An efficient color/grayscale image encryption scheme based on hybrid chaotic maps

Abstract

Image encryption has become the essential way to secure image information with the high frequency of multimedia information exchange on the Internet. In this paper, an effective chaotic color/grayscale image encryption algorithm is proposed. The algorithm uses a hybrid 2D composite chaotic map combined with a sine–cosine cross-chaotic map for the transformation required to scramble the image as a confusion phase. As for the diffusion phase, a 1D combined Logistic-Tent chaotic map is used to generate a chaotic self-diffusion matrix that is bitwise XORed with the scrambled image to produce the final cipher image. The proposed algorithm combines the merits of both 1D and 2D chaotic maps; it has a simple structure, easy implementation, and excellent chaotic features making its chaotic orbits more unpredictable for introducing more security. The simulation and analysis results proved that the algorithm has a promising security performance and has a high ability to resist statistical and differential attacks.

Full text

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Keywords:
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1. Introduction
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N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
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2. Background and related work
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N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
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N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
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G> AF L=JEK G> L@= E9H L@9L ?=F=J9L=K L@=E /@AK AK G>L=F 9;LM9DDQ :=
;9MK= L@=J= 9J= K=N=J9D <A>>=J=FL AL=J9LAN= HJG;=<MJ=K LG ;GE= MH OAL@
L@= A<=FLA;9D >J9;L9D 67 @9GLA; E9HK @9N= FME=JGMK 9HHDA;9LAGFK
AF AF>GJE9LAGF 9F< ;GEEMFA;9LAGF L=;@FGDG?A=K :AGDG?Q 9F< E=<A;AF=
9F< =D=;LJA;9D 9F< ;GEEMFA;9LAGF =F?AF==JAF? .AF;= )GO9<9QK
;@9GLA; E9HK 9J= MK=< AF ;@9GLA; ;JQHLG?J9H@Q ;@9GLA; LJ9FKHGJL H@=
FGE=F9 <A?AL9D AE9?= =F;G<AF? 9F< EG<=DAF? G> ;GEEMFA;9LAGF
;@9FF=DK 67
.=N=J9D AE9?= =F;JQHLAGF K;@=E=K :9K=< GF ;@9GLA; E9HK @9N= :==F
HJGHGK=< AF L@= DAL=J9LMJ= >GJ :GL@ ?J9QK;9D= 9F< ;GDGJ AE9?=K OAL@ L@=
9AE LG AF;J=9K= L@= GN=J9DD K=;MJALQ /@= C=Q A<=9 G> <=N=DGHAF? 9FQ AE
9?= =F;JQHLAGF KQKL=E :9K=< GF ;@9GK E9HK AK LG @9N= 9 ?GG< H=J>GJ
E9F;= 9F< LG J=KAKL :GL@ KL9LAKLA;9D 9F< ;JQHL9F9DQLA; 9LL9;CK 9K ;JQH
LGKQKL=E L@9L J=DA=K GF GF=LAE= H9< C=QK 6–7 'AM =L 9D 67 HJ=
K=FL=< 9 KLJ=9E;AH@=J 9D?GJAL@E <=H=F<AF? GF 9 JG:MKL DAF=9J ;@9GLA;
E9H LG ?=F=J9L= 9 GF=LAE= H9< C=Q LG >GJLA>Q L@= K=;MJALQ G> L@= 9D?G
JAL@E -=;=FLDQ KGE= J=K=9J;@=JK @9N= <=N=DGH=< 9 FME:=J G> =F;JQH
LAGF K;@=E=K :9K=< GF ) ) :9K=< K;@=E=K <=H=F< GF LOG
H@9K=K L@= WJKL H@9K= AK LG =F;G<= L@= AFHML HAP=DK LG L@= ) K=IM=F;=
9F< ?=F=J9L= L@= C=Q :Q MKAF? ) L@=GJQ 9F< L@= K=;GF< H@9K= AK LG
?=F=J9L= L@= ;AH@=J :Q MKAF? ) GH=J9LAGF JMD=K 6–7 2M =L 9D
67 HJGHGK=< 9 ;GDGJ AE9?= =F;JQHLAGF K;@=E= :9K=< GF EMDLAHD= AE
HJGN=<  ;@9GLA; KQKL=EK 9F< ) K=IM=F;= GH=J9LAGFK OAL@ 9 K9LAK
>9;LGJQ K=;MJALQ D=N=D #GO=N=J L@= ;GEHML9LAGF9D ;GEHD=PALQ AK @A?@
KAF;= AL MK=K L@J== <AKLAF;L E9HK 9F< J=IMAJ=K ) ;GEHMLAF? =F;G<AF?
9F< <=;G<AF? L@9L AK FGL A<=9D >GJ 9 DA?@LO=A?@L 9HHDA;9LAGF (GJ=GN=J
L@= KQKL=E @9K DAEAL=< =>>=;LAN=F=KK 9?9AFKL ;JGHHAF? 9LL9;C 'AM =L 9D
67 HJGHGK=< 9 ?J9Q AE9?= =F;JQHLAGF 9D?GJAL@E MKAF? ) 9F< LOG
;@9GLA; E9HK HA=;=OAK= DAF=9J ;@9GLA; E9H 9F< @=:QK@=N ;@9GLA;
E9H /@= KQKL=E ;GMD< := NMDF=J9:D= LG <A>>=J=FLA9D 9LL9;C <M= LG 0$
N9DM=K 9F< AL @9K 9DKG DAEAL=< =>>=;LAN=F=KK 9?9AFKL FGAK= 9LL9;C /@= :AL
D=N=D H=JEML9LAGF AK HJ=K=FL=< 9K 9F AE9?= =F;JQHLAGF L=;@FAIM= LG
;@9F?= L@= HD9AF AE9?= HAP=DK N9DM=K 9K K@GOF AF 6–7 $F 67 'AM =L
9D HJ=K=FL=< 9 KLJ=9E;AH@=J 9D?GJAL@E <=H=F<AF? GF 9 JG:MKL DAF=9J
;@9GLA; E9H LG ?=F=J9L= 9 HK=M<GJ9F<GE C=Q LG AF;J=9K= L@= K=;MJALQ
#GO=N=J L@= K;@=E= @9K @A?@ ;GEHML9LAGF ;GEHD=PALQ 9F< L@= ;GKL G>
L@= AEHD=E=FL9LAGF G> KG>LO9J= 9F< @9J<O9J= AF;J=9K=K <M= LG L@= ;GE
HD=P KLJM;LMJ= 9F< L@= EMDLAHD= H9J9E=L=JK MK9?= /=F? =L 9D HJ=K=FL=<
9 K;@=E= :9K=< GF L@= :ALD=N=D H=JEML9LAGF <=H=F<AF? GF 9 ;@9GLA;
KQKL=E LG =F;JQHL ;GDGJ AE9?=K 67 -=;=FLDQ L@= >J9;L9D E9LJAP AK HJG
HGK=< LG := MK=< AF AE9?= =F;JQHLAGF 9K AF 67 29F? =L 9D HJG
HGK=< 9 FGN=D ?J9Q =F;JQHLAGF 9D?GJAL@E G> >J9;L9D KGJLAF? E9LJAP !.(
9F< ?DG:9D HAP=D <A>>MKAGF OAL@ LOG ;@9GLA; K=IM=F;=K 67  K=EA
L=FKGJ E9LJAP AK 9DKG HJGHGK=< 9K 9 ;@9GLA; =F;JQHLAGF E=L@G< LG :=
MK=< AF AE9?= =F;JQHLAGF 9K AF 6–7 29F? =L 9D 67 HJGHGK=< 9
FGN=D ?J9QK;9D= ;@9GLA; AE9?= =F;JQHLAGF 9D?GJAL@E >GJ GGD=9F F=L
OGJC =F;JQHLAGF /@= =F;JQHLAGF 9D?GJAL@E AK FGL GFDQ >GJ AE9?= =F


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 7. 9 +D9AF $E9?= : AH@=J AE9?= ; =;JQHL=< $E9?= G>  ]   AE9?=  ]  '=F9 AE9?= 9F<  ]   AE9?=
Table 1
/GL9D C=Q KH9;= ;GEH9JAKGF J=KMDLK
GDGJ $E9?=K "J9QK;9D= $E9?=K
D?GJAL@EK &=Q .H9;= D?GJAL@EK &=Q .H9;=
/@= HJGHGK=<
9D?GJAL@E
/@= HJGHGK=<
9D?GJAL@E
-=> 67 -=> 67
-=> 67 -=> 67
-=> 67 -=> 67
-=> 67 -=> 67
-=> 67 -=> 67
-=> 67  ] -=> 67
;JQHLAGF :ML 9DKG ;9F := MK=< LG =F;JQHL 9 ;GEHD=P F=LOGJC !AF9DDQ 9K
>GJ GF=<AE=FKAGF ;@9GLA; E9H  9F< EMDLA<AE=FKAGF ;@9GLA; E9H
K=N=J9D J=K=9J;@=K @9N= :==F HJGHGK=< 29F? =L 9D 67 HJGHGK=< 9
;@9GLA; AE9?= =F;JQHLAGF K;@=E= L@9L <=H=F<AF? GF H=J;=HLJGF EG<=D
9F< @A?@<AE=FKAGF 'GJ=FR ;@9GLA; KQKL=E /@= 9D?GJAL@E @9K 9 KAEHD=
KLJM;LMJ= 9F< =9KQ LG AEHD=E=FL :ML AL AK FGL K=;MJ= =FGM?@ 9K AL @9K DGO
K=9J;@ KH9;= LG J=KAKL :JML= >GJ;= 9LL9;C <M= LG ALK C=QK H9;= 9F< @9K 9DKG
DAEAL=< =>>=;LAN=F=KK 9?9AFKL ;JGHHAF? 9LL9;C $F 67 29F? =L 9D HJ=
K=FL=< 9 ;@9GLA; ;GDGJAE9?= =F;JQHLAGF K;@=E= L@9L ;GE:AF=K ;@9GLA;
E9H JFGD<’K ;9L E9H 9F< #GHW=D< ;@9GLA; F=MJ9D F=LOGJC /@=
K;@=E= K=;MJALQ D=N=D AK ?GG< :ML L@= ;GEHML9LAGF9D ;GEHD=PALQ AK @A?@
<M= LG EMDLAHD= E9HK MK9?= AF 9<<ALAGF LG =F;G<AF? 9F< <=;G<AF? G> L@=
#GHW=D< ;@9GLA; F=MJ9D F=LOGJC 'MG =L 9D HJ=K=FL=< 9 ?J9QK;9D= =F
;JQHLAGF KQKL=E :9K=< GF  :9C=J E9H 9F<  DG?AKLA; E9H LG GN=J
;GE= L@= <J9O:9;CK G>  ;@9GLA; E9HK 67 +9C =L 9D HJGHGK=< 9
;GDGJ AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF LOG  KAF= ;@9GLA; E9HK
67 /@= 9D?GJAL@E AK ;@9J9;L=JAR=< :Q :=AF? 9 KAEHD= 9F< AL =F@9F;=K
L@= K=;MJALQ D=N=D "= =L 9D 67 HJ=K=FL=< 9 :ALD=N=D AE9?= =F;JQHLAGF
9D?GJAL@E :Q MKAF? L@=  ;9L E9H 'GJ=FR KQKL=E L@= J=N=JK=  ;9L
E9H 9F< 9F =F@9F;=< ;@9GLA; E9H OAL@ (9JCGN HJGH=JLA=K /@= 9D?G
JAL@E @9K 9 ?GG< K=;MJALQ D=N=D 9F< ;9F J=KAKL <A>>=J=FL LQH=K G> 9LL9;CK
$FKHAJ=< :Q L@= 9:GN= <AK;MKKAGFK L@AK H9H=J @9K :==F HJGHGK=< ;
;GJ<AF? LG L@= 9F9DQKAK 9F< J=NA=O G> L@= HJ=NAGMK OGJCK AF L@= W=D< L@=
HJGHGK=< OGJC HJ=K=FL=< AF L@= ;MJJ=FL H9H=J LJA=K LG GN=J;GE= L@=
<J9O:9;CK >GMF< AF L@= J=D9L=< OGJCK 9F< ;9F ?J=9LDQ ;GEH=L= OAL@
GL@=JK =F;JQHLAGF 9D?GJAL@EK 9K K@GOF D9L=J
3. Introduction to chaotic systems
3.1. Logistic map
*F= G> L@= EGKL CFGOF ;@9GLA; E9HK AK 9 DG?AKLA; E9H L@9L @9K
OA<=DQ KHJ=9< AF E9FQ W=D<K KM;@ 9K AE9?= =F;JQHLAGF 9F< K=;MJ= ;GE
EMFA;9LAGF /@= DG?AKLA; E9H AK ;@9J9;L=JAR=< :Q ALK KAEHD= KLJM;LMJ=
9F< IM9KAJ9F<GEF=KK @GO=N=J AL @9K DGO K=;MJALQ <M= LG ALK DGO ;GE
HD=PALQ /@= 'G?AKLA; E9H AK 9 K=;GF<<=?J== HGDQFGEA9D E9HHAF? ;@9J
9;L=JAR=< :Q L@= =IM9LAGF



N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 8a. 9 9F< : K@GO L@= L=KL J=KMDLK G> C=Q K=FKALANALQ 9F9DQKAK G>  ]   ;GDGJ AE9?= ; < 9F< = G>  ]  '=F9 ;GDGJ AE9?= > 9F< ? G>
 ]   ?J9QK;9D= AE9?= @ 9F< A G>  ]  '=F9 ?J9QK;9D= AE9?= 9F< B G>  ]   ?J9QK;9D= AE9?= !GJ AFL=JHJ=L9LAGF G> L@= J=>=J
=F;=K LG ;GDGMJ AF L@AK W?MJ= D=?=F< L@= J=9<=J AK J=>=JJ=< LG L@= O=: N=JKAGF G> L@AK 9JLA;D=
Fig. 8b. /@= L=KL J=KMDLK G> C=Q K=FKALANALQ 9F9DQKAK G> ;GDGJ 9F< ?J9QK;9D=  ]  '=F9 AE9?= !GJ AFL=JHJ=L9LAGF G> L@= J=>=J=F;=K LG ;GDGMJ AF L@AK W?MJ= D=?=F<
L@= J=9<=J AK J=>=JJ=< LG L@= O=: N=JKAGF G> L@AK 9JLA;D=
Table 2
/@= <A>>=J=F;= G> ;AH@=J=< AE9?= 9>L=J =F;JQHL=< '=F9 AE9?=
F;JQHLAGF &=Q GDGJ $E9?= "J9QK;9D= $E9?=
-=< @9FF=D "J==F @9FF=D DM= @9FF=D
&=Q9   
&=Q:   
&=Q;   
&=Q<   
&=Q>   
O@=J= Di∈67iAK L@= FME:=J G> AL=J9LAGFK 9F< ‘G’AK L@= N9DM= G>
AFL=J=KL OAL@AF L@= AFL=JN9D  7  :A>MJ;9LAGF HDGL G> L@= DG?AKLA; E9H
AK K@GOF AF !A? 
3.2. Tent map
/@= L=FL E9H AK KAEAD9J LG L@= DG?AKLA; E9H $L AK GF= G> L@= EGKL
CFGOF ;@9GLA; E9HK OA<=DQ KHJ=9< AF E9FQ W=D<K KM;@ 9K ;@9GLA; ;JQH
LG?J9H@Q /=FL E9H AK 9 ;GFLAFMGMK ;GEHGKAL= G> LOG DAF=9J >MF;LAGFK
H=J>GJEAF? GF L@= AFL=JN9D G> 9 MFAL /=FL E9H AK MK=< LG <=WF= L@=
KLJ=L;@AF? 9F< >GD<AF? G> 9  =D9KLA; :9F< G> D=F?L@ GF= N=JQ LAE= L@=
E9H AK J=H=9L=< L@= :9F< KLJ=L;@=K LG LOA;= ALK D=F?L@ 9F< >GD<K AFLG AL
K=D> 67 /@= L=FL E9H @9K 9 KLJ9A?@L>GJO9J< >GJE 9F< ALK =IM9LAGF AK
DAF=9J >GJ ;=JL9AF H9J9E=L=JK F=N=JL@=D=KK AL ;9F <AKHD9Q ;GEHD=P :=
@9NAGJ 9F< =N=F ;@9GLA; H@=FGE=F9 67 (9L@=E9LA;9DDQ 9K K@GOF AF
I  L@= L=FL E9H AK OJALL=F 9K

O@=J= ∈67 9F< AK 9 J=9D HGKALAN= FME:=J  :A>MJ;9LAGF HDGL G>
L@= L=FL E9H AK K@GOF AF !A?  67
4. The proposed algorithm
/@AK K=;LAGF <=K;JA:=K 9 F=O =F;JQHLAGF 9D?GJAL@E L@9L AF;GJHGJ9L=K
L@= E=JALK G>  OAL@  ;@9GLA; E9HK LG J=KAKL N9JAGMK LQH=K G> 9LL9;CK
KM;@ 9K L@= ;D9KKA;9D 9LL9;CK <A>>=J=FLA9D 9LL9;C KL9LAKLA;9D 9LL9;C 9F<
:JML= >GJ;= 9LL9;C /@= D9QGML G> L@= HJGHGK=< 9D?GJAL@E AK <=HA;L=< AF
!A?K 9 9F< : /@=K= W?MJ=K K@GO L@= =F;JQHLAGF D9QGML >GJ ;GD
GJ=< AE9?=K 9F< ?J9Q AE9?=K J=KH=;LAN=DQ /@= HJGHGK=< 9D?GJAL@E <=
H=F<K E9AFDQ GF L@= ;GF>MKAGF 9F< <A>>MKAGF H@9K=K $F L@= ;GF>MKAGF
H@9K= HAP=D K@M>XAF? AK >MDWDD=< :Q ?=F=J9LAF? +.- OAL@  KAF;GKAF=
;JGKK;@9GLA; E9H /@=F  'G?AKLA;/=FL ;@9GLA; E9H AK MK=< LG ?=F=J
9L= +-. 9F< :ALOAK= 3*-=< OAL@ L@= K;J9E:D=< AE9?= AF L@= <A>>MKAGF
H@9K= (GJ= <=L9ADK 9J= =PHD9AF=< AF L@= >GDDGOAF? KM:K=;LAGFK


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 9a. #AKLG?J9E G> 9 HD9AF AE9?= 9F< : ;AH@=J AE9?= G>  ]   ;GDGJ AE9?= !GJ AFL=JHJ=L9LAGF G> L@= J=>=J=F;=K LG ;GDGMJ AF L@AK W?MJ= D=?=F< L@=
J=9<=J AK J=>=JJ=< LG L@= O=: N=JKAGF G> L@AK 9JLA;D=
4.1. Confusion phase
GF>MKAGF 9AEK LG E9C= L@= J=D9LAGFK@AH :=LO==F :GL@ ;AH@=JAE9?=
9F< L@= C=Q ;GEHD=P 9K HGKKA:D= /@AK AK <GF= :Q E9CAF? =9;@ :AL G> L@=
;AH@=JAE9?= <=H=F<AF? GF EMDLAHD= H9JLK G> L@= C=Q O@A;@ @A<= L@= J=
D9LAGF :=LO==F :GL@ /@AK E9C=K AL @9J< LG J=LJA=N= L@= C=Q >JGE L@= ;A
H@=JAE9?= 9F< =N=F A> GF=:AL ;@9F?= AF L@= C=Q OADD := ;GEHD=L=DQ 9>
>=;L=< L@= ;AH@=JAE9?= 9F< L@=J= OADD := 9 @M?= <A>>=J=F;= AF L@= ;A
H@=JAE9?=
/@=  KAF;GKAF= ;JGKK;@9GLA; E9H O9K J=;=FLDQ HJ=K=FL=< :Q
(GF<9D 9F< =@=J9 67 LG ;GFKLJM;L 9F =>W;A=FL AE9?= =F;JQHLAGF
;JQHLGKQKL=E /@AK E9H AK MK=< LG J=EGN= L@= J=D9LAGFK@AH :=LO==F L@=
F=9J:Q HAP=DK :Q ?=F=J9LAF? HK=M<GJ9F<GE K=IM=F;=K O@A;@ 9J= MK=<
LG K;J9E:D= L@= AE9?= HAP=DK AF GJ<=J LG :J=9C L@= @A?@ ;GJJ=D9LAGF :=
LO==F L@= 9<B9;=FL HAP=DK OAL@AF L@= HD9AF AE9?= /@AK  E9H AK ;@9J
9;L=JAR=< :Q ALK ;GEHD=PALQ O@A;@ E9C=K AL EGJ= K=;MJ= /@= E9L@=
E9LA;9D <=>AFALAGF G> L@= KAF=;GK ;@9GLA; E9H AK 9K >GDDGOK 67


O@=J=  9J= LOG AFALA9D H9J9E=L=JK    ∈67 9F< Z9F< E9J=
LOG ;GFLJGD H9J9E=L=JK O@=J= Z, E∈67/@= H=J>GJE9F;= G> L@=
 KAF;GKAF= ;@9GLA; E9H O9K 9KK=KK=< :Q L@= 'Q9HMFGN =PHGF=FL
H@9K= <A9?J9E :A>MJ;9LAGF 9F9DQKAK 9F< O9K L=KL=< :Q )$./ KL9LAKLA;9D
L=KLAF? 9F< H9KK=< 9DD L@=K= L=KLK /@AK KA?FAW=K L@9L  KAF;GKAF=
;@9GLA; E9H AK LJMDQ J9F<GE 9K J=;GEE=F<=< :Q )$./ 9K ADDMKLJ9L=< AF
67 $LK H@9K= <A9?J9E K@GOK L@9L L@= <AKLJA:MLAGF G> <9L9 ;GN=JK 9
EM;@ D9J?=J J=?AGF O@A;@ AF<A;9L=K L@9L L@= HJGHGK=< E9H ;GN=JK L@=
O@GD= J=?AGF )G ;DMKL=JK 9J= >GMF< LG 9 H9JLA;MD9J J=?AGF O@A;@ 9K
KMJ=K L@= J9F<GEF=KK 9F< MFA>GJE <AKLJA:MLAGF G> L@= HK=M<GJ9F<GE
K=IM=F;= LG J=9DAR= @A?@ <A>>MKAGF 9:ADALQ /@MK L@= E9H AK ;GF;DM<=< LG
:= ;@9GLA; 9F< @9K ?GG< =J?G<A;ALQ $L 9DKG 9LL9AFK @QH=J;@9GLA; :=@9N
AGJ O@A;@ AK ;GFKA<=J=< 9 ?GG< ;JAL=JAGF >GJ AE9?= =F;JQHLAGF 9F< AL AK
N=JQ <A>W;MDL >GJ 9LL9;C=JK LG HJ=<A;L L@= K=;J=L C=Q /@= :A>MJ;9LAGF <A9
?J9EK 9J= <=HA;L=< AF !A?  9F< !A?  OAL@ J=KH=;L LG N9JQAF? G> 9F<
5 J=KH=;LAN=DQ 67
4.2. Di?usion phase
/@= E9AF A<=9 G> <A>>MKAGF AK LG =DAEAF9L= L@= ;GJJ=D9LAGF :=LO==F
:GL@ G> HD9AF AE9?= 9F< ;AH@=J AE9?= O@A;@ J=IMAJ=K 9FQ ;@9F?= AF
GF= :AL G> L@= HD9AF AE9?= 9L D=9KL @9D> G> L@= ;AH@=J AE9?= :ALK K@GMD<
9DKG := ;@9F?=< 9F< NA;= N=JK9 /@AK ;GMD< := <GF= :Q E9CAF? L@= ;A
H@=J=< N9DM=K K=FKALAN= LG K=;J=L C=QK 9F< HD9AF N9DM=K 9K K==F AF L@= >GD
DGOAF? K=;LAGFK /@AK AK =FGM?@ LG HJ=N=FL L@= 9LL9;C=J >JGE J=N=9DAF?
L@= HD9AF AE9?= >JGE L@= ;AH@=J=< GF= 9F< J=KAKL <A>>=J=FL LQH=K G> 9L
L9;CK
*F= G> L@= ;GFLJA:MLAGFK G> L@AK ;MJJ=FL OGJC AK LG =F@9F;= L@= H=J
>GJE9F;= G> L@= <A>>MKAGF HJG;=KK NA9 AFLJG<M;AF? 9 E=J?= :=LO==F L@=


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 9b. #AKLG?J9E G> 9 HD9AF AE9?= 9F< : ;AH@=J AE9?= G>  ]  '=F9 ;GDGJ AE9?= !GJ AFL=JHJ=L9LAGF G> L@= J=>=J=F;=K LG ;GDGMJ AF L@AK W?MJ= D=?=F< L@=
J=9<=J AK J=>=JJ=< LG L@= O=: N=JKAGF G> L@AK 9JLA;D=
Fig. 9c. #AKLG?J9E G> ?J9Q K;9D=  ]  HD9AF AE9?= G> 9  :  AE9?= ; AE9?= 9F< < ;AH@=J AE9?=
LOG >9EGMK HGO=J>MD  ;@9GLA; E9HK /=FL 9F< 'G?AKLA; (9HK /=FL
E9H AK ;GE:AF=< OAL@ 'G?AKLA; E9H LG J9AK= L@=AJ K=;MJALQ D=N=D 9K HJ=
K=FL=< AF 67 O@=J= L@AK ;GE:AF9LAGF O9K MK=< LG ?=F=J9L= L@= AFHML
;GFLJGD H9J9E=L=JK G> JFGD< 9L E9H AF L@= ;GF>MKAGF H@9K= #GO=N=J
L@AK ;GE:AF9LAGF G> L@= LOG E9HK AK MK=< E9AFDQ AF L@= <A>>MKAGF H@9K=
AF GMJ OGJC LG ?=F=J9L= 9 HK=M<G J9F<GE K=IM=F;= AF 9 KAEHD= O9Q
J9L@=J L@9F O@9L O9K 9<GHL=< AF 67 /@AK K=IM=F;= AK :ALOAK= 3*-=<
OAL@ L@= K;J9E:D=< AE9?= LG ?=L L@= WF9D ;AH@=J AE9?= /@=  ;@9GLA;
E9HK O=J= L=KL=< :Q )$./ KL9LAKLA;9D L=KLAF? 9F< H9KK=< 9DD L@= L=KLK
O@A;@ KA?FAW=K L@= ;@9GLA; E9H AK LJMDQ J9F<GE 9K J=;GEE=F<=< :Q
)$./ 67 $F ;GEH9JAKGF OAL@ 67 9F< J=;=FL J=K=9J;@=K 9K OADD :=
K==F AF L@= KAEMD9LAGF 9F< 9F9DQKAK K=;LAGF GMJ HJGHGK=< 9D?GJAL@E @9K


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Table 3
#AKLG?J9EK 19JA9F;=K ;GEH9J=< <A>>=J=FL K=;J=L C=QK AF L@= HJGHGK=< 9D?GJAL@E
AH@=J=< $E9?= *JA?AF9D &=Q
GDGJ  ]   N=J9?=819J      
GDGJ  ]  '=F9 N=J9?=819J      
"J9QK;9D=  ]   AE9?=      
Table 4
+=J;=FL9?= G> N9JA9F;=K <A>>=J=F;= G> @AKLG?J9EK ;GEH9J=< LG <A>>=J=FL K=;J=L
C=QK AF L@= HJGHGK=< 9D?GJAL@E
AH@=J=< $E9?=     
GDGJ  ] 

N=J9?=819J
    
GDGJ  ]  '=F9
N=J9?=819J
    
"J9QK;9D=
 ]  
AE9?=
    
9 :=LL=J K=;MJALQ H=J>GJE9F;= @9K L@= 9:ADALQ LG J=KAKL KL9LAKLA;9D 9F< <A>
>=J=FLA9D 9LL9;CK 9F< ;9F ;GEH=L= OAL@ L@=E /@= E9L@=E9LA;9D =IM9
LAGFK G> L@= 'G?AKLA; E9H 9>L=J <ANA<AF? AL AFLG LOG AFL=JN9DK 9J= ?AN=F 9K

O@=J= G
/@= /=FL E9H AK <ANA<=< AFLG >GMJ AFL=JN9DK 9F< KM:KLALML=< AF I
 J=KMDLAF? AF I 

/@= :=@9NAGJ G> L@= DG?AKLA;L=FL ;@9GLA; E9H AK =N9DM9L=< :Q 'Q9
HMFGN =PHGF=FL 9F< :A>MJ;9LAGF 9F9DQKAK 9K =PHD9AF=< AF 67
F;JQHLAGF 9F< <=;JQHLAGF HJG;=KK=K 9J= ADDMKLJ9L=< AF <=L9AD
L@JGM?@ L@= >GDDGOAF? LOG KM:K=;LAGFK
4.3. Encryption scheme
#=J=AF L@= KL=HK J=IMAJ=< >GJ L@= AEHD=E=FL9LAGF G> :GL@ ;GF>MKAGF
9F< <A>>MKAGF H@9K=K 9J= AFLJG<M;=< KKME= L@= AE9?= MF<=J ;GFKA<=J
9LAGF AK 9 ?J9QK;9D= GJ 9 ;GDGJ AE9?= G> KAR= - ]  ] + O@=J= - J=HJ=
K=FLK L@= JGO D=F?L@  J=HJ=K=FLK L@= ;GDMEF D=F?L@ 9F< + AK L@= -"
;GDGJ H9F=D O@A;@ =IM9DK L@J== AF ;9K= G> ;GDGJ AE9?= 9F< GF= AF ;9K= G>
?J9QK;9D= AE9?= /@= HJGHGK=< 9D?GJAL@E <=K;JA:=K L@= <=L9AD=<
HJG;=KK=K G> L@= =F;JQHLAGF H@9K= L@9L @9K :==F 9HHDA=< AF L@= ;9K= G> 9
?J9QK;9D= AE9?= GF L@= O@GD= AE9?= GJ AF L@= ;9K= G> 9 ;GDGJ AE9?= GF
=9;@ ;GDGJ ;@9FF=D
+JGHGK=< D?GJAL@E  F;JQHLAGF +JG;=KK
$FHML +D9AF$E9?= 9F< C=Q
*MLHML AH@=JAE9?=
Table 5
<B9;=FL HAP=DK ;GJJ=D9LAGF KMEE9JQ G> HD9AFL=PL 9F< ;AH@=JL=PL ;GDGJ AE9?=K
/=KL $E9?= /=KL $E9?= .AR= GJJ=D9LAGF -=< @9FF=D "J==F @9FF=D DM= @9FF=D
+D9AF $E9?= AH@=J $E9?= +D9AF $E9?= AH@=J $E9?= +D9AF $E9?= AH@=J $E9?=
  ]  #GJARGFL9D      −
1=JLA;9D  −  −  −
A9?GF9D  −  −  
  ]  #GJARGFL9D  −  −  −
1=JLA;9D  −    −
A9?GF9D    −  
  ]  #GJARGFL9D    −  −
1=JLA;9D  −  −  
A9?GF9D  −  −  
9:GGF  ]  #GJARGFL9D    −  −
1=JLA;9D    −  
A9?GF9D      
AJHD9F=  ]  #GJARGFL9D    −  
1=JLA;9D      −
A9?GF9D      
+=HH=JK  ]  #GJARGFL9D  −    −
1=JLA;9D    −  −
A9?GF9D  −  −  
'=F9  ]  #GJARGFL9D  −  −  
1=JLA;9D  −    
A9?GF9D  −    


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Table 6
<B9;=FL HAP=DK ;GJJ=D9LAGF KMEE9JQ G> HD9AFL=PL 9F< ;AH@=JL=PL ?J9QK;9D= AE
9?=K
/=KL
$E9?=
.AR= +D9AF $E9?= GJJ=D9LAGF AH@=J $E9?= GJJ=D9LAGF
# 1  # 1 
  ]      − 
  ]      − 
  ]     − − 
  ]     −  −
  ]     −  
  ]       
'=F9  ]       −
#GMK=  ]     −  −
  ]       −
  ]      − −
  ]     − − −
'=F9  ]      − −
  ]       
  ]      − −
 KKA?F N9DM=K >GJ L@= ;GFLJGD H9J9E=L=JK Z, E, D0, G ∊67 9F<
AFALA9D H9J9E=L=JK u∊67 9F< x0∊67 /@= ;GF>MKAGF C=Q OADD :=
 6 Z, E, 7 9F< L@= <AYMKAGF C=Q OADD :=  O@=J= H
AK L@= ;GDGJ ;@9FF=D FME:=J  >GJ J=<  >GJ ?J==F 9F<  >GJ :DM= AF
;9K= G> ;GDGJ AE9?=
 !GJ A   H <G
 GFN=JL +D9AF$E9?= =9;@ ;@9FF=D AF ;9K= G> ;GDGJ AE9?= LG
N=;LGJ /A = {    ……,} OAL@ KAR=  ] ) O@=J=
)  -GO ] GD

/G H=J>GJE L@= ;GF>MKAGF H@9K=
 <G
 



 !GJ B   ) <G


 /G H=J>GJE L@= <AYMKAGF HJG;=KK KM:KLALML= OAL@ L@= <AYMKAGF
C=Q AF I  LG G:L9AF D.

 -=K@9H= L@= K=IM=F;=K 


/@=K= KL=HK 9J= KMEE9JAR=< 9F< <=HA;L=< AF !A?K 9 9F< : >GJ ;GD
GJ=< 9F< ?J9Q AE9?=K
4.4. Decryption scheme
/@= <=;JQHLAGF HJG;=KK ;9F := ;GFKA<=J=< 9K 9 J=N=JK= G> L@= =F;JQH
LAGF HJG;=KK 9K <=K;JA:=K AF HJGHGK= 9D?GJAL@E 
+JGHGK=< D?GJAL@E  =;JQHLAGF +JG;=KK
$FHML AH@=J$E9?= 9F< C=Q
*MLHML +D9AF AE9?=
Fig. 10a. GJJ=D9LAGF D9QGML G> HD9AF AE9?= 9F< ;AH@=J AE9?= >GJ '=F9  ]  ;GDGJ AE9?= !GJ AFL=JHJ=L9LAGF G> L@= J=>=J=F;=K LG ;GDGMJ AF L@AK W?MJ= D=?=F< L@=
J=9<=J AK J=>=JJ=< LG L@= O=: N=JKAGF G> L@AK 9JLA;D=


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 10b. GJJ=D9LAGF D9QGML G> HD9AF AE9?= 9F< ;AH@=J AE9?= >GJ '=F9  ]  ?J9Q AE9?=
Table 7
GJJ=D9LAGF ;GEH9JAKGF >GJ '=F9 ;GDGJ AE9?=
GJJ=D9LAGF +JGHGK=< D?GJAL@E  ]  -=> 67 -=> 67 +JGHGK=< D?GJAL@E  ]  -=> 67 -=> 67 -=> 67
-=< @9FF=D
#GJARGFL9D − − − − −  −
1=JLA;9D −  − −   
A9?GF9D  −  − −  −
"J==F @9FF=D
#GJARGFL9D   − − −  
1=JLA;9D  −   − − −
A9?GF9D −    −  
DM= @9FF=D
#GJARGFL9D  −     −
1=JLA;9D −      −
A9?GF9D  − −  − − −
Table 8
GJJ=D9LAGF ;GEH9JAKGF >GJ ?J9QK;9D= AE9?=
GJJ=D9LAGF #GJARGFL9D 1=JLA;9D A9?GF9D
+JGHGK=< D?GJAL@E '=F9  ]    −
-=> 67  − −
-=> 67 −  –
-=> 67   −
+JGHGK=< D?GJAL@E #GMK=  ]  −  −
-=> 67  − 
+JGHGK=< D?GJAL@E '=F9  ]   − −
-=> 67   −
-=> 67   −
-=> 67  − −
 /@= <=;JQHLAGF HJG;=KK ;9F := ;GFKA<=J=< 9K 9 J=N=JK= G> L@=
=F;JQHLAGF HJG;=KK
 !GJ A   H <G
 -=9< L@= ;AH@=JAE9?=  9F< ;GFN=JL =9;@ ;@9FF=D -" LG 9
N=;LGJ )  -GO ] GD
 2AL@  L@= 'G?AKLA;/=FL E9H GMLHML E9LJAP AK ?=F=J9L=<
:Q KM:KLALMLAF? AF I  LG G:L9AF 
Table 9
-=KMDLK KMEE9JQ G> $F>GJE9LAGF FLJGHQ >GJ ;GDGJ AE9?=K
/=KL $E9?= /=KL $E9?=
.AR=
-=< @9FF=D "J==F @9FF=D DM= @9FF=D
+D9AF
$E9?=
AH@=J
$E9?=
+D9AF
$E9?=
AH@=J
$E9?=
+D9AF
$E9?=
AH@=J
$E9?=
  ]       
  ]       
  ]       

9:GGF
 ]       

AJHD9F=
 ]       

+=HH=JK
 ]       
'=F9  ]       



/G H=J>GJE L@= ;GF>MKAGF H@9K=


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Table 10
-=KMDLK G> $F>GJE9LAGF FLJGHQ >GJ ?J9QK;9D= AE9?=K
/=KL $E9?= .AR= +D9AF AE9?=
$F>GJE9LAGF
FLJGHQ
AH@=J $E9?=
$F>GJE9LAGF
FLJGHQ
-=>
67
-=>
67
  ]     
  ]     
  ]     
  ]     
  ]     
  ]     
'=F9  ]    – –
#GMK=  ]    – –
  ]     
  ]     
  ]     
'=F9  ]    – –
9:GGF  ]    – –
9E=J9E9F  ]    – –
  ]     
  ]     
Table 11
$F>GJE9LAGF =FLJGHQ ;GEH9JAKGF >GJ ;GDGJ '=F9 ;AH@=J AE9?=
F;JQHLAGF D?GJAL@E AH@=J $E9?=
- " 
+JGHGK=< D?GJAL@E >GJ  ]  '=F9 AE9?=   
-=> 67   
+JGHGK=< D?GJAL@E >GJ  ]  '=F9 AE9?=   
-=> 67   
Table 12
$F>GJE9LAGF =FLJGHQ ;GEH9JAKGF >GJ ?J9QK;9D= '=F9 ;AH@=J AE9?=
F;JQHLAGF D?GJAL@E AH@=J $E9?=
+JGHGK=< D?GJAL@E '=F9  ]  
-=> 67 
-=> 67 
+JGHGK=< D?GJAL@E #GMK=  ]  
-=> 67 
+JGHGK=< D?GJAL@E '=F9  ]  
-=> 67 
-=> 67 
-=> 67 
-=> 67 
-=> 67 
Table 13
-=KMDLK KMEE9JQ G> )+- 9F< 0$ >GJ  ]  ;GDGJ AE9?=K
"J9H@ -=< @9FF=D "J==F @9FF=D DM= @9FF=D
)+- 0$ )+- 0$ )+- 0$
'=F9      
9:GGF      
+=HH=JK      
AJ +D9F      
G9L GF 9 '9C=      
 For B   ) <G
 



 !GJ B  )  − <G

 =F<
Table 14
-=KMDLK KMEE9JQ G> )+- 9F< 0$ >GJ ?J9QK;9D= AE9?=K
/=KL
$E9?=
.AR= )+- -=>
67
-=>
67
0$ -=>
67
-=>
67
  ]       
  ]       
  ]       
  ]       
  ]       
  ]       
'=F9  ]   – –  – –
#GMK=  ]   – –  – –
  ]       
  ]       
  ]       
'=F9  ]   – –  – –
  ]       
  ]       
Table 15
GEH9JAKGF J=KMDLK G> )+- 9F< 0$ >GJ '=F9 ;GDGJ AE9?=
F;JQHLAGF D?GJAL@E -=< @9FF=D "J==F @9FF=D DM= @9FF=D
)+- 0$ )+- 0$ )+- 0$
+JGHGK=< D?GJAL@E
'=F9  ] 
     
-=> 67      
+JGHGK=< D?GJAL@E
'=F9  ] 
     
-=> 67      
-=> 67      
-=> 67      
Table 16
GEH9JAKGF J=KMDLK G> )+- 9F< 0$ >GJ '=F9 ?J9QK;9D= AE9?=
F;JQHLAGF D?GJAL@E )+- 0$
+JGHGK=< D?GJAL@E '=F9  ]   
-=> 67  
-=> 67  
-=> 67  
+JGHGK=< D?GJAL@E #GMK=  ]   
-=> 67  
+JGHGK=< D?GJAL@E '=F9  ]   
-=> 67  
-=> 67  
-=> 67  
-=> 67  


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 11a. AF9JQ $E9?= /=KL >GJ 2@AL= ;GDGJ AE9?= 9F< L@=AJ #AKLG?J9EK !GJ AFL=JHJ=L9LAGF G> L@= J=>=J=F;=K LG ;GDGMJ AF L@AK W?MJ= D=?=F< L@= J=9<=J AK J=>=JJ=< LG
L@= O=: N=JKAGF G> L@AK 9JLA;D=
Fig. 11b. AF9JQ $E9?= /=KL >GJ D9;C ;GDGJ AE9?= 9F< L@=AJ #AKLG?J9EK !GJ AFL=JHJ=L9LAGF G> L@= J=>=J=F;=K LG ;GDGMJ AF L@AK W?MJ= D=?=F< L@= J=9<=J AK J=>=JJ=< LG
L@= O=: N=JKAGF G> L@AK 9JLA;D=
Fig. 11c. AF9JQ $E9?= /=KL >GJ O@AL= 9F< D9;C ?J9QK;9D= AE9?=K 9F< L@=AJ #AKLG?J9EK


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 11d. AF9JQ AE9?= L=KL >GJ  ]  '=F9 AE9?= 9F< L@=AJ @AKLG?J9EK
 -=K@9H= L@= K=IM=F;=


5. Experimental results
PH=JAE=FLK O=J= H=J>GJE=< LG =N9DM9L= L@= H=J>GJE9F;= 9F< K=;M
JALQ AKKM=K G> L@= HJGHGK=< 9D?GJAL@E /@=Q O=J= H=J>GJE=< MKAF? (/
' -: 9F< ;GF<M;L=< GF ?=F=J9D AE9?= K=LK 9F< J=HJ=K=FL9LAN=
=PH=JAE=FL9D AE9?=K 9K K@GOF AF !A? 9–; OAL@ 9KKMEAF? Z 
E    D0  G  9F< ;GFKL9FL H9J9E=L=J
u  DD =PH=JAE=FLK O=J= <GF= OAL@ 9 ;GEHML=J L@9L @9K L@= >GD
DGOAF? @9J<O9J= ;@9J9;L=JAKLA;K  "#R +0 $FL=D A 9F< 2AF<GOK
 GH=J9LAF? KQKL=E /@= J=KMDLK G> L@= =F;JQHLAGF 9F< <=;JQHLAGF
H@9K=K 9J= K@GOF AF !A?  K K@GOF AF L@= W?MJ= L@= ;AH@=J AE9?=K
9J= G:NAGMKDQ MFJ=;G?FAR9:D= >MDDQ FGAKQ 9F< FG AF>GJE9LAGF ;9F := J=
LJA=N=< >JGE AL
6. Security and performance analysis
/@= HJGHGK=< =F;JQHLAGF K;@=E= AK L=KL=< 9?9AFKL C=Q KH9;= 9F9DQKAK
LG J=KAKL ;D9KKA;9D 9LL9;CK :JML= >GJ;= 9LL9;C C=Q K=FKALANALQ 9F9DQKAK J=
KAKL9F;= LG KL9LAKLA;9D 9LL9;C 9F< J=KAKL9F;= LG <A>>=J=FLA9D 9LL9;C /@AK
H9JL G> L@= =PH=JAE=FLK K@GOK L@= J=KMDLK G> ?J9QK;9D= 9F< ;GDGJ AE9?=K
G> L@= 9:GN= 9LL9;C E=L@G<K


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 12. "9MKKA9F )GAK= G>  ]  '=F9 AE9?=
Fig. 13. .9DL  +=HH=J )GAK= G>  ]  '=F9 $E9?=
Table 17
/@= +.)- J=KMDLK :=LO==F L@= <=;JQHL=< AE9?=K 9F< L@= GJA?AF9D AE9?=K MF
<=J FGAK= 9<<ALAGF
)GAK= /QH= +9J9E=L=JK  ] 
 ;GDGJ
AE9?= +.)- <
 ] 
;GDGJ
'=F9 AE9?=
+.)- <
 ]  
?J9QK;9D= AE9?=
+.)- <
.9DL 
+=HH=J
)GAK=
   
   
   
"9MKKA9F
)GAK=
   
   
   
6.1. Key space analysis
/G <=>=F< :JML= >GJ;= 9LL9;C L@= LGL9D C=Q KH9;= K@GMD< := D9J?=J
L@9F  /G ?=F=J9L= L@= K=;J=L C=Q L@=J= 9J= WN= H9J9E=L=JK AF L@AK
;JQHLGKQKL=E 5  P  " /@=J=>GJ= L@= ;GEHML9LAGF9D HJ=;AKAGF G>
L@= HJGHGK=< ;JQHLGKQKL=E AK >GJ >GMJ H9J9E=L=JK 9F<
/@MK L@= LGL9D C=Q KH9;= ;9F := ;GMFL=<
JGM?@DQ 9K  /9:D=  K@GOK L@= ;GEH9JAKGF J=KMDLK OAL@ L@=
;MJJ=FL =F;JQHLAGF 9D?GJAL@EK $L AK G:NAGMK L@9L GMJ C=Q KH9;= @9K @A?@
HJ=;AKAGF 9F< AL K@GMD< <=>=F< L@= :JML= >GJ;= 9LL9;C
6.2. Key sensitivity analysis
K 9F AF<A;9LAGF G> 9 ?GG< =F;JQHLAGF 9D?GJAL@E L@= C=Q K=FKALANALQ
9F9DQKAK K@GMD< AF<A;9L= L@9L 9FQ KE9DD ;@9F?= AF C=Q :ALK @9K 9 E9BGJ
=>>=;L GF L@= ;AH@=J AE9?= O@A;@ E=9FK 9F =FLAJ=DQ <A>>=J=FL =F;JQHL=<
AE9?= /@= HJGHGK=< 9D?GJAL@E O9K L=KL=< :Q <=;JQHL=< OAL@ L@=
OJGF? C=Q :Q ;@9F?AF? GFDQ GF= H9J9E=L=J 9F< L@= GL@=JK J=E9AF 9KAK
$L AK G:NAGMK >JGE !A? 9 9F< :9 L@9L L@= <=;JQHL=< AE9?=K 9J=
;GEHD=L=DQ <A>>=J=FL AF J=KHGFK= LG L@= ;@9F?=K AF L@= C=Q /@=J=>GJ=
L@= HJGHGK=< =F;JQHLAGF K;@=E= AK K=FKALAN= LG L@= K=;J=L C=QK !MJL@=J
EGJ= L@= HJGHGK=< 9D?GJAL@E C=Q K=FKALANALQ O9K L=KL=< 9K AF 67 K
K@GOF AF !A? 9 9F< :: L@= K9E= HD9AF AE9?= ;GDGJ?J9QK;9D= '=F9
AE9?= AK =F;JQHL=< OAL@ <A>>=J=FL C=QK /@= WJKL C=Q AK L@= GJA?AF9D
&=Q  6 7 9F< L@= K=;GF< C=QK 9J= &=Q O@A;@ @9K GF=
G> L@= K=;J=L C=QK OAL@ 9 LAFQ ;@9F?= 9F< GL@=J C=QK J=E9AF 9KAK
/@= <A>>=J=F;= G> ;AH@=J=< AE9?=K 9K K==F AF /9:D=  HJGN=K L@= @A?@
K=FKALANALQ G> L@= HJGHGK=< 9D?GJAL@E LG L@= K=;J=L C=Q ;@9F?=K
6.3. Statistical analysis resistance
6.3.1. Histogram analysis
 @AKLG?J9E AK 9 ?J9H@A;9D J=HJ=K=FL9LAGF G> L@= HAP=D’K N9DM=K <AKLJA
:MLAGF G> L@= AE9?= AH@=JAE9?=K K@GMD< @9N= 9 MFA>GJE @AKLG?J9E LG
<=>=F< 9?9AFKL KL9LAKLA;9D 9LL9;CK !A? 9!A? :!A? ; K@GO L@=
@AKLG?J9E G> L@= HD9AF 9F< L@=AJ ;AH@=J AE9?=K >GJ ;GDGJ 9F< ?J9QK;9D=
AE9?=K /@= W?MJ=K K@GO L@9L L@= ;AH@=J AE9?=K @9N= 9 MFA>GJE <AKLJA:
MLAGF EGJ= L@9F L@= HD9AF AE9?= 9F< L@= 9D?GJAL@E ;9F J=KAKL L@AK LQH=
G> 9LL9;C


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 14. -=KMDLK G> ;MLLAF? LL9;C
/G =N9DM9L= L@= @AKLG?J9E MFA>GJEALQ G> L@= =F;JQHL=< AE9?= L@=
N9JA9F;= G> L@= @AKLG?J9E O9K ;9D;MD9L=< 9K <=WF=< AF I  67

O@=J= HV AK L@= N=;LGJ G> L@= @AKLG?J9E N9DM=K 9F< HV = {HV1, HV2,
HV3,….., HVn}, HVi9F< HVj9J= L@= FME:=JK G> HAP=DK O@A;@ L@=AJ ?J9Q
N9DM=K 9J= =IM9D LG A 9F< B J=KH=;LAN=DQ 9F< nAK L@= FME:=J G> L@= @AK
LG?J9E :AFK /@= DGO=J N9DM= G> N9JA9F;=K G> L@= =F;JQHL=< AE9?=
K@GOK L@= @A?@=J MFA>GJEALQ G> AL /@= N9JA9F;=K O=J= ;9D;MD9L=< >GJ L@=
K9E= GJA?AF9D AE9?= L@9L O9K =F;JQHL=< :Q <A>>=J=FL C=QK O@=J= L@=
WJKL C=Q AK L@= GJA?AF9D C=Q 9F< L@= K=;GF< C=QK 9J= &=Q O@A;@ @9K GF=
G> L@= K=;J=L C=QK OAL@ 9 LAFQ ;@9F?= 9F< GL@=J C=QK J=E9AF 9KAK
  9K K@GOF AF /9:D= 
/G E=9KMJ= L@= MFA>GJEALQ G> =9;@ H9J9E=L=J AF L@= K=;J=L C=QK L@=
H=J;=FL9?= G> N9JA9F;= <A>>=J=F;=K :=LO==F L@= WJKL C=Q L@= GJA?AF9D
C=Q 9F< L@= K=;GF< C=Q &=Q O=J= ;9D;MD9L=< 9K K==F AF /9:D=  K
K==F AF /9:D=  EGKL G> L@= K=;J=L C=QK D=9< LG 9 ?GG< N9JA9F;= XM;LM9
LAGF 9F< L@MK D=9<K LG 9 ?GG< MFA>GJEALQ /G E=9KMJ= L@= @AKLG?J9E <A>
>=J=F;= 9?9AFKL HD9AFL=PL AE9?=K <A>>=J=FL AE9?=K OAL@ <A>>=J=FL LQH=K
9F< KAR=K O=J= L=KL=< 9K AF<A;9L=< AF /9:D=  /@= J=KMDLK AF /9:D= 
K@GOK L@9L L@= @AKLG?J9E <=H=F<K GF L@= HD9AF AE9?= AF L@= HJGHGK=<
9D?GJAL@E O@=J= L@= C=Q @9K 9F 9N=J9?= N9DM= G>  >GJ


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
Fig. 15. -=KMDLK G> <9L9 DGKK
GDGJ  ]   AE9?= O@AD= @9NAF? 9F 9N=J9?= N9DM= G>
 >GJ ?J9QK;9D=  ]   AE9?= !AF9DDQ 9K K@GOF AF
/9:D=  9F< /9:D=  L@= HJGHGK=< 9D?GJAL@E ;9F J=KAKL 9FQ KL9LA;9D 9L
L9;CK
6.3.2. Correlation
GJJ=D9LAGF K@GOK L@= ;GFF=;LAGFK :=LO==F LOG J9F<GE N9JA9:D=K
O@A;@ AK MK=< LG <=EGFKLJ9L= L@= J=D9LAGFK@AH G> AE9?= HJG;=KKAF? :=
LO==F LOG 9<B9;=FL HAP=DK /@=J= AK 9 @A?@ ;GJJ=D9LAGF :=LO==F L@= HAP
=DK G> HD9AFAE9?=K 9F< L@=AJ F=A?@:GJAF? HAP=DK /@=J=>GJ= AL AK NMDF=J
9:D= LG KL9LAKLA;9D AF>GJE9LAGF 9LL9;CK /@=J=>GJ= LG 9NGA< L@9L L@= ;GJ
J=D9LAGF :=LO==F F=A?@:GJAF? HAP=DK AF L@= ;AH@=J AE9?= EMKL := J=
<M;=< O@A;@ <A< :Q ;GF>MKAGF L@9L K;J9E:D= L@= HD9AF AE9?=K 9F< <A>
>MKAGF L@9L ;@9F?=< N9DM=K G> L@= HAP=DK 67 /@= HAP=D ;GJJ=D9LAGF AK
;9D;MD9L=< 9K <=WF=< AF IK  9F<  /@= ;GJJ=D9LAGF 9EGF? HAP=DK
O9K ;GEHML=< 9F< KMEE9JAR=< AF /9:D=K  9F< /9:D= 


K K@GOF AF /9:D= /9:D=  9F< !A? 9 9F< : L@= ;GJJ=D9LAGF
;G=>W;A=FLK G> HD9AFAE9?= AK ;DGK= LG  GF L@= GL@=J @9F< L@= ;GJJ=D9


N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
LAGF ;G=>W;A=FL G> L@= ;AH@=JAE9?= AK D=KK L@9F  /@AK AF<A;9L=K
L@9L L@= ;GJJ=D9LAGF G> L@= =F;JQHL=< AE9?= AK ?J=9LDQ J=<M;=< 9F< L@=
HJGHGK=< 9D?GJAL@E @9K 9 @A?@ J=KAKL9F;= LG KL9LAKLA;9D 9LL9;C !A? 9
9F< : K@GOK L@= @GJARGFL9D N=JLA;9D 9F< <A9?GF9D ;GJJ=D9LAGF >GJ
:GL@ HD9AF 9F< ;AH@=J AE9?=K H9AJK G> 9<B9;=FL HAP=DK /9:D=K  9F<
/9:D=  K@GO L@= ;GEH9JAKGF J=KMDLK OAL@ L@= ;MJJ=FL =F;JQHLAGF 9D?G
JAL@EK L@= ;GEH9JAKGF K@GOK L@9L L@= HJGHGK=< 9D?GJAL@E @9K ?GG<
H=J>GJE9F;= 9F< ;9F ;GEH=L= OAL@ GL@=J =F;JQHLAGF 9D?GJAL@EK
6.3.3. Information entropy
FLJGHQ AK 9 KL9LAKLA;9D E=9KMJ= G> J9F<GEF=KK 9F< MF;=JL9AFLQ L@9L
MK=< LG <=K;JA:= L@= L=PLMJ= G> L@= HD9AF AE9?= /@= N9DM= G> L@= AF>GJ
E9LAGF =FLJGHQ AK  >GJ 9F A<=9DDQ J9F<GE AE9?= 67 /@= AF>GJE9LAGF
=FLJGHQ G> L@= ;AH@=JAE9?= K@GMD< := ;DGK= LG  67 $L AK G:NAGMK L@9L
GMJ ;AH@=J AE9?=K >MDWDD L@AK ;GF<ALAGF 9K K@GOF AF /9:D=K  9F< /9:D=
 /@=J=>GJ= L@= HJGHGK=< 9D?GJAL@E ;9F J=KAKL AF>GJE9LAGF =FLJGHQ
9F9DQKAK 9LL9;C :=;9MK= G> L@= @A?@ J9F<GEF=KK G> L@= ;AH@=J AE9?=
/@= E9L@=E9LA;9D ;9D;MD9LAGF L@9L J=HJ=K=FLK =FLJGHQ AK K==F AF I


O@=J= J=HJ=K=FLK L@= HJG:9:ADALQ G> KQE:GD $F /9:D= /9:D=
 9F< /9:D=  9 ;GEH9JAKGF @9K :==F E9<= :=LO==F J=KMDLK G> L@=
HJGHGK=< 9D?GJAL@E OAL@ L@= ;MJJ=FL =F;JQHLAGF 9D?GJAL@EK #=J= AL AK
?GG< LG ;D9JA>Q L@9L GMJ 9D?GJAL@E HJ=;=<=K GL@=J 9D?GJAL@EK >GJ 9DEGKL
9DD L=KL AE9?=K >GJ L@AK ;JAL=JAGF
6.3.4. Di?erential attack analysis
A>>=J=FLA9D 9LL9;C GJ <A>>=J=FLA9D ;JQHL9F9DQKAK ;GEH9J=K L@= N9JA9
LAGFK AF L@= HD9AF AE9?= OAL@ N9JA9LAGFK AF L@= =F;JQHL=< AE9?= LG WF<
L@= <=KAJ=< C=Q GJ HD9AFL=PL E=KK9?= !GJ <A>>=J=FLA9D 9LL9;C 9F9DQKAK
LOG H9J9E=L=JK O=J= =N9DM9L=< L@= WJKL GF= AK F9E=< 9 FME:=J G>
HAP=D ;@9F?= J9L= )+- 9F< L@= K=;GF< GF= AK L@= MFAW=< 9N=J9?=
;@9F?= G> AFL=FKALQ 0$ )+- 9F< 0$ ;9F := ;9D;MD9L=< 9K AF IK
–



O@=J=  9F<  9J= LOG AE9?=K G> L@= K9E= KAR= J=HJ=K=FLAF? :=>GJ=
9F< 9>L=J EG<AW;9LAGF G> L@= =F;JQHL=< AE9?= )+- 9F< 0$ J=KMDLK
9J= KMEE9JAR=< 9F< K@GOF AF /9:D=  9F< /9:D=  /@= N9DM=K G>
)+- 9F< 0$ 9J= ;DGK= LG L@= =PH=;L=< N9DM=K >GJ )+- O@A;@ AK
;DGK= LG  9F< 0$ O@A;@ AK ;DGK= LG  67 /@AK ADDMK
LJ9L=K L@9L L@= HJGHGK=< 9D?GJAL@E @9K ?GG< H=J>GJE9F;= LG J=KAKL <A>
>=J=FLA9D 9LL9;C  ;GEH9JAKGF :=LO==F L@= HJGHGK=< 9D?GJAL@E 9F< L@=
;MJJ=FL =F;JQHLAGF 9D?GJAL@EK AK K@GOF AF /9:D= /9:D=  9F< /9:D=

6.3.5. Classical types of attacks
K &=J;C@G>>’K HJAF;AHD= KL9L=K L@= 9LL9;C=JK HJAE9JQ ?G9D AK LG
:J=9C 9 ;JQHLGKQKL=E 9F< =PLJ9;L L@= HD9AFL=PL >JGE L@= ;AH@=JL=PL /@=
9LL9;C=J GFDQ F==<K LG W?MJ= GML L@= K=;J=L C=Q 9K L@= K=;MJALQ G> 9 ;JQH
LGKQKL=E EMKL <=H=F< GF L@= ;@GA;= G> ALK C=QK GFDQ :=;9MK= L@= 9D?G
JAL@E AK 9DJ=9<Q AF L@= HM:DA; <GE9AF 67 /@=J= 9J= <A>>=J=FL
;D9KKA;9D LQH=K G> 9LL9;CK
AH@=JL=PL *FDQ LL9;CK * /@= 9LL9;C=JK GFDQ @9N= 9;;=KK LG 9
;GDD=;LAGF G> ;AH@=JL=PLK
&FGOF +D9AFL=PL LL9;C &+ L@= 9LL9;C=J @9K 9 K=L G> HD9AFL=PLK
9F< L@= ;GJJ=KHGF<AF? ;AH@=JL=PLK
@GK=F +D9AFL=PL LL9;C + L@= 9LL9;C=J ;9F G:L9AF L@= ;AH@=J
L=PLK ;GJJ=KHGF<AF? LG 9F 9J:ALJ9JQ K=L G> HD9AFL=PLK G> @AK GOF ;@GGK
AF?
@GK=F AH@=JL=PL LL9;C  L@= 9LL9;C=J ;9F G:L9AF L@= HD9AF
L=PLK ;GJJ=KHGF<AF? LG 9F 9J:ALJ9JQ K=L G> ;AH@=JL=PLK G> @AK GOF ;@GGK
AF?
/@= ;@GK=FHD9AFL=PL 9LL9;C AK L@= EGKL JG:MKL 9LL9;C KG A> L@= HJG
HGK=< 9D?GJAL@E ;9F J=KAKL L@= ;@GK=F HD9AFL=PL 9LL9;C AL ;9F J=KAKL 9DD
HJ=NAGMK LQH=K G> 9LL9;C /@= HJGHGK=< 9D?GJAL@E AK N=JQ K=FKALAN= LG L@=
AFALA9D H9J9E=L=JK $> GF= G> L@= AFALA9D H9J9E=L=JK @9K 9 LAFQ ;@9F?= L@=
;AH@=JAE9?= OGMD< := LGL9DDQ <A>>=J=FL 9K K==F AF !A?  9F< /9:D= 
=KA<=K L@9L 9 :AF9JQ AE9?= L=KL @9K :==F <GF= O@=J= L@= HJGHGK=< 9D
?GJAL@E @9K :==F 9HHDA=< GF 9 O@AL= AE9?= 9F< :D9;C AE9?= J=KH=;
LAN=DQ K AL AK K==F >JGE L@9L L=KL AF !A?  L@= ;AH@=J AE9?=K 9J= ;GE
HD=L=DQ FGAK= 9F< L@=AJ ;GJJ=KHGF<AF? @AKLG?J9EK @9N= 9 MFA>GJE <AKLJA
:MLAGF !MJL@=JEGJ= L@= HJGHGK=< 9D?GJAL@E @9K @A?@ )+- 9F< 0$
N9DM=K 9K K@GOF AF /9:D=  9F< /9:D=  .G L@= HJGHGK=< 9D?GJAL@E
;9F J=KAKL ;@GK=FHD9AFL=PL 9LL9;C 9F< 9DD HJ=NAGMK LQH=K G> 9LL9;CK 6
7
6.3.6. Binary image test
AF9JQ AE9?=K 9J= L@= KAEHD=KL CAF< G> AE9?= L@9L AK OA<=DQ MK=< AF
<A>>=J=FL 9HHDA;9LAGFK 9K AF<MKLJQ 9HHDA;9LAGF 9F< E=<A;9D 9HHDA;9LAGF
/@= :AF9JQ AE9?= AK 9 :D9;CGJO@AL= AE9?= /@= :AF9JQ AE9?=K O=J=
L=KL=< LG := KMJ= L@9L L@= HJGHGK=< 9D?GJAL@E OGJCK O=DD >GJ :GL@ O@AL=
9F< :D9;C ;GDGJ?J9QK;9D= AE9?=K 9F< L@=AJ @AKLG?J9EK 9K K==F AF !A?
9–<!A? :!A? ;!A? <
6.3.7. Robustness analysis
-G:MKLF=KK 9F9DQKAK AK 9 E=L@G< >GJ =N9DM9LAF? L@= J=KAKL9F;= LG <9L9
;@9F?= GJ DGKK O@=F 9F AE9?= AK LJ9FKEALL=< L@JGM?@ 9 F=LOGJC F =>
>=;LAN= =F;JQHLAGF 9D?GJAL@E K@GMD< := JG:MKL LG FGAK= 9F< ;MLLAF? 9L
L9;C !GJ L=KLAF? 9FLAFGAK= 9LL9;C ;9H9:ADALQ "9MKKA9F FGAK= 9F< K9DL
9F< H=HH=J FGAK= O=J= MK=< LG 9LL9;C !A?  K@GOK L@= <=;JQHL=< '=F9
AE9?= 9>L=J 9<<AF?   9F<  G> FGAK= <=FKALQ MKAF? "9MKKA9F
FGAK= 9F< !A?  K@GOK L@= <=;JQHL=< '=F9 AE9?= 9>L=J 9<<AF? 
 9F<  G> K9DL  H=HH=J FGAK= LG L@= ;AH@=J '=F9 AE9?= /9:D= 
ADDMKLJ9L=K L@= +.)-  IK  9F<  J=KMDLK :=LO==F L@= <=;JQHL=<
AE9?=K 9F< L@= GJA?AF9D AE9?=K .K ADDMKLJ9L=< AF !A?  9F< !A?  L@=
<=;JQHL=< AE9?=K 9J= FGAKQ :ML KLADD J=;G?FAR9:D= .G L@= HJGHGK=< 9D
?GJAL@E AK ;@9J9;L=JAR=< :Q =>>=;LAN=F=KK 9?9AFKL L@=K= LQH=K G> FGAK= 9L
L9;CK
!GJ L=KLAF? 9FLA;MLLAF? ;9H9:ADALQ L@= ;MLLAF? AK H=J>GJE=< 9L <A>>=J
=FL HGKALAGFK 9L L@= J9LAG G>    9F< L@= ;ML ;AH@=JL=PL AK MLA
DAR=< >GJ <=;JQHLAGF K K@GOF AF !A?  L@= HJGHGK=< 9D?GJAL@E @9K
?GG< J=KAKL9F;= 9?9AFKL ;MLLAF? 9LL9;C =N=F O@=F L@= ;MLLAF? J9LAG AK \
L@= E9AF ;GFL=FL G> L@= AE9?= AK KLADD NA=O9:D= !A?  ADDMKLJ9L=K L@9L
L@= HJGHGK=< 9D?GJAL@E @9K 9DKG 9 ?GG< J=KAKL9F;= LG <9L9 DGKK 9F< L@=
<=;JQHL=< AE9?= ;9F KLADD := NA=O9:D= 9F< J=;G?FAR9:D=
6.4. Encryption quality
/@= =F;JQHLAGF IM9DALQ 67 AK MK=< LG E=9KMJ= L@= D=N=D G> 9;;MJ9;Q
:=LO==F L@= GJA?AF9D AE9?= 9F< L@= <=;JQHL=< AE9?= /@=J= 9J= LOG ;JA
L=JA9 9J= MK=< LG =N9DM9L= =F;JQHLAGF IM9DALQ /@= WJKL ;JAL=JAGF AK L@=
E=9F KIM9J= =JJGJ (.  L@= E9L@=E9LA;9D ;9D;MD9LAGF L@9L J=HJ=K=FLK
(. AK HJ=K=FL=< AF I 



N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
O@=J= + J=HJ=K=FLK L@= GJA?AF9D AE9?= 9F< +’J=HJ=K=FLK L@= <=;JQHL=<
AE9?= /@= K=;GF< ;JAL=JAGF AK L@= H=9C KA?F9D LG FGAK= J9LAG +.)- L@=
E9L@=E9LA;9D ;9D;MD9LAGF L@9L J=HJ=K=FLK +.)- AK HJ=K=FL=< AF
I 

2@=F L@= +.)- ≥ <: L@= ;GEH9J=< AE9?=K K==E LG := A<=FLA;9D
K >GJ L@= HJGHGK=< 9D?GJAL@E (. AK R=JG L@=J=>GJ= +.)- AK AF> O@A;@
ADDMKLJ9L=K 9F< HJGN=K L@9L L@= HJGHGK=< 9D?GJAL@E AK 9 DGKKD=KK =F;JQH
LAGF 9D?GJAL@E
7. Conclusion
$F L@AK OGJC 9F =>W;A=FL 9F< J=DA9:D= ;@9GLA; ;GDGJ?J9QK;9D= AE9?=
=F;JQHLAGF 9D?GJAL@E AK HJGHGK=< /@= 9D?GJAL@E MK=K 9 @Q:JA<  ;GE
HGKAL= ;@9GLA; E9H ;GE:AF=< OAL@ 9 KAF= –;GKAF= ;JGKK;@9GLA; E9H >GJ
L@= LJ9FK>GJE9LAGF J=IMAJ=< LG K;J9E:D= L@= AE9?= AF L@= ;GF>MKAGF
H@9K= /@=F  ;GE:AF=< 'G?AKLA;/=FL ;@9GLA; E9H AK MK=< LG ?=F=J
9L= 9 ;@9GLA; K=D><AYMKAGF E9LJAP L@9L :ALOAK= 3*-=< GH=J9LAGF OAL@
L@= K;J9E:D=< AE9?= LG HJG<M;= L@= WF9D ;AH@=JAE9?= 19JAGMK =PH=JA
E=FLK O=J= H=J>GJE=< LG ADDMKLJ9L= L@9L L@= 9D?GJAL@E AK KLJGF?DQ J=KAK
L9FL 9?9AFKL <A>>=J=FL LQH=K G> 9LL9;CK KM;@ 9K <A>>=J=FLA9D 9LL9;C 9F< KL9
LAKLA;9D 9LL9;C +=J>GJE9F;= 9F9DQKAK 9F< =PH=JAE=FL9D J=KMDLK G> C=Q
K=FKALANALQ @AKLG?J9E 9F9DQKAK AF>GJE9LAGF =FLJGHQ C=Q KH9;= 9F9DQKAK
9F< ;GJJ=D9LAGF 9F9DQKAK @9N= :==F HJGN=< L@= @A?@ K=;MJALQ 9F< J=DA9
:ADALQ G> L@= HJGHGK=< =F;JQHLAGF 9D?GJAL@E
Uncited reference
67
Declaration of Competing Interest
/@= 9ML@GJK <=;D9J= L@9L L@=Q @9N= FG CFGOF ;GEH=LAF? WF9F;A9D
AFL=J=KLK GJ H=JKGF9D J=D9LAGFK@AHK L@9L ;GMD< @9N= 9HH=9J=< LG AFXM
=F;= L@= OGJC J=HGJL=< AF L@AK H9H=J
References
67  GHH=JKEAL@ /@= 9L9 F;JQHLAGF .L9F<9J<  . 9F< ALK KLJ=F?L@ 9?9AFKL
9LL9;CK $( % -=K =N    – @LLHK<GAGJ?J<

67  (MJM?9F + &9JL@A?9A&ME9J .MJN=Q GF AE9?= =F;JQHLAGF K;@=E=K :AG
;JQHLG?J9H@Q 9F< =>W;A=FL =F;JQHLAGF 9D?GJAL@EK (G:AD= )=LO HHD 
@LLHK<GAGJ?K
67 - "M=KEA ( !9J9@  &9;@GMJA =L 9D  FGN=D ;@9GK:9K=< AE9?= =F;JQHLAGF
MKAF? ) K=IM=F;= GH=J9LAGF 9F< .=;MJ= #9K@ D?GJAL@E .# )GFDAF=9J QF
   – @LLHK<GAGJ?K
67 ' &G;9J=N @9GK:9K=< ;JQHLG?J9H@Q 9 :JA=> GN=JNA=O $ AJ;MALK .QKL (9? 
  – @LLHK<GAGJ?
67 " DN9J=R . 'A .GE= 9KA; JQHLG?J9H@A; -=IMAJ=E=FLK >GJ @9GK9K=<
JQHLGKQKL=EK $FL % A>MJ;9LAGF @9GK    – @LLHK<GAGJ?
.
67 4 5@GM =L 9D $E9?= =F;JQHLAGF MKAF? +!A:GF9;;A LJ9FK>GJE 9F< <=;GEHGKALAGF
*HL GEEMF    – @LLHK<GAGJ?BGHL;GE

67 # 'AM  &9<AJ 4 )AM @9GK:9K=< ;GDGJ AE9?= :DG;C =F;JQHLAGF K;@=E= MKAF? .
:GP  0 –$FL % D=;LJGFA;K GEEMF    – @LLHK<GAGJ?
B9=M=
67  19AK@ ( &ME9J GDGJ AE9?= =F;JQHLAGF MKAF? (.1 2/ 9F< JFGD<
LJ9FK>GJE AF >J9;LAGF9D !GMJA=J <GE9AF *HLAC   – @LLHK<GAGJ?
BABD=G
67 34 29F? =L 9D $E9?= =F;JQHLAGF MKAF? H9JLALAGF=< ;=DDMD9J 9MLGE9L9
)=MJG;GEHMLAF?   – @LLHK<GAGJ?BF=M;GE

67 # @=F =L 9D *HLA;9D @QH=JKH=;LJ9D AE9?= =F;JQHLAGF :9K=< GF AEHJGN=< @AJACGN
E9HHAF? 9F< ?QJ9LGJ LJ9FK>GJE *HL '9K=JK F?   – @LLHK<GA
GJ?BGHLD9K=F?
67 ( 29F? 34 29F? =L 9D  FGN=D ;@9GLA; KQKL=E 9F< ALK 9HHDA;9LAGF AF 9 ;GDGJ
AE9?= ;JQHLGKQKL=E *HL '9K=JK F?   – @LLHK<GAGJ?
BGHLD9K=F?
67 34 29F? 5( 'A  ;GDGJ AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF #GH>A=D< ;@9GLA;
F=MJ9D F=LOGJC *HL '9K=JK F?   – @LLHK<GAGJ?B
GHLD9K=F?
67 4 'MG % 4M =L 9D  FGN=D ;@9GLA; AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF AEHJGN=<
:9C=J E9H 9F< DG?AKLA; E9H (MDLAE=<A9 /GGDK HHD   –
@LLHK<GAGJ?K
67 4 5@GM ' 9G ' @=F  F=O  ;@9GLA; KQKL=E >GJ AE9?= =F;JQHLAGF .A?F9D
+JG;=KK   – @LLHK<GAGJ?BKA?HJG
67 $ #MKK9AF / .@9@ ( "GF<9D HHDA;9LAGF G> .:GP 9F< ;@9GLA; E9H >GJ AE9?=
=F;JQHLAGF (9L@ GEHML (G<=DD  –  – @LLHK<GAGJ?
BE;E
67 " 4= $E9?= K;J9E:DAF? =F;JQHLAGF 9D?GJAL@E G> HAP=D :AL :9K=< GF ;@9GK E9H
+9LL=JF -=;G?F '=LL    – @LLHK<GAGJ?BH9LJ=;

67 " @=F (9G & @9JD=K  KQEE=LJA; AE9?= =F;JQHLAGF K;@=E= :9K=< GF 
;@9GLA; ;9L E9HK @9GK .GDALGFK !J9;L9DK    – @LLHK<GAGJ?
B;@9GK
67 # A9: F =>W;A=FL ;@9GLA; AE9?= ;JQHLGKQKL=E :9K=< GF KAEMDL9F=GMK
H=JEML9LAGF 9F< <AYMKAGF GH=J9LAGFK $   – @LLHK<GA
GJ? ..
67 # A9: ( DK=E9JQ .=;MJ= AE9?= ;JQHLGKQKL=E OAL@ MFAIM= C=Q KLJ=9EK NA9
@QH=J;@9GLA; KQKL=E .A?F9D +JG;=KK   – @LLHK<GAGJ?B
KA?HJG
67 ( JAF<@9 ) "GMF<=F  ;@9GK:9K=< AE9?= =F;JQHLAGF 9F< DGKKD=KK
;GEHJ=KKAGF 9D?GJAL@E MKAF? @9K@ L9:D= 9F< @AF=K= -=E9AF<=J /@=GJ=E HHD
.G>L GEHML   – @LLHK<GAGJ?B9KG;
67 T S9NM[GZDM . &9U9J =L 9D .=;MJ= AE9?= =F;JQHLAGF 9D?GJAL@E <=KA?F MKAF? 9
FGN=D ;@9GK:9K=< .GP @9GK .GDALGFK !J9;L9DK   – @LLHK<GA
GJ?B;@9GK
67 3 /GF? ( MA $E9?= =F;JQHLAGF K;@=E= :9K=< GF  :9C=J OAL@ <QF9EA;9D
;GEHGMF< ;@9GLA; K=IM=F;= ;AH@=J ?=F=J9LGJ .A?F9D +JG;=KK   
– @LLHK<GAGJ?BKA?HJG
67 # 29F?  3A9G =L 9D JQHL9F9DQKAK 9F< =F@9F;=E=FLK G> AE9?= =F;JQHLAGF MKAF?
;GE:AF9LAGF G> L@=  ;@9GLA; E9H .A?F9D +JG;=KK   – @LLHK
<GAGJ?BKA?HJG
67 ' 'AM . (A9G  F=O KAEHD= GF=<AE=FKAGF9D ;@9GLA; E9H 9F< ALK 9HHDA;9LAGF >GJ
AE9?= =F;JQHLAGF (MDLAE=<A9 /GGDK HHD    – @LLHK
<GAGJ?K
67 0 'GJ=FR +J=<A;L9:ADALQ G=K L@= !D9H G> 9 MLL=JXQK 2AF?K AF J9RAD .=L G>> 9
/GJF9<G AF /=P9K -=KGF9F;= –%GMJF9D G> .;A=F;= <M;9LAGF  
–
67 ) 'GJ=FR =L=JEAFAKLA; FGFH=JAG<A; XGO % LEGKH@=JA; .;A   
– @LLHK<GAGJ?)!*
67  *=KLJ=A;@=J  @AKLGJQ G> ;@9GK L@=GJQ A9DG?M=K DAF )=MJGK;A   
– @LLHK<GAGJ?).;G=KLJ=A;@=J
67 /4 'A % 4GJC= +=JAG< L@J== AEHDA=K ;@9GK E (9L@=E9LA;9D (GFL@DQ  
 – @LLHK<GAGJ?
67 -( (9Q .AEHD= E9L@=E9LA;9D EG<=DK OAL@ N=JQ ;GEHDA;9L=< <QF9EA;K AF -
#MFL /4 'A % &=FF=<Q #  )MKK=  <K /@= /@=GJQ G> @9GLA; LLJ9;LGJK
.HJAF?=J )=O 4GJC )4  HH –
67 (% !=A?=F:9ME ,M9FLAL9LAN= 0FAN=JK9DALQ >GJ 9 D9KK G> )GFDAF=9J
/J9FK>GJE9LAGFK % .L9LAKLA;9D +@QK   – @LLHK<GAGJ?
!
67 ( "MLROADD=J ,M9FLME ;@9GK .;A E    – @LLHK<GAGJ?
K;A=FLA>A;9E=JA;9F
67 3 5@9F? 4 9G  )GN=D @9GLA; (9H 9F< 9F $EHJGN=< @9GK9K=< $E9?=
F;JQHLAGF .;@=E= .;A 2GJD< %   @LLHK<GAGJ?

67 & 'BMH;G =L 9D @9GK9K=< JQHLG?J9H@Q /@=GJQ D?GJAL@EK 9F< HHDA;9LAGFK
.HJAF?=J =JDAF #=A<=D:=J?  HH – 
67 34 29F? ' 49F? - 'AM  ;@9GLA; AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF
H=J;=HLJGF EG<=D )GFDAF=9J QF   –
67 # 'AM  &9<AJ 3 .MF @9GK:9K=< >9KL ;GDGMJ AE9?= =F;JQHLAGF K;@=E= OAL@ LJM=
J9F<GE FME:=J C=QK >JGE =FNAJGFE=FL9D FGAK= $ / $E9?= +JG;=KK   
–
67 5 "9G  @=F 2 5@9F? =L 9D GDGMJ AE9?= =F;JQHLAGF 9D?GJAL@E MKAF? GF=LAE=
C=Q 9F< !J!/ $ / $E9?= +JG;=KK    –
67 3 29F? . 29F? 4 5@9F? =L 9D  GF=LAE= H9< ;GDGJ AE9?= ;JQHLGKQKL=E :9K=<
GF .# 9F< EMDLAHD= ;@9GLA; KQKL=EK *HL '9K=JK F?   –
67 # 'AM 34 29F? GDGJ AE9?= =F;JQHLAGF :9K=< GF GF=LAE= C=QK 9F< JG:MKL
;@9GLA; E9HK GEHML (9L@ HHD   –
67 3 2M # &9F9 % &MJL@K;  F=O ;GDGJ AE9?= =F;JQHLAGF K;@=E= :9K=< GF )
K=IM=F;=K 9F< EMDLAHD= AEHJGN=<  ;@9GLA; E9HK HHD .G>L GEHML  
– @LLHK<GAGJ?B9KG;
67 34 29F? 4, 5@9F? 3( 9G  FGN=D ;@9GLA; AE9?= =F;JQHLAGF K;@=E= MKAF?
) K=IM=F;= GH=J9LAGFK *HL '9K=JK F?   –
67  &MDKGGE  3A9G  -=@E9F =L 9D F =>W;A=FL 9F< FGAK= J=KAKLAN= K=D=;LAN=
AE9?= =F;JQHLAGF K;@=E= >GJ ?J9Q AE9?=K :9K=< GF ;@9GLA; E9HK 9F< )
;GEHD=E=FL9JQ JMD=K (MDLAE=<A9 /GGDK HHD    @LLHK<GAGJ?
KP
67 ( &ME9J  $I:9D + &ME9J  F=O -" AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF
) =F;G<AF? 9F< =DDAHLA; ;MJN= AYA=#=DDE9F ;JQHLG?J9H@Q .A?F9D +JG;=KK 
 – @LLHK<GAGJ?BKA?HJG
67 % @=F 5' 5@M ' 5@9F? 4 5@9F? , 49F? PHDGALAF? K=D>9<9HLAN=
H=JEML9LAGF–<AYMKAGF 9F< ) J9F<GE =F;G<AF? >GJ K=;MJ= 9F< =>W;A=FL AE9?=
=F;JQHLAGF .A?F9D +JG;=KK   – @LLHK<GAGJ?BKA?HJG



N. Khalil et al. Optics and Laser Technology xxx (xxxx) 107326
67 0 -=@E9F 3 'A9G - K@J9> . 0DD9@ # 29F?  ;GDGJ AE9?= =F;JQHLAGF
L=;@FAIM= MKAF? =P;DMKAN=*- OAL@ ) ;GEHD=E=FL9JQ JMD=K :9K=< GF ;@9GK L@=GJQ
9F< .# *HLAC   – @LLHK<GAGJ?BABD=G

67 # 'AM 34 29F?  &9<AJ; $E9?= =F;JQHLAGF MKAF? ) ;GEHD=E=FL9JQ JMD= 9F<
;@9GLA; E9HK HHD .G>L GEHML   –
67 # 'AM 34 29F? GDGJ AE9?= =F;JQHLAGF MKAF? KH9LA9D :ALD=N=D H=JEML9LAGF 9F<
@A?@<AE=FKAGF ;@9GLA; KQKL=E *HL GEEMF   –
67 4 5@9F?  3A9G F AE9?= =F;JQHLAGF K;@=E= :9K=< GF JGL9LAGF E9LJAP :ALD=N=D
H=JEML9LAGF 9F< :DG;C <AYMKAGF GEEMF )GFDAF=9J .;A )ME=J .AEMD  
 –
67  A9;GFM 1 $GF=K;M " $9F9 =L 9D  F=O :ALD=N=D H=JEML9LAGF AE9?= =F;JQHLAGF
9D?GJAL@E $FL=JF9LAGF9D GF>=J=F;= GF GEEMFA;9LAGFK *((  H

67 4 'A  29F? # @=F  @QH=J;@9GK:9K=< AE9?= =F;JQHLAGF 9D?GJAL@E MKAF?
HAP=DD=N=D H=JEML9LAGF 9F< :ALD=N=D H=JEML9LAGF *HL '9K=JK F?  
–
67  AK@L ( M9 . M9 =L 9D  GDGJ $E9?= F;JQHLAGF /=;@FAIM= 9K=< GF AL
'=N=D +=JEML9LAGF 9F< DL=JF9L= 'G?AKLA; (9HK % $FL=DDA?=FL .QKL   
–
67 ' /=F? 3" 29F? % (=F?  ;@9GLA; ;GDGJ AE9?= =F;JQHLAGF MKAF? AFL=?J9L=< :AL
D=N=D H=JEML9LAGF (MDLAE=<A9 /GGDK HHD   –
67 " -9<O9F . :< D#9WR (' 9J9C9L  >J9;L9D:9K=< AE9?= =F;JQHLAGF
KQKL=E $ / $E9?= +JG;    –
67 3 5@9F? ' 29F? 4 )AM =L 9D $E9?= F;JQHLAGF D?GJAL@E 9K=< GF L@= #
!J9;L9D 9F< QF9EA; .=D>$FN=JLA:D= (9LJAP GEHML $FL=DDA?=F;= )=MJGK;A
 
67 4 3A9F 34 29F? !J9;L9D KGJLAF? E9LJAP 9F< ALK 9HHDA;9LAGF GF ;@9GLA; AE9?=
=F;JQHLAGF $F> .;A   –
67 5 @=F? 4 5@9G .=EAL=FKGJ HJG<M;L G> E9LJA;=K ;GFN=FA=FL F=O LGGD @AF
.;A MDD    –
67 % 49G %  !=F? ( (=F? *F KGDMLAGFK G> L@= E9LJAP =IM9LAGF 3   OAL@ J=KH=;L
LG K=EAL=FKGJ HJG<M;L % !J9FCDAF $FKL    –
67 '5 .MF  5@=F? 4( 2=A =L 9D "=F=J9DAR=< AFN=JK=K G> L=FKGJK NA9 9 ?=F=J9D
HJG<M;L G> L=FKGJK !JGFL (9L@=E9LA;K @AF9    –
67 34 29F? . "9G $E9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF L@= E9LJAP K=EAL=FKGJ
HJG<M;L OAL@ 9 ;GEHGMF< K=;J=L C=Q HJG<M;=< :Q 9 GGD=9F F=LOGJC $F> .;A 
 –
67 34 29F? . "9G  ;@9GLA; AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF 9 ;GMFLAF?
KQKL=E 9F< L@= K=EAL=FKGJ HJG<M;L (MDLAE=<A9 /GGDK HHD  
– @LLHK<GAGJ?K
67 34 29F? . "9G $E9?= =F;JQHLAGF 9D?GJAL@E >GJ KQF;@JGFGMKDQ MH<9LAF? GGD=9F
F=LOGJCK :9K=< GF E9LJAP K=EAL=FKGJ HJG<M;L L@=GJQ $F> .;A   –
67  +9C ' #M9F?  F=O ;GDGJ AE9?= =F;JQHLAGF MKAF? ;GE:AF9LAGF G> L@=  ;@9GLA;
E9H .A?F9D +JG;=KK   – @LLHK<GAGJ?BKA?HJG

67 ( "= - 4=  FGN=D AE9?= =F;JQHLAGF K;@=E= :9K=< GF  :AL E9LJAP 9F< ;@9GLA;
E9H OAL@ (9JCGN HJGH=JLA=K ?QHLA9F $F>GJE9LA;K %    – @LLHK
<GAGJ?B=AB
67 % .L9JJ=LL /@= L=FL E9H L@= @GJK=K@G= 9F< L@= H=F<MDME L@= ?=GE=LJQ G> ;@9GK
;GFLJGD 0FAN=JKALQ G> GDGJ9<G 9L =FN=J =FN=J * 0.  G;LGJ9D
<AKK=JL9LAGF
67 @LLHKKDA<=HD9Q=J;GEKDA<= 1AKAL=< 
67  (GF<9D +& =@=J9 . "9F?GH9<@Q9Q  K=;MJ= AE9?= =F;JQHLAGF K;@=E= :9K=<
GF 9 FGN=D  KAF=–;GKAF= ;JGKK;@9GLA; . E9H % -=9D/AE= $E9?= +JG;
 @LLHK<GAGJ?K
67 4, 5@9F? 4 #= + 'A 34 29F?  F=O ;GDGJ AE9?= =F;JQHLAGF K;@=E= :9K=< GF
)'(' KQKL=E 9F< ?=F=LA; GH=J9LAGFK *HL '9K=JK F?   
@LLHK<GAGJ?BGHLD9K=F?
67 ' #M9F? . 9A 3 3AGF? ( 3A9G *F KQEE=LJA; ;GDGJ AE9?= =F;JQHLAGF KQKL=E
OAL@ H=JEML9LAGF<AYMKAGF KAEMDL9F=GMK GH=J9LAGF *HL '9K=JK F?  
– @LLHK<GAGJ?BGHLD9K=F?
67 + +AF? % !9F 4 (9G ! 3M % "9G  @9GK 9K=< $E9?= F;JQHLAGF .;@=E=
0KAF? A?AL'=N=D +=JEML9LAGF 9F< DG;C AYMKAGF $ ;;=KK  
– @LLHK<GAGJ? ..
67 4, 5@9F? 34 29F?  F=O AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF FGF9<B9;=FL
;GMHD=< E9H D9LLA;=K HHD .G>L GEHML   –
67 4, 5@9F? 34 29F?  KQEE=LJA; AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF EAP=<
DAF=9J–FGFDAF=9J ;GMHD=< E9H D9LLA;= $F> .;A   –
67  ,9QQME =L 9D @9GK:9K=< ;GF>MKAGF 9F< <AYMKAGF G> AE9?= HAP=DK MKAF?
<QF9EA; KM:KLALMLAGF $   – @LLHK<GAGJ?
 ..
67 3 2M  29F? % &MJL@K # &9F  FGN=D DGKKD=KK ;GDGJ AE9?= =F;JQHLAGF K;@=E=
MKAF?  2/ 9F<  @QH=J;@9GLA; KQKL=E $F> .;A –  –
@LLHK<GAGJ?BAFK
67 34 29F? ' 'AM 4, 5@9F?  FGN=D ;@9GLA; :DG;C AE9?= =F;JQHLAGF 9D?GJAL@E
:9K=< GF <QF9EA; J9F<GE ?JGOL@ L=;@FAIM= *HL '9K=JK F?   –
67 4 5@GM ' 9G '+ @=F $E9?= =F;JQHLAGF MKAF? 9 F=O H9J9E=LJA; KOAL;@AF?
;@9GLA; KQKL=E .A?F9D +JG;=KK    –
67 54 #M9 4 5@GM $E9?= =F;JQHLAGF MKAF?  DG?AKLA;9<BMKL=<KAF= E9H $F> .;A
  –
67 34 29F? ' /=F? 3 ,AF  FGN=D ;GDGJ AE9?= =F;JQHLAGF 9D?GJAL@E :9K=< GF
;@9GK .A?F9D +JG;=KK   –
67 )) +9J==C 1 +9LA<9J && .M< JQHLG?J9H@Q MKAF? EMDLAHD= GF=<AE=FKAGF9D
;@9GLA; E9HK GEEMF )GFDAF=9J .;A )ME=J .AEMD    –
67 #. 4= )- 5@GM '# "GF? (MDLAAE9?= ;GEHJ=KKAGF=F;JQHLAGF K;@=E= :9K=<
GF IM9L=JFAGF <AK;J=L= >J9;LAGF9D #9JLD=Q LJ9FK>GJE 9F< AEHJGN=< HAP=D 9<9HLAN=
<AYMKAGF .A?F9D +JG;=KK   
