Moire Cryptography
Moire´ Cryptography Yvo Desmedt
Tri Van Le
Department of Computer Science PO Box 4530, Florida State University Tallahassee, FL 32306, USA, and
Department of Computer Science PO Box 4530, Florida State University Tallahassee, FL 32306, USA.
Royal Holloway College University of London, UK.
[email protected]
[email protected] ABSTRACT
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1.
INTRODUCTION
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Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. CCS’00, Athens, Greece. Copyright 2000 ACM 1-58113-203-4/00/0011 .. 5.00
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UO,- I 2. CONCEPTS AND TECHNIQUES
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2.1 Digital Printers
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2.2 Moir´e Cryptography Model
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F MOIR $ E )VISUAL &0 9 ,! SCHEMES $ 9! 7A %+)Q?2 BR 7 !;h$ ! * > 8+ - $P!$+ - ./ &W+ ! -8X(n .ë! ./- / X./ $ ./- $" " - þ -I! $ -8bJ0 @ -8V!$+ - ./ L F- 7 ! - !F- ! ./4 &;' !$ !! L01 ) 7A h#
3.1 Moir´e schemes 3.1.1 Main Ideas
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# 7A \ 2p -$ - 8 =(n "O,- -$ Z(p - 50B!+!; * $ 4 1T - ' 2p $ 6$"U B$ ,! " L ,P 9 4 7A 38
%a0 = - 509!+!;# -$ Z -! 7 /./ 7# 9(C4 "01 -8PQ?2 6R !$+ - ./ oT ³oô-õ õ ¯C·eHji-õ ô-õ"¯iö > V - !$+ - ./ &o0 F + ? "=( - F -K4! $ 2(n* (n , 2V!X ; -4$+@^# "/ V! $% / .8 P$ ! !- b - KQ?2 3R ;#! )&01 - 601 2 K# "' L! $ \ .8 B$ ! * !; = 'Q?2 BR ;#! FP \! !2 L(:
50H!+-!- $ `T - =!$+ - ./ P $ =7 !V$ "#F; ! - / $ ! 3$ - ! Y : "0 7 S - -; !3 50
2p , 2* + " P "' ? 9! ;# ' 17 !4
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? S> P+ %E = 3 ;#"&c IE0 9 -#7 \ .@A '
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aT 0 ! ; &01 -! K \# K , " L ,? - 9 6 ./ 38
-$ - ' !-2 -83- $ \ " 012 F- BQ?2 9R ;#! (C \ 3 4$+@U \; U 6Q? KR ;#! L(C\ - B01
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- B ?7 !;)$%! 8+- , 3.1.2 Encryption
t ]+E}ny ~ %zw;t6%/+!tAt,!tE|;vy È ü'ýhþÿ þ %} Nw; }z % 9z!%|!y }v {)-%wb}n-FIz!%?wtXt,%}5%z+ vCw!t {/}n-oÇ ~ C ~ SvCw,xF xA~z%vn}n } !Gñò #ó "%$" w& t ':¥ () =Y* + % } ¥ (/.^0 \1ò 2 , %%-} \¥ (/.^0 \1ò ' 2 3 %}vCÇ%{/}n- % y ~w;tvC}v~w-4 0v 65%zCÇ y }Z y z!!y 7{ 8 w; t /z 3vnwt,5|%w;t,%w-}1~aÇ + vn0v :9\v4x#< ; vC}{ = ?> > @ vCvCAv 6B3 y z+{+|;}A 42 CG~vC!z AD 0 8 Eò 3 ~"~#¿B v4¿A + D-%z F . vC'}n-9,vtvCw,xP xA~z+vC}nÍt,%%y z+v+!tFvCH w G y }v~w , , Proof
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3.1.3 Decryption
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a0 T !+!;# -$ P, K "$+ L 1 =$ "# 3Q?W[2 6R ;#! - L M N(À&W - 3F ( K;O
= -!4 = O-
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T - 1 8 L M N(Í&W - 3F ( K;O
= -!4 = O-
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T 2 -p 1 8 7A 1( / . ;#F(B - UQ?2 G R -! _(B Lc- I/a
$"-! 9 B8 6 a0 ?50= O,;# 1 "0 2p ,% - / . " " X- $
3-"0í /7 ! - / ^ - Q?2 R ;#T ! )& ' $%@F# "K(: - '- $ S©$ ! !- 6 Y* B(W - 9c I5 &01 4 6 - 901 2 6 "/(W B- $ &
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3.2 Discussions
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SUMMARY
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Acknowledgements
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q %s ÆKREFERENCES E - ! & ; &; ¡ &-- ¡ ¨ ! Y ¾'; " F$ ; - 2 4 (n17 !;h$ ! 8+- , )-!~z!%}vy ? fo~'|;}5%g z G;y v%wy+%& / " q £"s ; -.L& . 1£i h£Ä&D"ÌÌAÁ ;¤ $% B8 7A U ¡ 8 -I -& ., q ¢#s ÆK ¨ - 4@ Æ (n 8-+ 48/$ ! 8+ - $B@A > ¨4$+ ;#+ Q? !01 h& jA$"O,- - T\ Å -$"&; LQ? % 4 ./2 h& 2 & lkdm kn }v~w ofo~'|;}5%zfo~w"Ç"%z!%wy+2 qsr m lkdm k n i ut;~z!v¿ n i ut;~z!¿&;7A -./ 9r ( p wp wyx-z15{GLfo~w Ç"%z %w;y+|;z!~"y+ !tvCw,x+&p-8 ¢"2¢ h¢#Á& Q?, 7 & j& 3&p"ÌÁÌ \« ! q rs ¡ "74 ¾ ; -. ð $ 2a012 -|> e4 e , 2c;$ h¥ .@ \ - 8= -!
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Tri Van Le
Department of Computer Science PO Box 4530, Florida State University Tallahassee, FL 32306, USA, and
Department of Computer Science PO Box 4530, Florida State University Tallahassee, FL 32306, USA.
Royal Holloway College University of London, UK.
[email protected]
[email protected] ABSTRACT
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1.
INTRODUCTION
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UO,- I 2. CONCEPTS AND TECHNIQUES
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"0V 9 -$ EKE "&0 E! ./! 509 O,- S3 -
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- B ?7 !;)$%! 8+- , 3.1.2 Encryption
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3.1.3 Decryption
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a0 T !+!;# -$ P, K "$+ L 1 =$ "# 3Q?W[2 6R ;#! - L M N(À&W - 3F ( K;O
= -!4 = O-
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T - 1 8 L M N(Í&W - 3F ( K;O
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T 2 -p 1 8 7A 1( / . ;#F(B - UQ?2 G R -! _(B Lc- I/a
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3-"0í /7 ! - / ^ - Q?2 R ;#T ! )& ' $%@F# "K(: - '- $ S©$ ! !- 6 Y* B(W - 9c I5 &01 4 6 - 901 2 6 "/(W B- $ &
$ ! !- 9 Y () 1! $ - =a ST 50Ba o( Y 1 B7 !; 2? 2p ,! 0 = - 94$% T
3.2 Discussions
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J .K " - " `4$% J$ uI 46 G! À> ($ "&B Y 2* ./ P ;"7A H ./-I!+# " ;#?01 - µ- H!+-!- $ ./#7 -8H 4 7A 2 G - ? - %"&E - L .K " - " V- $ L * $ ./ 9$ 4 T -9 !4 9-! 8?2L "S4$% BB! * $% /! ;# &Q?2 L R !$+ - ./ ? !H -I/8 -I./ !! " 4$ ./ ; -§ 4 +# 4.
SUMMARY
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Acknowledgements
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q %s ÆKREFERENCES E - ! & ; &; ¡ &-- ¡ ¨ ! Y ¾'; " F$ ; - 2 4 (n17 !;h$ ! 8+- , )-!~z!%}vy ? fo~'|;}5%g z G;y v%wy+%& / " q £"s ; -.L& . 1£i h£Ä&D"ÌÌAÁ ;¤ $% B8 7A U ¡ 8 -I -& ., q ¢#s ÆK ¨ - 4@ Æ (n 8-+ 48/$ ! 8+ - $B@A > ¨4$+ ;#+ Q? !01 h& jA$"O,- - T\ Å -$"&; LQ? % 4 ./2 h& 2 & lkdm kn }v~w ofo~'|;}5%zfo~w"Ç"%z!%wy+2 qsr m lkdm k n i ut;~z!v¿ n i ut;~z!¿&;7A -./ 9r ( p wp wyx-z15{GLfo~w Ç"%z %w;y+|;z!~"y+ !tvCw,x+&p-8 ¢"2¢ h¢#Á& Q?, 7 & j& 3&p"ÌÁÌ \« ! q rs ¡ "74 ¾ ; -. ð $ 2a012 -|> e4 e , 2c;$ h¥ .@ \ - 8= -!
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