based on the DWT and a Chaotic Cipher

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Transcript of C25_ an Encryption Scheme for Images Based on the DWT and a Chaotic Cipher