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Vérification de protocoles cryptographiques en présence de théories équationnelles

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(1)Vérification de protocoles cryptographiques en présence de théories équationnelles Pascal Lafourcade. To cite this version: Pascal Lafourcade. Vérification de protocoles cryptographiques en présence de théories équationnelles. Autre [cs.OH]. École normale supérieure de Cachan - ENS Cachan, 2006. Français. �tel-00133494�. HAL Id: tel-00133494 https://tel.archives-ouvertes.fr/tel-00133494 Submitted on 26 Feb 2007. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(38) , ÁÂX #dD MOÀ: dDX q Å Q'b Á“XRQMXR¾\]JÀ Å L,U,XR¾½¾TX] Å . QTSbÀ =D âL,Á8NV SWd¢¾®UDSWdDd,O!b S?C ¾P / ÀÅ QTX( , XQ' , X\ÀÂSWQT¼‘U,X<NPSbd©¼ ¾ Å W X!/ ÀøV ! " DD âL9V XÀ“ÀÂXx¼5QTX

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(40) Å d » SWL,Q5À Å ¿=Sbd,d,X Å N\¿„Á Å dx X X¾5À Å  Sbd2? Á. Á Å ÀÂÁ¾TO< âL,Á=Q': b d,Xd¢¾ Å L¼½XÁ“dU,X= X}À Å q ¿=SWQ Å ¾TSbÁÂQTX}U? d Å NPÁ“âL,X( bX}QTXNPXQ' Á“X Å LD¼½¼½Á5ÀøV Xxd,¼½XN)¿DÀ“XU,Xx¼ NPXN)¿,QTX¼ÏU,L Å ¿=SWQ Å ¾TSbÁÂQTX UCV ; d{ SWQTN Å ¾TÁÄâL,X SWdDU Å N Xxd¾ Å ÀÂXU,X Å QT¼½XÁ“ÀÂÀ“X » SWL,QMÀ“XL?Q Å ( L,XxÁÂÀZ  Å À“XL?QTXxL©# À“SWQT¼MU,X%N Sbd Å d,d,OX »„Å ¼½¼½OxX XxdÀÂXxL?QFx SbN »uÅ b d,Á“X# X¼A SbÁ“¼½ÁÂd,¼ˆXR¾Fb SbÁ“¼½ÁÂdDX¼ˆÃ¢L,Á‘NV Sbd¾, SW¾TS O©U Å d,¼ˆÀÂXx¼ÏU,Á=> OQTXd¾T¼sÀ“S- Å L # âL,X@R] V Å Á  Q S- ( L » Ox¼+d,X‘¼½Sbd¾ »„Å ¼0SbL?¿DÀ“Á“O¼ »uÅ QJSaQTU,QTX‘U9V ŧ»D»„Å QTÁ ¾TÁ“Sbd}[¾TO » Å d,Á“XD Á“d Xxd¾(?D [¢OR¿ Å ¼ ¾TÁ“Xd D L ( Á Å ¢D KMÁx SbÀ Å ¼ D K Å ¾' Å À“ÁÂX)XR¾ Å ¾', ÁÂXxL)„D U,X)N@4 NPX%âL,X%ÀÂXx¼[] SbL,XL,QT¼‘UDX%b Å d¾TXU „D À“X¼"~ S.SW¾TXL#M„D ÀÂXx¼ » XR¾TÁ¾T¼¿ Å Áb d,XxL?QT¼®X¾®À“X¼ ¼TâL Å ¾'

(41) , XL?QT¼'U,L  [ Q âL,Á¢¾TSbL,¼>XdD¼½XN)¿DÀ“X7 Sbd¾½QTÁ¿DL,Xxd¾I®/ À Å ¿=Sbd,dDX Å N)¿DÁ Å d+ X U,XSx XR¾ Å a QTO Å ¿DÀÂX À Å ¿9SaQ Å ¾TSbÁÂQTX J Xx¼‘QTXNPXQ' Á“XNPXd¾T¼MdDX)¼½XQ Å ÁÂXxd¾ »„Å ¼x SWN » À“XR¾T¼M¼½Á+] X%d,X%NPXd¾TÁ“Sbd,d,X »„Å ¼MÀÂXx¼MX$# 2 6 D »uÅ Q½¾TÁ LDÀÂÁR: QTX^ NPXxd¾[M\ L?QTOÀ“ÁÂX*D  Å QTÁ“Sbd¢D [¾TO » Å d,ÁÂX¢D [¢OR¿ Å ¼ ¾TÁ“Xd XR¾J[¾TO » Å dDXWD À“X¼>¿ Å ¼aX X¾TXL?Q+ ¼½X*;¼JYWZ0¼ ¾', XQ(*D OxÀ Å d,Á“X¢D ] Å QTSD [ Å dDU?QTÁÂdDXD q Q Å d 'Xd-D ,®QTSb¼ D  Å N=uD [¢X¿©XR¾‘ÀÂXx¼ Å L?¾½QTX¼ DD ÀÂXx¼N Å QT¼½XxÁÂÀ“À Å Á“¼½X¼. Å S=D ] Å N XR¾GM\ d,d,X^gÄ Q Å d

(42) xSWÁ“¼½XDD À“X¼ U Å dD¼½XL?QT¼5Z0ÀÂÁ“¼ Å ¿=XR¾' /D 0Á“XRQ½QTSW¾(0D ®SX S Å  X À“X¼TâL,XÀ“¼jõ] V Å Á »„Å ¼½¼½O U,XM¿=Sbd,¼5N SbNPXd¢¾T¼ D Å ÁÂdD¼½Á9âL,X ÀÂXx¼ NPXN)¿,QTX¼ UDLYa QTSbL » XsU,Á¾%UDLý¼ Å NPXU,Á >D U,L  š 3 XR¾ » ÀÂL,¼ »uÅ Q½¾TÁ LDÀÂÁR: QTXxN Xxd¾K Å ¾' Å ÀÂÁ“X » SWL,Q¼½Sbd Å Á“U,XFW Q Åa» , ÁÄâL,X1 bX QTXxNPXRQ' Á“X Å L,¼½¼½Á8¾TSbL,¼MÀ“X¼MNPXxN\¿DQTX¼ U,X%N Å  Å N Á“À“ÀÂX ÃLDÁrN}V Sbd¾ ¼½SbL?¾TXd.LX¾ Å x SbN »uÅ b d,O%U,L,Q Å d¢¾ U,X%d,SbN ^ ¿DQTXL,¼½Xx¼ Å d,d,OxX¼ D Å Á“d,¼½Á0âL,X ¾TSWL,¾TX¼<ÀÂXx¼ » XQT¼½Sbd,d,X¼)âL,Á¬NV Sbd¾ Åa»,» SWQ½¾TO L,d ¼½SbL?¾TÁÂXxd NPSWQ Å À¬UDX À“SbÁÂd SWL U,X » Q': ¼  nd.

(43)

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(49) »¼a ,?Á>uNPQTORX¾½NPQTÁÄXÃd¢LD¾ X¼ @Q'% Á ¾% %

(50) ,Á<>=QTX%NPX%d¾‘%UDX Q %XRQTd %N  %%%%%%%%%%%  --   _ \MZZ5[[  \ UÅ ¾ Å dZ+ xd+XU R»„Q1Å Z0» d¾TÅ Á“Q1SW d¾T[Á¾ SbÅ dd,U [ž QTU)d,U !QTU- %%%Å %%%%%%%%%%%%  -  _ ]S  ,-Á< >=_-QT XNPX]Sd¾T ,¼ Á<>=Å QT¼aX?NPN XOdž½¾.QTÁ“âL,[ Xx\ ¼    "%! » %%%Å %%%%Å %%%%%%%%%%%%%%%%  --  _-_-_ ]S ,V Á<>=L?¾½QTQTXXxNP¼ X d ,¾®Á>uU9QTV XxZ0N À , XxdÅ ¾TN ¼ Å À ¼a? NP"OR! ¾½Æ QTÁÄGÃLD%X%¼ p%%%%%%%%%%%%%%%%  Å Å - \Z Å  d¾ Å bX¼XR¾Á“d xSWd bOxd,Á“Xd¾T¼‘UDX¼G  ,Á>uQTXNPXxd¾T¼¼a?NPOR¾½QTÁÄâL,X¼X¾ Å ¼a.NPO¾½QTÁ“âL,Xx¼      f ZI  #?fX N » À“ XPX Y QTX SW¾T» S-QT SaSb¾TÀÂS-X x SWÀ“X<U,%X\%KMX%XxU Å N %^1[ %  ,%QTS¢XxU,XR%Q(@%%%%%%%%%%%%%%%%%%%% »  f _  V Å ¾½¾ ŠâL,XS%%%%%%%%%%%%%%%%%%    Æ 0À Å dUDX<À Å ¾' :x¼½X %%%%%%%%%%%%%%%%%% $#. &%. (' *). ,+. (­ 8ª128¯4\(0±®*ª1$ 06C*D/;:<7=$>-,/;(J@ ­®2"4M*D(¬-.(7=(0ª128¯7=* 4®-.( +*,$'4 µM/ °5±®28¯. 0/  21. 43. 65. ¸ ˆ·.qWz '¡b,v§z~o=yƒrwn>q‚oDv‚oC¡bo=|~w.ŸÏ¡q Cn8vxo„uq§„n >z{¨8pCw?Ÿ ¶ -_  +QTS » QTÁ“OR¾TOx¼G/fORQTÁ6DXRQ( %%%%%%%%%%%%%%%%% -_   [¢ X QTXR(¾  %%%%%%%%%%%%%%%%%%% -_   _ \ML?¾½QTX¼ » QTS » QTÁÂO¾TO ¼  %%%%%%%%%%%%%%% _   -_  \ML?'¾ ,Xd¢¾T<Á 6+ Å ¾TÁÂSbd 7%%%%%%%%%%%%%% _   -_  _ \Md,Sb2d ?N Å (¾ 8%%%%%%%%%%%%%%% _   -_  âL,Á¾TO p%%%%%%%%%%%%%%%% -_  _ e ¿ ] X ¾TÁ {¼U,X\À Å bOQT<Á 69 Å ¾TÁÂSbd  %%%%%%%%%%%%%%%.  .     . ?Á“Á. _ _. . f.  Æ Æ c c c.  !!.  . -.( 7f  ff  ff  ÆÆ.

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(55)  ! 

(56)  

(57). '. - _- _ - _-.  X<NPS¢U+:À“X  SbÀÂX ¢^  Å S OR¾TXxd,U,L »uÅ Q‘QTOO( RQTÁ¾TL?QTX0%%%%%%%% f   Á<9> ORQTXd¢¾TX¼5¾' ,OxSaQTÁ“X¼O‚âL Å ¾TÁÂSbd,d,XxÀÂÀ“X¼ xSbd,¼½ÁÂUDORQTOXx¼  %%%%%%%% Æ . Ž oC¡bu| zÄv‚·€Ÿ‚zø¦ n'|~w ¶ f \ »D» QT-S  ,X »„Å Q‘À“S- Å ÀÂÁ¾TO<U,X H (\MÀÂÀ“X¼ ¾TXQ(f%%%%%%%%%%%%% f    V ÁÂU,OxX<U,X H \MÀ“À“X¼ ¾TXRQ\Y+3Md,X% Sbd,¼ ¾½QTL ¾TÁÂSbd »„Å Q®¼ Å ¾TL?Q Å ¾TÁÂSbdR%%%%%% f   _ KMSa¾½QTX< X #¢¾TXxd,¼½Á“SWd©U,X<ÀøV Å À bSaQTÁÂ'¾ ,NPX\U,X H \MÀ“ÀÂXx¼ ¾TXRQ( %%%%%%%% f _ -S Å ÀÂÁ¾TO<¼½ÁÂN » À“X » SbL?Q‘ÀÂX\NPS¢+U :À“X\U,X  SbÀ“$X .^  Å SPO¾TXd,U,L %%%%%%%% f  -_   $O 6DdDÁ ¾TÁ“Sbd, ¼  %%%%%%%%%%%%%%%%% f  -_   [¢SbL,¼ ^ø¾TXRQTNPX¼®a¼ .d¢¾ Å #?ÁÄâL,X ¼  %%%%%%%%%%% f  -_   _ ¬QTXxL X ¼  %%%%%%%%%%%%%%% f  -_  _ \M d Å <À ?¼½X<UDX<À Å 'Q :( bÀÂX\U,X »„Å Á QTX\XR¾‘U,Xx¼5'Q :( bÀÂXx¼U,X » QT?S ] X ¾TÁÂSbd  %%%%%% f  -_  -S Å À“Á ¾TO<¼½Á“N » ÀÂX j%%%%%%%%%%%%%%%%% f \ »D» ÀÂÁ Å ¾TÁ“Sbd Å LNPS.U :xÀÂX  SbÀ X ¢^  Å SP¼ ¾ Å dDU Å QTU %%%%%%%%%%% f  - \Md Å <À ?¼½X<UDX¼5'Q : bÀ“X¼ (D) X¾ (C)  %%%%%%%%%%% f  - _ ¬QTSW¿DÀ :NPX\U,X<U,OxU,L ¾TÁÂSbd©U,X<ÀøV ÁÂd¾½QTLD¼ » SbL?Q‘À“X<NPS.U :À“X\U,X  SWÀ“$X .^  Å S ¼ ¾ Å d,U Å QTU 8 º › q‚out'| ?¦ wƒrwƒ8·.ƒ'pr¡Wv§z~o=yƒrw´|  z yuv‚qWp8Ÿw¢v o=|~w " $ &<Doý·vxw?yrƒ'p ¶ -Æ  MSbNPSbNPSaQ » ,Á¼½NPX %%%%%%%%%%%%%%%%%% Æ-   !%%%%%%%%%%%%%%%%%%% Æ     -S Å À“Á ¾TO  %%%%%%%%%%%%%%% Æ    _  OU,+L R¾TÁ“SWd©Xd©L,d,X\OR¾ Åa» X -%%%%%%%%%%% -Æ   _  

(58)  XR¾    G%%%%%%%%%%%%%%%%% Æ   -_  -S Å À“Á ¾TO  %%%%%%%%%%%%%%% Æ   -_  _  OU,+L R¾TÁ“SWd©Xd©L,d,X\OR¾ Åa» X -%%%%%%%%%%% -Æ  _ S] D<Á >uQTXxNP Xd"¾ ,SbNPSWNPSWQ » ,ÁÄâL,X %%%%%%%%%%%%%% -Æ  -_  -S Å À“Á ¾TO » SbL?Q‘À“X¼ Å ¾TSWNPXx ¼  %%%%%%%%%%%%%% Æ  -_    $O 6DdDÁ ¾TÁ“Sbd, ¼ %%%%%%%%%%%%%%% Æ  -_   _ CQ Å d,1¼ {SWQTN Å ¾TÁ“Sbd,¼‘U,X » QTXL Xx ¼  %%%%%%%%%% Æ  -_    XNPNPX » SbL?Q‘À Å 'Q : bÀÂX (D) S%%%%%%%%%% Æ  -_   f  -S Å À“Á ¾TO » SbL?Q®ÀÂXx¼ Å ¾TSWNPXx ¼  %%%%%%%%%%% -Æ  -_  _ ¾TLDU,X<U,X\À Å U,OxU,L ¾TÁ ¿DÁ“À“Á ¾TO\XxdL,d,X\OR¾ Åa» X » SWL,Q (GXCD) %%%%%% Æ  -_  -_    {.}  %%%%%%%%%%%%%%% Æ  -_  -_  _  {.} p%%%%%%%%%%%%%%%% -Æ  -_  ] Å ¼5¿„ÁÂd Å ÁÂQTX %%%%%%%%%%%%%%%%% Æ  -_  -  $O 6DdDÁ ¾TÁ“Sbd, ¼ %%%%%%%%%%%%%%% Æ  -_  - _ ¬QTXxL X¼ Å L » À“L,¼¿DÁ“d Å Á QTXx ¼  %%%%%%%%%%% Æ  -_  - ‘O(O RQTÁ¾TL?QTX » QT O 6#?X » SbL?Q‘À Å UDOU,L ¾TÁ ¿„ÁÂÀ“Á ¾TO\XdLDd,X\OR¾ Åa» X<U,X (GCD)   -Æ  S] D<Á >uQTXxNPXd"¾ ,SbNPSWNPSWQ » ,ÁÄâL,%X SbNPN%L?¾ Å ¾TÁ c %%%%%%%%%%% -Æ  - ] Å ¼ bOxd,ORQ Å À Z%%%%%%%%%%%%%%%%% Æ  -  KMSWL bX Å LNPS¢+U :À“X d%%%%%%%%%%%%%% Æ  -  _  -S Å À“Á ¾TO Å ¾TSbN ÁÄâL,X %%%%%%%%%%%%% Æ  -  ‘O¼½L,À¾ Å ¾T ¼ Z%%%%%%%%%%%%%%% -Æ  - _ ] Å ¼5¿„ÁÂd Å ÁÂQTX %%%%%%%%%%%%%%%%% -Æ  f ®O¼½L,NPO\U,Xx¼5QTOx¼½L,À ¾ Å ¾T¼ » SbL?Q‘ÀøV Á“d¾½QTL,¼ »uÅ ¼½¼½Á c %%%%%%%%%%%. .  . .  . . .   . . .  . .  . . . . . .   . .    .     . . .. ..        . Á#. º„º ÆbÆ Æbc Æbc Æ Æ Æ Æ cW` c cbÆ cbÆ c. ! ! !   . `. . ` `. _ f f. c  "! "! " (!  !_ !f !f !f. ! ! !! (    .  `c  `c `!.

(59)  

(60)  

(61). 1. œ yrƒ8·?n'w?yrƒr„yr¡bww?yuv‚q‚w´p>yrz >¡b,v§z{o=ywvsn>q‚out'| ?¦ wƒrwƒ8·.ƒ'pr¡Wv§z~o=yƒrw´|  z yuv‚qWp8Ÿ ¶ -c  +QTSW¿DÀ :NP X<U,X\UDOU,L ¾TÁÂSbdUDX\À V ÁÂd¢¾½QTL,¼UD O Á“U Å ¿DÀ“X\NPS¢UDL,ÀÂSÏL,d,X<¾' ,OSWQTÁ“X<OxâL Å ¾TÁ“Sbd,d,XÀ“À“X % -c    V L,d,Á 6+ Å ¾TÁ“SbdNPS.U,L,À“SPXx¼ ¾‘U, O xÁÂU Å ¿„ÀÂX %%%%%%%%%%% -c   _ V L,d,Á 6+ Å ¾TÁ“SbdNPS.U,L,À“SPXx¼ ¾‘ÁÂdDU, O xÁÂU Å ¿DÀ“X 5%%%%%%%%%% -c  _ +QTSW¿DÀ :NPX<U,X\ÀøV ÁÂd¾½QTLD¼Á“d,U,(O Á“U Å ¿DÀÂX\NPS.U,L,À“SPLDd,X<'¾ ,OSWQTÁ“X<OxâL Å ¾TÁÂSbd,dDXÀ“ÀÂX h%%%% -c  _  3M d » QTSW¿DÀ :NPX\Á“d,U, O xÁÂU Å ¿„ÀÂX p%%%%%%%%%%%%% -c  _  _  V L,d,Á 6+ Å ¾TÁ“SbdNPS.U,L,À“SPXx¼ ¾‘ÁÂdDU, O xÁÂU Å ¿DÀ“X 5%%%%%%%%%% -c  _  V L,d,Á 6+ Å ¾TÁ“SbdNPS.U,L,À“SPXx¼ ¾‘U, O xÁÂU Å ¿„ÀÂX %%%%%%%%%%% -c  -_   KMSbL XxÀÂÀ“X '¾ ,OxSWQTÁÂX<OxâL Å ¾TÁ“Sbd,d,XÀ“À“X Y E  %%%%%%%% -c  -_   _  V LDd,<Á 69 Å ¾TÁÂSbdNPS.U,L,À“S E X¼ ¾‘U,(O Á“U Å ¿DÀ“X  %%%%%%% -c  -_   X » QTSW¿DÀ :NPX\U,X\À V Á“d¾½QTL,¼‘X¼ ¾‘Á“d,U, O xÁÂU Å ¿„ÀÂX\NPS.U,L,À“S E +%%%%.   . . .     . s. s. s. (+. . -.‡  _„ q‚„+[2¡W?vxQTSW¼·.¾'¾TqW:xS-z{N ŸR vaSbXxz{À¼¨8Xx¼pCU,X%w.U,ŸPOR ¾TSbƒ8XdQTw.¾½NPŸÏQ ÁÂd,n>Á“dÁ“q‚¼ ¾ToD¾TXXv‚¼ ¼ oC0+¡bo=|~w.%%Ÿ ¶ %%%%%%%%%%%%%%%%%%%%%%%%%%%%    _W` Å   f [2? _V L,¼  ¾'d :xN QTXx SW¼¾TO$U,S-6„ X%d,SbÁ ¾TÀ“XSbÁ“SbdUDd,¾½ORQ¼ ¾TÅ XRÁ“QTd%NP¾TXÁ“¼d,%Á“¿D¼ Á“¾TXXd%UDXRO$QT%¼‘6Dd,L,Á“%d©¼ Y¼a?¼ ¾'%%:NP%%X<%%U,X% Sbd%%¾½Q %%Á“d¾TX%%¼¿D%%Á“Xd©%%U,O$6„d,Á %%%%%%%%%%%  __b_ _  » Å  ¹ ‹ y>z21'¡b,v§z~o=y ¶ ¸„º !   ‘!  Xx À  Å  ¾TÁ“Sbd, ¼V L,Xxd,dÁ¾½6+QT X<LD¾TÁ“d,SbÁ<d69 XxÅ ¼ ¾T¾‘ÁÂSbd,d©O xXRX¾‘¼½¼ ÀÂX ÁÂQT» XQT SW¿DÀ:NP%X\U,X\%¼½%O xL?QTÁÂ%¾TO%%%%%%%%%%%%%%%%  _b_bÆc Å Å    _  V L,d,Á6+ Å ¾TÁ“SbddCV Xx¼ ¾ »„Å ¼¼½LEϼ Å d¾TXr%%%%%%%%%%%  _bc ! !  _ 3M!  d,_ Á 6+ Å ¾T Á“SbÁ“Xd dXxd¾½QTX<LD+d,%Á<69 %¾TÁÂSbd©%XR¾‘%O‚âL %¾TÁÂSbd,%¼U,%Á“S % d¾T%Á“Xd,dD%X¼  %%%%%%%%%%%%%  _b_ c !!  _-_-   _ [.SWXÀ“¼L?¾TOxÁ“âSbL ÅdUC¾TÁ“VSbO‚d,üL Å U,¾TÁ“Á“S Sbd, Å ¼À“dÁÂd,¾TÁÂO XxÅ d,Á d,QTXxXx¼¼"» U,/ ÅÁ“S ÀøV» LD d,Å Á<69d¾T Á“X¾Td,ÁÂSbdDd X¼‘U Å d,¼ +%%%[%%  _W`! !!  __ _ 3M,MdOd,Å OÀQ bSWÀCQTL,Á¾' d, ,ÁNP6+ X\¾TU9Á“VSbLDÅ d d,Á<69 Å ¾TÁÂSbd©» @OÀ“Å ONP%Xxd¾ Å%Á QT%X"%%%%Å %%%%%%%%%%%%%%  ba f_ !!  _-_-  _ Å 3M3MddQTÅ ÅOÀ b¼½L,SWQTÀ¾ Á ¾' ,¾NP¾TX X\  DU9d,V LDÁ“âd,L,Á<69X\ U9Å ¾TV L,ÁÂSbd,dÁ6+ ¾TÁ“SWd % %%%%%%%%%%%%%%%%  aa ff !   Á“¼½L,d,Á6+ Å ¾TÁ“Sbd %Å %%%%%%Å %%%%%%%%%  b c Œ ·.Ÿo=| pCv§z{o=yƒ8wŸ 83 ŸRv ?¦ w.Ÿ „ƒr·.n'w,y8ƒruy„v§Ÿ ƒ  ·.¨Cp8,v§z{o=y8Ÿ ¶      Åa »,  » XÀ“¼KMN SW¾ Å ¾'¾T ,Á“SbOd,N ¼Å XR¾T¾‘ÁÄÃUDLDO$X6D¼ d,Á¾TÁ“SWdD%¼ =%%%%%%%%%%%%%%%%%%%%%%%%%%% ( 7 ff`` Å    _ ‘O¼½LDÀ ¾ Å ¾T¼‘N Å ¾' ,OxN Å ¾TÁÄâL,X¼ ,%%%%%%%%%%%%%  f`   _ [2?O¼ ¾'¾' ,:xS.N U,XxX<¼ UDX U,QTO O» ¼½SbXxÀ“d,L?U ¾TÅ Á“SWdd ¾T¼[%ˆU9VO‚â%L %Å ¾TÁÂSb%d,¼  %%%%%%%%%%%%%%%%%%%%%%%%  ff¢_  › `q‚ oC ¡b·?ƒ>O 6Dprd,q‚ÁÂw¾TÁÂSbƒrd,w¼ ƒ8·.%¡¢z Ÿ‚z~%o=y ¶ %%%%%%%%%%%%%%%%%   f !   ``   _ +8XQTQTXNPLXX¼ ¼ DDG¼½Sb%L,¼ ^ø%¾TXQTN %Xx¼ D9 %Å R%¾TXxL?%QT¼ %%%%%%%%%%%%%%%%%%%%%%%%  fÆW`. ... #.   `   ``   ``   _    f. *,(+& ª  2"­®2 ¯¢6879±®*„/ -?6  / @ -.*D±M¯ý$¬7u-?/. . . .   . Z/2Z[h].   .  

(62) .  

(63) . . . . . ' . . #.

(64)  ! 

(65)  

(66).  `-`-_ZI `#?ŧ Á“»D ¼ »¾Tš XXdÀC[¢ xUDX<SbL}ÀÂU9L?QT¾TV OxL,Á“¼½Sbd,L,d=X\À¾ ¼½Å SbSb¾‘d,À“L?UD¼½¾TXX<ÁÂQ1SbÀ“dhS Å ¾½ ÅQTSbÁÀÂÁ d,¾TX¼½O<XQ1U  Å d,¾½¼‘QT%ÁÀ“ XX0% Å %%¼ »„ż½%%¼½Ác %%%%%%%%%%%%%%%%%%%%%%%%%%%%%  ÆÆbÆb__  `-`- fÆ  XV L,NPdýNP¼aX\?¼U,¾'X<:xN À“S-Xs Å U,À“ÁXF¾TO< SbORd¾TXx¾½d,Q U,Á“L d¾TÅ XL=¼\¿„ Å ÁÂXx¼ ÅdýÅ RU,¾TO$Á6D dDÁ[%XQT¼)%L,dý%¼a?%¼ ¾':NP%XsU,XA% xSbd¾½%Q %ÁÂd¾T%Xx¼)L,d,%Xˆ%OR¾ %X   Æaf  Å Å Åa» ¿„ÁÂXxdUDO$6Dd,Á  %%%%%%%%%%%%%%%%%%%  ÆbÆ  `-`- c  VV L,L,d©d©¼a¼a??¼¼ ¾'¾'::NPNPX\X L,d,X\¿„ORÁ¾ XxÅad» XUDO$¿D6DÁ“Xd,d©Á bU,XO QT6D¼d,LDÁdX¼aQT?¼¼ ¾'L,:d©NP¼aX\.U,¼ ¾'O :xNPXd,X U d¾‘¿„UCÁÂXxV O‚dÃLU,O$6„¾TÁ“d,SbÁd,[¼ 7%%%%%%%%  ÆbÆ c!   ``   _ ‘[2?O¼ U,¾'L+: RNP¾TÁ“X<SWd©U,X%U, X<SbÀd¾½Q ¼½Å Á bÁ“dd ¾TX¾T¼GL?QTÅ X I¾T%XL?Q %» QT%O¼½XQ1 %Å d¾(» %I%%Å %%%%Å %%%%%%%%%%%%  ÆcW` Å Å `   3Md,X Å L,¾½QTX Å Q Å R¾TOQTÁ¼ Å ¾TÁ“SbdU,X¼‘¼a?¼ ¾':NPX¼¿DÁ“XdUDO$6Dd,Á“¼ %%%%%%%  cbÆ   `- ! +QTS- OxU,L?QTX\U,X<U,O( Á“¼½ÁÂSbd8%%%%%%%%%%%%%%%%%  cbc   ‡ o=y8¡¢|øp8Ÿ‚z{o=yw¢vsn¬w.q§Ÿxn¬w.¡Wv§z „w?Ÿ ¶  œ y8ƒrw  ¹„¹ ME. ME. . ". . #?Á.

(67)  

(68)  

(69). #?ÁÂÁ.

(70)       &     ++QTQTSWSW¾T¾TS-S-  SbSbÀ“À“X<X<U,U,X\XKM[ XXNPU+ Á QÅ N ^1[-[  ?QTS.NPXÁÂUDQxXRV ¼"Q(d5% ,QTX%XR^ % ¼½¼ %+QTSW%¾TS-% SbÀ  %G%%%%%%%%%%%%%% Å Å Å +QTSW¾TS- SbÀ“X<U9V O

(71) Å d bX<U,X% xÀÂX(rU,X  ÁEPX^ MXÀ“ÀÂN Å dG%%%%%%%%%%  ++QTQTSWSW¾T¾TS-S-  SbSbÀ“À“X<X<U,U,XX\KMXXXd,U+dD ÁÂd WN^1[^1[-Å  ( ? SAQTS./XUD xXRÀÂQ"X(r/¼a? xÀÂNPX(rOR¾½¼aQT?ÁÄNâL,OX¾½QTÁ“âL,%X%%%%%%%%%%%%%%%%%.  f  _- f _- f  _ _- f  _- f  f _- f  Æ _- f  c _- f  _- f  _- -Æ  _- -Æ  _ _- -Æ . Å. +QTSW¾TS- SbÀ“X<U9V Å L?¾' ,Xd¢¾TÁ<6+ Å ¾TÁÂSbdU,X "5L,À“À  %%%%%%%%%%%%% +QTSW¾TS- SbÀ“Xb Z   bÁÂQTXUZJâL,Á Å À“Xd¾ +QTÁ Å $  %%%%%%%%%% +QTSW¾TS- SbÀ“X! \0  ;d,Á¾TÁ Å À'< X \ aQTXxXNPXd¢¾ i%%%%%%%%%%% +QTSW¾TS- SbÀ“X b ÁÂUDX$  SbL?¾' ,XxU q QTS  ,%%%%%%%%%%%%%. . ! +QTSW¾TS- SbÀ“X<U,X\KMX XU+. Å N^1[-  ?QTS.XUDXRQ½^  S W X  %%%%%%%%%%% +QTSW¾TS- SbÀ“X<U,X\U,O xSWN » ¾TX\¼½X QTXR¾‘U9V OÀ“X ¾TÁÂSbdh/ » À“L,¼½Á“XL?QT¼ Å L?¾TSWQTÁ¾TO¼ %%%%%% +QTSW¾TS- SbÀ“X<U9V O

(72) Å d bX<U,X% xÀÂX(j K0 %%%%%%%%%%%%%. #?Á“ÁÂÁ. !. _bc. !_  _ _. W ` bÆ  ! f`.

(73) 

(74) % 

(75) . . 

(76) . #?Á.

(77)  

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