c25_ an encryption scheme for images based on the dwt and a chaotic cipher
TRANSCRIPT
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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
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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,
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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
h NATIONAMarch 17-19
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
AL RADIO S9, 2009, Facul
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
SCIENCE COlty of Enginee
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
ONFERENCering, Future U
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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
CE (NRSC20Univ., Egypt
DIO SCIENCE Cpound, New Cair
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
CONFERENCE, Nro, Egypt, March
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
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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
h NATIONAMarch 17-19
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
AL RADIO S9, 2009, Facul
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
SCIENCE COlty of Enginee
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
ONFERENCering, Future U
NATIONAL RADiversity, 5th Comp
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
CE (NRSC20Univ., Egypt
DIO SCIENCE Cpound, New Cair
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
CONFERENCE, Nro, Egypt, March
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
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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.
h NATIONAMarch 17-19
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
AL RADIO S9, 2009, Facul
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
SCIENCE COlty of Enginee
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
ONFERENCering, Future U
NATIONAL RADiversity, 5th Comp
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
CE (NRSC20Univ., Egypt
DIO SCIENCE Cpound, New Cair
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
CONFERENCE, Nro, Egypt, March
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
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26th
Figu
(
Figure 4
Map #
0 1 2 3 4 5 6 7
h NATIONAMarch 17-19
re 2. Origina
(a)
4. For ‘house
Type
Logistic Logistic Logistic Logistic
Quadratic Quadratic Quadratic Quadratic
AL RADIO S9, 2009, Facul
Parameters
al image ‘hou
’ (a) Scrambl
Map parameter
4.00 3.98 3.96 3.94 0.50 0.49 0.48 0.47
SCIENCE COlty of Enginee
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
ONFERENCering, Future U
NATIONAL RADiversity, 5th Comp
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
CE (NRSC20Univ., Egypt
DIO SCIENCE Cpound, New Cair
er encrypting
(c
and (c) Scram
set Ohop
co92370 461335 93397722870 124295 287040 536734 339678 7
09) C25
CONFERENCE, Nro, Egypt, March
g ca.
c)
mbled cd.
rbit pping ode 42 97 3 15
21 56 38 72
55
NSRC’2009 17-19, 2009
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In the seccan be sethe coeffcoefficien
26th
Figure 5. E
(
Figure 7. Fo
cond exampleeen in Fig 8. Tficient matricent matrices ca
Figure
h NATIONAMarch 17-19
Encrypted an
(a)
or ‘house’ (a)
e we will use aThe combined es are sufficiean be seen.
e 8. Original i
AL RADIO S9, 2009, Facul
nd scrambled
) Descramble
a larger imageeffect of encr
ently scrambl
image ‘Maria
SCIENCE COlty of Enginee
26th NFuture Un
‘house’.
(b)
ed ch, (b) Des
e, ‘Mariam’ isryption and scled in (a), (b)
am’. Fi
ONFERENCering, Future U
NATIONAL RADiversity, 5th Comp
Figure 6. Re
scrambled cv,
s 1024 X 768crambling can), and (c) of F
gure 9. Encry
CE (NRSC20Univ., Egypt
DIO SCIENCE Cpound, New Cair
ecovered ‘hou
(c
, and (c) Desc
pixels. The orn be seen in FiFig. 10. In Fi
ypted and scr
09) C25
CONFERENCE, Nro, Egypt, March
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’.
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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
h NATIONAMarch 17-19
. 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
AL RADIO S9, 2009, Facul
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
SCIENCE COlty of Enginee
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
ONFERENCering, Future U
NATIONAL RADiversity, 5th Comp
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
CE (NRSC20Univ., Egypt
DIO SCIENCE Cpound, New Cair
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
CONFERENCE, Nro, Egypt, March
(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.
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4. A. El-ZEncryptio5. S. El-wireless 6. M. Sob2001, vol7. S. Li, GB. Furht 8. S. LianEncryptio372–3769. G. GicomparisMultimed
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