• Aucun résultat trouvé

Understanding cache attacks

N/A
N/A
Protected

Academic year: 2021

Partager "Understanding cache attacks"

Copied!
22
0
0

Texte intégral

(1)

HAL Id: inria-00071387

https://hal.inria.fr/inria-00071387

Submitted on 23 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.

Understanding cache attacks

Anne Canteaut, Cédric Lauradoux, André Seznec

To cite this version:

Anne Canteaut, Cédric Lauradoux, André Seznec. Understanding cache attacks. [Research Report]

RR-5881, INRIA. 2006. �inria-00071387�

(2)

ISRN INRIA/RR--5881--FR+ENG

a p p o r t

d e r e c h e r c h e

Thèmes COM et SYM

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Understanding cache attacks

Anne Canteaut — Cédric Lauradoux — André Seznec

N° 5881

Avril 2006

(3)
(4)

Unité de recherche INRIA Rocquencourt

! #"$%&'"$(%)+*, .-'/02143+56"$(0&"7/89(:);*,/02-!<'=>'3!?

@ACB2D.EGFIHKJMLNEOIP'QLRSPUTVFWOXBYD#E2FKZY[\D#D^]C_a`bZ2cd_'OXFEYO6PVTUFeOfB2D#E2F6FfTUD^g$[\hb`bi']CEGF

jlkX[dmWEYOXFnHo[VpVE2F6EOIHcdqaF

r6cdqaq7[>keO6pVEskXE2ZtACE2kXZtAaEu_$v,wdx>xCyR{z|Ukf`bh~}d>\€Ry2x‚qacdƒ>E2F

„†…‡2ˆY‰‹ŠCŒdˆ> @AC`bFŽqacdq$EYkoq7[>`_'OtFŽ[>]VOŽOXAac‹Og7[\OfAOXACEnD#`ZkX[d‘’cdktZtAC`“OXE2ZOf]CkXE[d”OfAaEnqCkX[VZE2FXFf[\klcd_7p#OfACEMZYc>ZtACE

`b_C`“OX`bc\hoFeOXcdOfE†`bD#qac\ZOOfACEcdD#[\]C_'O^[\”6Fe`pVE‘’ZtAac\_C_CEYhŽ`_V”•[>kfDcdOf`b[\_—–KAC`ZtA˜`bF^qCkf[‹|U`pVE2p!gUT™c\_acdhbTUšY`b_Cƒ›OfAaE

ZYc>ZtACE†g$EYAac&|U`b[\]Ck‚pV]CkX`_Cƒ!c+FfT'D#D#EOXkf`ZE2_aZkXTUqVOf`b[\_œ;@AaEYkXE”•[\kXE\OXACEž|U]Chb_CEYktcdga`hb`“OWT![d”ncŸgah[VZt —Z`bqCACEYk

`bD.qahE2D.E2_'OXc‹OX`[>_˜gac\FfE2p™[>_˜h[U[\ U]Cq—OtcdgChbE2FAC`ƒ>AChbT!|‹cdkX`bE2Fs–K`OfA—OXACEžE2_aZkXTUqVOf`b[\_˜Z[>_'OfE¡UO^c\_ap—–K`“OXA˜OfAaE

OXc\kfƒ>EOXE2p.qChc‹Oe”•[>kfD›œŽJI]CkokfEGFe]ChOXF,OfACE2_žZhcdkX`“”•T#Ff[\D#EnFf`D‚]ChbcdOf`b[\_aFlkfE2q7[>keOXE2p#gUT.¢E2kf_aFeOfE2`_†c\_apFfAC[‹–£OfAacdO

OfAaEYTZ2cd_g7EskXEYqakf[VpV]aZYE2p[\_ChbTž`b_Ÿc.|\EYkXT†qac\keOX`bZY]ChcdkKZ[>_>OXE¡UO2œl¤n[‹–oE2|\E2k2U–EMq$[\`b_'O6[\]VOKOXAac‹OnFf[\D#Esz6¥P

 \E2Tga`“OtFIZ2cd_Ÿg$E^kXE2Z[‹|>EYkXE2pEY|>EY_Ÿ`”Žcdhbh~hb['[> U]Cq›OXc\gChEGFnhb`bE`_;OfACE.ZYc\ZtAaEg7EY”•[\kXEE2c>ZtAŸEY_aZYkfTUqVOX`[>_a`4œE\œb$`”

cdhbhZYc>ZtACED#`bFXFeEGFKcdkXEMc&|>[\`pVE2pœ

¦Ÿ§'¨9©fª^« ‰‹¬‡> @`bD#`_CƒcdOeOXc>Zt VFYCZ2c\ZtACEc‹OfOXc\Zt VF2CFe`pVEY‘­ZtAac\_C_CE2h9cdOeOtc\Zt VFYVzn¥oP

® ¯•°±¯³² ´&µ·¶t¸·¹Wº »,¼'½\¾G¿ À ÁÂÃV ÄeÅÇÆ À ÈtÉGÄeÆÇÊ ËU¹ Ì9Í&¹WÎÐϋÑeÒ ÓW¹WÔ&¹’Õ À ֋µÐÑtÏ&ÓW¹ À

×tØtÙÇÙYÚVÛ³ÜÇÝXÙÞÚÇÝXßÞVà•ÜÇÚtáÇâ&ãXä'ېåÝtßâÝtá2æfßç2èÇéGã’ÙYâ&ãeÝVÛ³êÇâ

ë

¯•±~¯·ìY²!´&µ·¶t¸·¹’ºl»í>îG¿~À9ÌÑtïK´&ð&ÎÔ&¹ŽÁ9¹eÑtð&ñóòó¹WðIÀ$ÊÇÆÇÅtôõ±¹eÏGÏ&¹WÎ,Ì9¹WÔ&¹’ÕnÀ7֋µÐÑtÏ&ÓW¹ŽÀö Út÷tÙYÚYäXéGãWâ&ã ö ÝVېêÇâ

(5)

‡



HoEYOsc\keOX`bZYhE.D#[\_'OfkXEi']CE#hbcD#`bZYkf[\‘­c\kXZtAC`OfEGZÇOX]CkfE.pV]™qCkf[VZYE2FXFeE2]CkEOshOtc‹Os`b_C`“OX`bc\hŽpV]—ZYc>ZtACE

`b_a]CE2_>OOf[>]aFžpVE2]V¡ Fe]Ckhbc i>]7cd_'Of`O™p`b_V”•[>kfDc‹OX`[>_£”•[\]CkX_C`bE+qac\k†hcd_7cdhbTUFfE;pV] ZY[\D#q$[\kfOfEYD#E2_>OpVE;hc

DYD#[\`bkXE‘’ZYc\ZtAaEMc\];Z[\]akXFKpVE^hE¡2ZY]VOf`b[\_Ÿp]C_;c\hƒ>[\kX`“OXACD#EpCE^ZtAC`$kXEYD#EY_'OnFfTUDYOfkX`bi']CE>œ c#|']ah_!2kXc\gC`‘

hb`“O"npVEKh#`bD#qCh2D#EY_'OXcdOf`b[\_†p]C_†cdhbƒ\[>kf`OfAaD.Eqac\k,gChb[UZ2F,]VOX`hb`bFXcd_'OopCE2FOtcdgChbE2F,|‹c\kf`bE6pV[\_7Z”•[\kfOfEYD#E2_>OŽc&|>E2ZhbE

Z[>_'OfE¡UOXEp$]VOX`hb`FfcdOf`b[\_#EOŽc&|>E2ZhbcMqChc‹OXE‘4”•[\kXD#E|U`F%2E\œ'&6['FkGFe]ChOXcdOXF,ZYhbc\kf`(aEY_'Olcd`b_aFf`ChbE2F,Ff`D‚]ChbcdOf`b[\_aFktcdqC‘

q$[\kfOYEGF,qac\kŽ¢EYkX_aFWOXEY`b_#EOlD#[\_'OfkXEY_'OŽi']CEnZYEYhbhEGFW‘’Z`V_aE6q7E2]C|\E2_'O*)OfkXE6kXEYqCkX[VpV]C`OfEGF,i>]aEnpCcd_7FlpVE2FŽZ[\_'OXE¡UOfEGF

OfkXB2FIqac\keOX`bZY]Ch`bEYktF2œM@[\]VOXE”•[>`bF29_C[\]aFID#EOfOf[\_7FIE2_+2|'`pVE2_aZE‚hbcžq7['FfFf`ga`hb`“O".pCE‚kXEOXkf[>]C|\E2knZE2keOX`bc\_aFnga`“OtFMpCE

ZhbE”,pVEh#zn¥oPD)YD#EspCcd_aFhbEZYc>F[-,hEGFOXc\gChEGFKFeEMOXkf[>]C|\E2_>O6pCc\_aFhbEZ2c\ZtACEsc&|‹cd_'OKZtAac\i']CE[>q.2kXcdOf`b[\_pCE

ZtAC`$kXEYD#E2_>OGœ

/ « ˆ2‡ © Œ10 ‡ž zOeOXc>i']CE2Fqac\k6ZYc\_acd]V¡ZYc\ZtA22F2UcdOeOtc\i']CE2FKFf]CkKhbEsZYc\ZtAaE\Cz6¥P

(6)

! "

‚~ l

PU`pVE‘’ZtAac\_C_CEYhcdOeOXc>Zt VFc\kfEZkXTUqVOXc\_acdhbTVFeEGFŽ–KAa`bZtAOXc\ \Esc\pV|‹c\_>Otcdƒ>En[d”Fe[>D#EMqaA'TVFf`bZ2cdh9`b_V”•[\kXDc‹Of`b[\_hEGcd >E2p

gUT+cŸZkXTUqVOf[>ƒ\ktcdqCAa`bZ‚pVEY|U`ZE$#•E>œƒ7œ#Of`bD#`_Cƒ7q$[‹–EYksZ[>_aFe]aD.qCOf`b[\_œ2œYœ%œžPU`b_aZE#OXACE(aktFWO–[\kX Ÿ[d”'&n[VZtACE2k

(

yG}*)­CFeE2|\E2kXc\h$ZYhbc>FfFfE2F[d”Fe`pVE‘’ZtAac\_C_CEYhcdOeOXc>Zt VFohb`b \EpV`9EYkXEY_'OX`bc\hq7[‹–EYkcd_ac\hTVFf`bFoAac&|>EIg$EYE2_(akXD#hTžE2FeOXcdgC‘

hb`bFfACE2p

(

x)­œ$+6_'OX`hkfEGZE2_>OXhT>D.['FWO‚[d”OfACEGFeEc‹OeOtc\Zt VFc\kfE†g7c\FfE2p—[\_ Ffq$E2Z`(7Z#”•EGc‹OX]CkfEGF[\”KFf[\D#EžFf[d”³OW–cdkXE

`bD.qahE2D.E2_'OXc‹OX`[>_aFK[\”OXACEgac>Fe`ZMOfktcd_7FW”•[>kfDc‹OX`[>_aF`b_'|>[\hb|\EGpž`b_›OfACEOXcdkXƒ\EYOfEGpc\hƒ>[\kX`“OXACD›œ-,a[\k6`b_aFeOXcd_7ZE\7c

Of`bD#`_aƒc‹OfOXc>Zt cdƒ'cd`b_aFeOIz6¥oP;pV]CEOX[&I[UEY]C_CEc\_ap/.I]C`FXi>]7c‹OfE2k

(

y0 1),cdqCqah`bE2Fn`“”,OXACE‚LŸ`¡7Ho[\hb]CD#_aFKOXkXc\_aFe‘

”•[\kXDc‹OX`[>_]aFfE2FKc.qac\keOX`bZY]Chcdk`D#qChbEYD#E2_>Otc‹OX`[>_[\”~OXACEsD^]ChOf`bqChb`bZ2c‹OX`[>_`b_325476890:ǜ

¢]VO2>`“Oo`bF,]7Fe]ac\hhbT^g$EYhb`bEY|\EGp‚OfAacdOŽFe]aZtA#–E2c\ '_aE2FXFeEGF[d”z6¥oP#pV[s_a[dOŽcdqaq7EGcdk,”•[>k,[\qVOX`D#`bšYE2p#`bD#qChbEYD#EY_V‘

OXcdOf`b[\_aF–KAa`bZtA—cdkXEpVE2pV`ZYcdOfEGp;OX[$ >}&‘­gC`OMqakf[VZEGFfFf[\ktF2œ<;’_™OfAC`FZ2c\FfE\g$[dOXA—L;`“¡7Ho[\hb]CD#_aFsc\_ap™PV]Cga¢T'OfE2F

Ofktcd_7FW”•[>kfDc‹OX`[>_aFŽc\kfEI`D#qChbEYD#E2_>OXE2pgUTh[U[\ U]CqžOXc\gChEGF`_[\ktpVEYkoOf[#pVE2ZYkfEGc\FfE6OXACEEY_aZYkfTUqVOX`[>_Of`bD#E\œlz6¥P

EY_7ZkXT'qCOf`b[\_›cd_ap›pVEGZkXT'qCOf`b[\_OfACE2_ŸD#c\`_ahTžZY[\_aFf`FWO6[\”c#FfE2i']CEY_7ZEs[d”D#EYD#[\kXTc>ZYZEGFfFfE2FoOX[#OfACEGFeEshb[U[\ U]Cq

OXc\gChbE2F2œ=+n_V”•[\kfOf]a_ac‹OXEYhbT\UD#EYD#[\kXTc\ZYZYE2FXFeEGFŽc\kfE6_a[dOKcdhb–c&TVF,q$EYkf”•[\kXD#E2p`b_ZY[\_aFeOXc\_>OoOf`bD#E\œ>;’_†qac\keOX`bZY]ChcdkG

OfAaE]aFfEž[\”nZYc>ZtACE†D#EYD#[\kXT™Aac\F.c;ƒ>kfEGc‹O^`bD#qac\ZO‚[\_ OfACEhbcdOfEY_7ZT˜cd_ap [\_˜OXACEžq$[‹–oE2k‚ZY[\_aFf]CD#qVOf`b[\_ [d”

cD.E2D#[\kXT;c\ZYZYE2FXFYœ‚@`D#`b_CƒŸcd_ac\hTVFf`bFI[\kq$[‹–oE2kMc\_acdhbTVFe`FMD#c&TOXACEY_—qCkX[‹|U`bpVE.Fe[>D#E.Ff`bpCE‘’ZtAacd_C_aEYh`_C”•[\kf‘

Dc‹OX`[>_!–KAC`ZtA—ZYcd_!g7EEY¡VqCh[>`“OXE2p!gUT›OfACE†ZYkfTUqVOtcd_ac\hTVFeO2c\FMD#EY_'OX`[>_CE2p!gUT?&n[VZtACE2k

(

yG}1)Žcd_ap@&EYhFeE2TAB

CED

(

y\y)­œs@ACE(7kXFeOIqCktc\ZOf`ZYc\h`bD#qChE2D#EY_'OXcdOf`b[\_aFI[d”oFf`pVE‘’ZtAacd_a_CEYhc‹OfOXc\Zt VFngac\FfE2pŸ[>_;OXACE.c\_acdhbTVFe`F6[\”lOfAaE

ZYc>ZtACEg7E2Aac&|U`[>]Ck”•[\klcMgChb[VZt ‚ZY`qCAaEYklcdkXEKpV]CEOX[@Ff]C_C[U[F=CGD

(

}>w*)7cd_7p‚j,c\ƒ\E

(

yGx1)­œ@ACE2_>Z2c\ZtACEKcdOeOXc>Zt VF

cdƒ'cd`b_aFeOzn¥oP›pVkXEY– c.hb[dO6[\”c‹OfOfE2_>OX`[>_ŸpV]CkX`_Cƒ.OXACEshbc>FWOOXACkfE2ET\E2c\kXF

(

}HC~ydyHa7}Uy&w*)4œ

¤6[‹–EY|>EYkGYcdhbh‹OXACE2FfElkXE2ZE2_'O–o[>kf VF9ktcd`FeEDcd_UTn[>q7E2_i']CE2FeOf`b[\_aF2œ~LŸ['FWO_C[dOtcdgChbT\&ckfE2hE2|‹cd_'O~Z[>D.q7cdkX`bFf[\_

g$EOW–EYEY_›cdhbhqCkXE2FfEY_'OXE2pZYc\ZtAaEMcdOeOXc>Zt VFYVg$[dOXA`b_OfEYkXDF[d”,Z[>D.qahEY¡U`OWTžc\_apž[\”qakXc>ZÇOf`ZYc\hcdqCqChb`ZYcdga`hb`“OWT>V`bF

FeOf`bhhD#`FfFf`b_Cƒaœ>,C[>k`_aFeOXc\_aZE>CFe[>D#EM[\”~OXACE2FfEsc‹OeOtc\Zt VFcdkXEspVE2pV`ZYcdOfEGp†OX[.E2D^g$E2pCpCE2p›pVEY|U`ZEGFYVFf[\D#E[dOfAaEYktF

cdkXEshb`D#`OfE2pOX[†D^]ah“OX`“‘­]aFfEYkIFfTVFWOXEYDF2œ¢[dOXAOfACE‚qCAUTUFf`ZYcdh~_ac‹OX]CkfEs[\”OfACE]7FeEGpŸFe`pVE‘’ZtAac\_C_CEYh~`_V”•[>kfDcdOf`b[\_

cd_7p£OfACE+c>FfFf]CD#qVOX`[>_aFDc\pVE+[\_£OfACE!`_a`“OX`bc\hIFeOXc‹OXEŸ[d”OfAaE!ZYc>ZtACE›D#EYD#[\kXT g$E”•[>kfEŸE2_aZkXTUqVOf`b[\_ AC`bƒ\AahT

`b_a]CE2_aZEOfAaE›c\qCqChb`bZ2cdgC`bhb`“OWT˜[\”Mc—ZYc>ZtACEcdOeOXc>Zt 9œ z6_a[dOfAaEYk[\q$EY_ qCkX[\gChbEYD›Ž–KAa`bZtA pV[UE2F._C[\Oc\kf`FfEž”•[>k

Zhc\FXFf`bZ2cdhFe`pVE‘’ZtAac\_C_CEYh,cdOeOXc>Zt VFY9`FnOX[ŸpVEOXEYkXD.`b_CE.–KAC`ZtA!qac\kXc\D#EOfE2kXFn`_!OfAaE.D#`ZkX[d‘’cdktZtAC`OfE2ZOf]CkXE[\”ŽOfAaE

qCkX[VZE2FXFf[\k,`bD.q7c\ZÇOoOfACEIEBI†Z`bEY_7ZT.[d”OfAaEIc‹OfOXc>Zt .c\_ap#–KACEOXACEYkoOfAaEnZkXTUqVOXc\_acdhbTVFe`FlZYc\_†g$EnD#[\]C_'OXE2p#[\_†c\hh

>}‹‘4ga`“OKqCkX[VZE2FXFf[\ktFŽ[>kK_C[dOGœ

;’_!OfAC`Fsqac\q7E2k2–EFeAa[‹– OfA7c‹O^ZYc>ZtACE#c‹OeOtc\Zt VFZYc\_™g$EZhc\FXFe`(aEGp!c>ZYZ[>kXpC`_CƒOf[OXACE†Z[>_apV`Of`b[\_aFMOXACEYT

kXE2i']C`bkfEI[\_†OXACE`_a`“OX`bc\hFWOtc‹OfEM[d”~OfACEsZYc>ZtACEnD#E2D.[>kfT>œ,@ACE2FfEMZY[\_apC`“OX`[>_aF`_7]CEY_aZYEnOXACEqCktc\ZÇOX`bZ2cdh9cdqCqah`ZYcd‘

gC`bh`OWT›[d”OfAaE‚c‹OfOXc>Zt UFncd_apOXACEOWTUq$E[d”ŽpVE2|U`bZYE2F6[>_Ÿ–KAC`ZtA›OfACE2T›Z2cd_Ÿg$E^D#[\]a_>OXE2pœ6L;[\kXEY[‹|\E2k2V–Eq$[\`b_'O

[\]COKOfAacdOKOfACE_7c‹Of]akfEGF[d”OfACE^Z2c\ZtACEE $EGZÇOXF6–KAC`bZtAŸc\kfE[\g7FeE2kf|>E2pg'T†OfACE^cdOeOtc\Zt \E2kAC`ƒ>AChbTž|‹cdkXT†–K`OfA›OfAaE

ZYc>ZtACE^`b_C`Of`cdh,FeOXc‹OXE\œsLŸ['FWO_C[dOtcdgChbT\9`”oEGc\ZtA;E2_aZkXTUqVOf`b[\_;`Fc\FXFe]aD.EGp›Of[g7E#q$EYkf”•[\kXD#E2p›”•kX[\D cd_!EYD#qVOWT

ZYc>ZtACEn[>kŽ”•kX[\D c.ZtAC['FeE2_žZYc>ZtACEn`b_C`Of`cdhFWOtc‹OXE\'OfACE2_žOXACEIOf`bD.`b_Cƒ.[\kq$[‹–oE2kocd_7cdhbTUFf`FŽDcd`b_ChbT†pVEOXE2ZOXFZYc>ZtACE

D#`bFXFfE2F2œ=JI]CEMOf[‚OfAaEFeOfkX]aZOf]CkXEn[\”~OfAaEMZ2c\ZtACEMD#EYD#[\kXT\VFf]aZtAc\_c‹OfOXc>Zt #c\ƒ>c\`_aFeOzn¥oPEY_ac\gChbE2FŽOf[#kfEGZ[‹|>EYk

OfAaEsD.['FWO6Ff`ƒ>_C`(7ZYc\_>OKgC`OXF6[d”EGc\ZtA \E2T†gUT>OXE\œ

Ho[\_U|>EYktFeE2hT>,`“”MOfACE›[>_ChT c\FXFe]CD#qVOX`[>_ [>_ OXACE;ZYc>ZtACE`b_C`Of`cdh6FeOXcdOfE›`bF.OXAac‹Ožc\hhKhb[U[\ U]Cq OXcdgahEGF#]aFeEGp

”•[\kOXACEEY_7ZkXT'qCOf`b[\_™h`bE`_™OXACE†ZYc>ZtACE‚g$E”•[>kfEEGc\ZtA!EY_aZYkfTUqVOX`[>_OXACEY_˜Ff]aZtA™Z2c\ZtACE#D#`FfFfE2FspV[›_C[\O[VZYZ]ak

cd_UTUD#[\kXE\œ@AC`bFAUTUq$[dOfAaE2Ff`bF,ZY[\kXkfEGFeq$[\_apaF~OX[OfACE6Ff`Of]acdOf`b[\_.[UZ2Z]CkXkX`_CƒM`b_#pC`9EYkXEY_'OŽZ[>_'OfE¡UOtFY‹”•[>k,`_7FWOtcd_aZYE

`b_kfE2D.[\OfEOX`D#`b_Cƒ^c‹OfOXc>Zt UF2œ¤n[‹–oE2|\E2k2‹E2|\EY_`b_.OfAC`FŽZ2c\FfE\'Fe[>D.EOX`D#`b_Cƒ|‹cdkX`c‹Of`b[\_7FD#c&T.FWOX`hbhag$E6[>gaFeE2kf|>E2p

[\_ Ff]Cq$EYktFfZ2cdhcdkqCkX[VZEGFfFf[\ktF#cd_ap Z2cd_ g$E;]aFfE2p£”•[\kD#[\]C_'Of`b_Cƒ c\_ c‹OeOtc\Zt 9œLK!E+–K`hbhMFfAC[‹– OfAacdO†OfAaE2FfE

Of`bD#`_aƒžZtAacdktc\ZOfE2kf`FWOX`bZ2FKpVEYq$EY_7p›[\_›OfAaE–KAC[\hbED#`ZkX[d‘’cdktZtAC`“OXE2ZOf]CkXEI[\”OfACE‚qCkf[VZYE2FXFe[>k2œŽ@AaEEBI†Z`bEY_7ZT[d”

OfAaE.cdOeOXc>Zt ;cd_apŸOfACE#q$[>Ff`“OX`[>_aFn[\”lOfAaE.`b_U|\[>h|>E2p› \E2TŸgC`OXFIOfACE2_!|‹c\kfT›–K`OfA;OXACE#qCkX[UZYE2FXFe[>k2aOfACEZY[\D#qC`bhE2k

cd_7pŸOfAaE‚`bD#qChE2D#EY_'OXcdOf`b[\_œs@AC`FFWOX]apVTŸqac\keOX`bc\hhbTŸZhcdkX`(aEGFIFf[\D#E‚[\gaFfEYkX|‹c‹Of`b[\_7F6kXEYq$[\kfOfE2p;g'T;¢E2kf_aFeOfE2`_NM

Ff[\D#E^[\”,OfACE. \E2Tga`“OtFI–KAa`bZtA™cdkXEkfEGZ[‹|>EYkXE2p`_+OfACE#Ff`D‚]ChbcdOf`b[\_aFIqCkXE2FfEY_'OfEGpŸ`b_ (y)49EGFeq$E2ZY`bc\hhbTOfACE.D#[>FeO

Ff`ƒ>_C`($ZYcd_'OgC`OXF,[\”7E2c>ZtA‚ >EYTsgUT'OfE>>cdkXEpVE2pV]7ZE2p‚”•kX[\DuOXACEKcd_ac\hTVFf`bF[\”$ZYc>ZtACED#`bFXFeEGFYœ@ACE2FfEKZYc>ZtACED.`FXFeEGF

cdkXEsDcd`b_ChbT›pC]CEsOf[žOfACE‚FeTVFeOfEYD Z2cdhbhbF6c\_ap›OX[žFe[>D#E^cdkXkXc&TžD#c\_C`bqC]Chc‹Of`b[\_7F6–KAC`ZtA;cdkXEq$EYkf”•[\kXD.EGpg7EY”•[\kXE

E2c>ZtA+E2_aZkXTUqVOf`b[\_œ.@ACEYkXE”•[>kfE>Z[\_'OXkXc\kfTOf[›–KAacdOM–c\FM[>kf`bƒ\`b_acdhbhbTg$EYhb`bEY|\EGpOXACE#q7E2ke”•[>kfDcd_7ZE.kfE2q7[>keOXE2p

`b_

(

y)UZ2cd_s[>_ChTg$Eoc>ZtAC`E2|\EGp`“”VOXACEZ2c\ZtACEŽ`_C`Of`cdhUFeOXc‹OXEŽ`FE2D.qCOWT\œOK ACEY_sOXACEZYc\ZtAaEl`bF~`_a`“OX`bc\hhbTh['c\pVEGps–K`“OXA

OfAaEhb[U[\ U]Cq^OXcdgahEGFY‹D#[>FeO,[d”COXACE2FfEKZYc>ZtACEŽD#`FfFfE2FpV[_C[\O[VZYZY]Ck,cd_UTUD#[\kXE\œ~¤n[‹–oE2|\EYkG&–oEqCkXE2FfEY_'O,cn|‹cdkX`cd_'O

[d”6¢EYkX_aFeOfE2`_$F^cdOeOtc\Zt +–KAa`bZtA c\qCqChb`EGF`b_˜OfAC`F^Z2c\FfE†cd_ap –KAC`bZtA˜E2_acdgahEGFOf[;kXE2ZY[‹|\E2kFe[>D.Ež`_V”•[>kfDcdOf`b[\_

[\_OfAaEs[dOfAaEYkK \E2TgC`OXF2œl@AC`bF6`_V”•[>kfDcdOf`b[\_ZY[\D#E2F”•kX[\D Feq$E2ZY`(7ZM”•EGc‹OX]CkfEGF[d”OfACEsD#`ZkX[d‘’cdktZtAC`“OXE2ZOf]CkXE2FŽ[d”

Ff[\D#EqCkf[VZYE2FXFe[>kXF2œ

(7)

@AC`F6qac\q7E2kn`Fn[>kfƒ'cd_C`bšYEGp›c\F”•[>hhb[‹–6FYœ'K™E(7kXFeOMpVEGFfZYkf`bg$EsOfACE‚g7E2Aac&|U`[>]Ck6[\”,OfACE.ZYc\ZtAaED#EYD#[\kXTc\_ap

–EMFfAC[‹– AC[‹– `“O6c 9E2ZOXFD#EYD#[>kfT†c>ZYZEGFfFfE2F2œ,PUE2ZOf`b[\_ ^`b_U|\E2FeOf`bƒ>cdOfEGFoc\hh9qCkXEY|U`b[\]aF–[\kX .kXEYhc‹OXE2p†Of[ZYc>ZtACE

c‹OfOXc>Zt UFn`_7Zhb]apV`b_Cƒg$[dOXAŸOf`bD#`_aƒcdOeOXc>Zt VFncd_7p;Fe`bD#qChbE‚q$[‹–oE2kIc\_acdhbTVFeEGFYœ K™E.qCkf[>q7['FeE‚cžZhc\FXFf`(7Z2c‹OX`[>_Ÿ[d”

ZYc>ZtACEc‹OeOtc\Zt VFc\ZYZY[\ktpV`b_CƒOX[^OXACEsZYc\ZtAaEnE 9E2ZOXFOXACEYT†EY¡VqCh[>`“OGœ,z6D#[\_Cƒ#cdhbh$OfAC['FeEc‹OfOXc>Zt UF2UkfE2D#[dOfEIOf`bD#`_aƒ

c‹OfOXc>Zt UF^cdkXE†qacdkfOf`Z]ahbc\kfhbT+`bD#q7[>keOtcd_'O”•[\k.ZkXTUqVOf[>ƒ\ktcdqCAC`Z#qCkX[VpV]aZÇOtF^c\_ap˜–EžpV`FfZY]aFfFOfACEq7['FfFf`bgC`hb`OWT+OX[

D#[\]C_'OFe]7ZtA£c\_ c‹OfOXc>Zt —c\ƒ>c\`_aFeOFeEGZkXEO‚ >EYT c\hƒ>[\kX`“OXACDFYœ @ACE2_PVE2ZÇOX`[>_ H™gCkX`E aT˜kXE2ZYc\hhF‚AC[‹– z6¥P

`Fn]aFf]ac\hhbT`bD#qChbEYD#EY_'OfEGp;gUT›h[U[> ']aq›OXcdgahEGFYœPUE2ZOf`b[\_!w#`b_U|\EGFWOX`ƒ'c‹OfEGFKOXACE^`b_a]CE2_aZE‚[d”,OXACE.Z2c\ZtACE^`_C`Of`cdh

FeOXc‹OXEc\_ap[\”COfAaED#`ZkX[d‘’cdktZtAC`OfE2ZOf]CkXE,[\_^OfACEKZ2c\ZtACEŽOf`bD.`b_Cƒc‹OfOXc\Zt pCE2FXZkX`g$E2psgUT¢EYkX_aFeOfE2`_œz |&c\kf`cd_'O[d”

¢EYkX_aFeOfEY`b_$F~zn¥oPOX`D#`b_CƒMcdOeOtc\Zt M`bF~OfACE2_^qCkXE2FfEY_'OXE2p`b_‚PUE2ZOf`b[\_^€a‹–KAC`ZtAkfE2h`bE2F~[\_^cIpV`$E2kfE2_>Oc\FXFe]aD.qCOf`b[\_

[\_!OfAaE†ZYc\ZtAaE.`b_C`Of`cdhlFeOXcdOfE\œ ;’_—|U`E2– [\”oOXACE[\gVOtcd`b_CE2p!kXE2Ff]Ch“OtF[\_!OfACEE $EGZÇOX`|>EY_CEGFfFM[d”OfAaE†c‹OeOtc\Zt 9–E

Z[>_aZhb]apVEOfAacdOI`OMpVE2q7E2_apCFI[\_›OfAaE^–KAC[>hED#`ZkX[d‘’cdktZtAC`OfE2ZOf]CkXE[d”,OXACE^qCkX[VZEGFfFf[\kGœ-K™E(7_acdhbhT›FfAC[‹– OfAacdO

Ff[\D#EsZhc\FXFe`ZYc\h9ZY[\]C_'OXEYkXD.EGc\Ff]CkXE2FoEY_ac\gChEMOX[#OfAU–c\keOOXAC[>FfEsZYc\ZtAaEnOX`D#`b_Cƒ†c‹OfOXc\Zt VF2œ

o

PU`b_aZE.OXACEƒ>c\q+g$EOW–EYEY_!OfAaEhbcdOfEY_7ZT;[\”oD#EYD#[\kXT;cd_7p;OXACE†Feq$EYEGp+[\”oqCkX[VZEGFfFf[\ktFn`FsFeOf`bhhl`b_aZYkfEGc\Ff`_Cƒ

(

)4

OfAaEgC]aFsgac\_apV–K`pUOfA c\_ap+OfACEžc>ZYZYE2FXFMFfq$EYE2p!OX[›OfACEDcd`b_—D#EYD#[\kXT;Aac&|>E.g$E2ZY[\D#E#OfAaEh`bD#`“OX`_Cƒ›”·c>ZÇOX[\ktF

`b_›OfACE[‹|>EYktcdhbhqCkX[UZYE2FXFe[>kOfACkX[\]aƒ\ACqC]CO2œ@AC`bFng7[\OeOXhE2_CE2Zt `bFn[‹|\EYktZ[>D#EIgUT›ZYc\ZtAaEsD.E2D#[\kXT\œz ZYc>ZtACEs`bFnc

FfD#c\hh9qC`bE2ZYE[d”~AC`bƒ\A›Ffq7E2E2p†D#E2D.[>kfT>œ=;­OKc\`DFc‹O \E2EYqC`b_Cƒ‚OfACE^Hoj + c>Foga]aFeTc\Foq7['FfFf`gahEgUTD#`_C`bD#`š2`_aƒ

OfAaEh['c\pdFWOX[\kXEIhc‹OXEY_aZYTžOX[#OfACE^D#c\`_ŸD#E2D.[>kfT>œoLŸ[VpVE2kf_›qCkX[VZEGFfFf[\ktFAac&|\EOW–[hE2|\E2hbF[\”[>_V‘’ZtAC`qŸZ2c\ZtACE>

kXE2Ffq7EGZÇOf`b|\E2hT Z2cdhbhEGp ŽyŸcd_ap }Cœ ¥Žc>ZtA [\”nOXACEYD D#c&T g7EŸpVEGpV`bZ2c‹OXE2p Of[˜c™Feq$E2ZY`bc\hKqC]CkXq7['FeE #·pac‹OXc™[>k

`b_aFWOXkf]7ZÇOf`b[\_7F%ngC]VOŸ`b_ OXACE™Ff[d‘’ZYc\hhbE2p ¤ncdkX–cdktp cdktZtAC`“OXE2ZOf]CkXEŸOfAaE Žy!Z2c\ZtACE!`bF]aFf]acdhbhbT FfqChb`“OŸ`b_'Of[ c\_

`b_aFWOXkf]7ZÇOf`b[\_ZYc\ZtAaEncd_apc‚pCc‹OtcZYc>ZtACE\œ@ACE }sZ2c\ZtACEnZ2cd_†Aa[\hp#g7[\OfAž`b_aFeOfkX]aZÇOX`[>_aFŽc\_ap†pCcdOXc>`Oo`FŽhcdkXƒ\E2k

gC]VOnFfhb[‹–oE2koOXAacd_OXACE lyZYc>ZtACE\œ

z ZYc\ZtAaE!`F›pV`|U`pVE2p `_'OX[ gChb[VZt VF@#·[\k›hb`_CEGF%ž[d” (C¡VE2p Fe`bšYE sOWTUqC`bZ2cdhgChb[VZt  Fe`bšYEGFc\kfE >}CI€H7yG}\x

gUT'OfE2F2œ ;­O‚`F–[\kfOfA—_C[\Of`Z`b_CƒŸOfA7c‹OOXACEOfAaE lycd_ap }›ZYc\ZtAaE2FsDc&T+A7c&|\E†pV`$E2kfE2_'O‚gChb[VZt !Ff`š2E2F2œ›@AaE

ZYc>ZtACE†c\FXFf[UZY`bcdOf`b|U`“OWT™pVEOXEYkXD.`b_CEGFAC[‹– OfACEDcd`b_˜D.E2D#[\kXT+gChb[VZt UFD#c\q `b_>OX[;ZYc>ZtACE†gChb[VZt UF0M‚c\_ž‘­–c&T

c\FXFf[UZY`bcdOf`b|\EsZYc>ZtACE`bFIpV`b|'`pVEGp›`_'Of[†FfEOtF6[\”NgCh[VZt VF2œozuDcd`b_ŸD#EYD#[\kXTžgah[VZt Z2cd_OfAaEY_Ÿg$EDcdqCq$E2pOX[

cd_UT‚gCh[VZt .[d”csƒ>`|>EY_FeEYO2œ,@ACE6gah[VZt #FeE2hEGZÇOf`b[\_#–K`OfAC`b_žcFfEOo`bFŽq7E2ke”•[>kfD#E2p#gUT.cskfE2qChc\ZE2D#EY_'OŽcdhbƒ\[>kf`OfACD

hb` >E r + (

)­œ ,C[>kK`_7FWOtcd_aZYE\,`bƒ\]CkXE‚ypCE2FXZkX`g$E2FKcHd‘­–c&T#c>FfFf[VZ`c‹OX`|>EMZ2c\ZtACE>œ

Address Tag 1

Word[0−3]

Word[0−3]

Word[0−3]

Word[0−3]

Address Tag 2 Address Tag 3 4 Sets

Block 3 Block 0 Block 1 Block 2

Address Tag 0

,`bƒ\]CkXE#yM=Hd‘­–c&T†c\FXFe[VZ`c‹OX`|>EIZ2c\ZtACED#EYD#[\kXT

z6_`b_aZY[\D#`_aƒ^c\pCpCkfEGFfFOX[sOfAaEIZYc>ZtACE6`FŽFfqChb`“OŽ`b_'Of[^OfACkXEYE6q7cdkfOXF #,`bƒ\]akfEI}%McFfEOo_U]CD‚g7E2k2'cd_†c>pCpVkXE2FXF

OXc\ƒ.c\_apc^gChb[VZt †[ FfEO2œ,@[pVEOXEYkXD.`b_CEM–KACEOXACEYkOXACEsc\Z2ZE2FXFfE2pžpac‹OXc‚`FKFWOX[\kXE2p†`b_OfACEsZYc>ZtACE\U`OXFKc>pCpVkXE2FXF

OXc\ƒ›`bFsZY[\D#qacdkXE2p+–K`“OXA+OXACE†c\papVkfEGFfFIOtcdƒ[d”oEGc\ZtA™gChb[UZt +`_!OfACE†FfEOGœ ;’_™OXACE.”•[\hbh[‹–K`b_Cƒa–EZ[>_aFe`pVE2kc\_

‘4–c&Tc\FXFe[VZ`c‹OX`|>EIZ2c\ZtACEM[d”gUT'OfEGFYVpV`b|U`bpCE2p`_'Of[#gChb[VZt VFYUE2c>ZtAž[\” gUT>OXE2F2œ=;’_žOXAC`bFKZ2c\FfE\'OfAaEFf`bšYEM[d”

OfAaEsgCh[VZt †[-9FfEOK`F"!$#&%')(6*+ :-,gC`“OtF6cd_7p†OXACEFe`bšYE[\”OXACEFeEYOK_']aD^g$EYkK`F"!$#&%')(6/.10

.124365 :7,'œ

@ACEZ2c\ZtACEqac\kXc\D.EYOfE2kXFc 9E2ZOKOfACEsEY¡VE2Z]COf`b[\_Of`bD#Es[d”,cd_Ÿcdhbƒ\[>kf`OfACD OXAac‹O6]7FeEGF6cpCc‹Otc#cdkXkXc&T[\”Ff`š2E

8 Z[\D#q$[>FfE2p![d”EYhbEYD#EY_'OtF[d”KFe`bšYE9:.c\FM”•[\hbhb[‹–6FYœ@ACEcdkXktc&TŸ`bFDcdqaq7EGp!`b_'Of[›OXACE†ZYc>ZtACE.c>ZYZY[\ktpV`_aƒžOX[

`OXFMcdhb`ƒ>_CD#EY_'OMc\_ap›Of[žOfACE.Fe`bšYE;:[d”l`OXFIEYhbEYD#EY_'OtFYœ@ACE‚c\h`bƒ\_aD.E2_'On[d”ŽcpCc‹OtcžZYc\_Ÿg7E#Z[>_aFf`bpVE2kfEGpŸc\FIc

Z[>_aFeOfktcd`b_>O6[>_Ÿ`“OtFIc>pCpVkXE2FXFMo[\_ŸD#[>FeOIc\kXZtAC`OfEGZÇOX]CkfEGFOfAaE^c\pCpCkfEGFfFK[\”ŽcpCc‹Otc`FncD‚]Ch“OX`qahE‚[d”OfACE.Fe`bšYE^[d”

OfAaEMc>pCpVkXE2FXFeEGppCc‹OtcCœ,@ACEIc\kfktc&T^`FpV`|U`pVE2pž`_'OX[<!8= ,MgChb[UZt VFcd_ap†E2c\ZtAžgCh[VZt ZYc\_†AC[>hbp†cdOoD#[>FeO9! .12

.1>

,

EYhbEYD#E2_>OtFYœ@ACE2_a–KACE2_;cd_›EYhbEYD#E2_>OI[d”OfACE‚cdkXkXc&T`Fnc>ZYZEGFfFfE2pUOfACEkXEYhc‹OX`|>Ec\pCpCkfEGFfFf`_aƒ#Z2cd_›g$E^FeE2EY_;c>F

(8)

Set

Address Tag Offset

0x10 0x01

0x00F0FA

0x00F0FA 0xBCF3F1

0x74A051

0x48BCFF

Test

Set 1

,`bƒ\]CkXE} M,zKpCpVkXE2FXFf`_Cƒ#`b_cZ2c\ZtACEMD#EYD#[\kXT

cgChb[UZt !FeE2hEGZÇOf`b[\_—cd_7p!c\_![-9FfEOs`b_>OX[›OfACE#gChb[VZt 9œ#@AaEgCh[VZt ;[-9FfEOskXE2i']C`bkfEGF !$#&%' ( 6 . 2

. >

:7,†ga`“OtFscd_ap!OfAaE

gChb[VZt žFeE2hEGZÇOX`[>_ !#% ' (6

.12 :-,Y‘­gC`“OtFYœ

L;c\_'T[\OfACE2kD.E2D#[\kXTqacdktcdD#EOXEYktFoZ2cd_c 9E2ZÇOOXACEsg7E2Aac&|U`[>]Ck[d”~OXACEE¡VE2ZY]VOf`b[\_›Ff]aZtAc>FZ2c\ZtACEM–KkX`“OXE

q$[\hb`bZY`EGFYU@ ~¢MœYœ2œYœLŸ[\kXEY[‹|>EYkD#[VpVEYkX_qCkX[UZYE2FXFe[>kXF”•EGc‹OX]CkfEn|\EYkXT‚ZY[\D#qChbE¡#`_'OXEYktc\ZÇOX`[>_aFg$EOW–EYEY_ž`_aFeOfkX]aZ‘

Of`b[\_7FYœ @AaE;D#`bZYkf['FfZY[\qC`Z›E¡VE2ZY]VOf`b[\_ OX`D#E™[d”cd_UT FeEGi']CEY_aZYE;[d”s`b_aFeOfkX]aZÇOX`[>_aFžc\hbFf[ pVE2q7E2_apCF[\_ OfAaE2FfE

`b_>OXEYktc\ZOf`b[\_aF2œ>,C]CkfOfACE2k6pVEOtcd`bhbF[>_D#E2D.[>kfTžAC`E2kXc\kXZtAUT†Z2cd_g7E”•[>]C_ap`_

(

yG1)4œ

!K‚ K SKÇ Yo Yt

K ACE2_ cd_˜EYhbEYD#E2_>O`b_ c;pCcdOXcŸc\kfktc&TŸ`bF‚c\Z2ZE2FXFfE2p~OW–o[;Ff`“OX]ac‹OX`[>_aFsDc&T+[VZ2Z]CkGœF;­”KOXAC`bF^EYhbEYD#EY_'Ohb`EGF`b_

OfAaE^ZYc>ZtACED.E2D#[\kXT\VOXACE^c\Z2ZEGFfFK`F6Z2cdhbhEGpc#Aa`“O+7[\OfACE2kf–K`FeEMOXACEgChb[VZt žAac>FOf[g$Ehb[>c\pCE2p”•kf[>D OXACEDcd`b_

D#EYD#[\kXT\UOXAC`FnFf`“OX]ac‹OX`[>_`FKkXE”•EYkXkXE2pc\FKc#D#`bFXF2œl@ACEsq7[‹–EYk6ZY[\_aFf]CD#qVOX`[>_›c\_apžOf`bD.`b_Cƒ†[\”c#pVE2|U`bZYEsD#c&T

AC`bƒ\AChbT|‹cdkXTpVE2q7E2_apV`b_Cƒ[\_‚OfACED#EYD#[\kXTshbEY|\E2h #lyKZ2c\ZtACE> }MZYc>ZtACE\‹Dcd`b_.D.E2D#[\kXT %~–KACE2kfEOfAaED#E2D.[>kfT

c\Z2ZEGFfFfE2Flc\kfEKq$EYkf”•[\kXD#E2pœ@AC`FlD#E2c\_aF,OXAac‹Oo–KACEY_#OX`D#`b_Cƒ‚cFfE2i']CE2_aZEK[\”D.E2D#[\kXT.c>ZYZEGFfFfE2F2‹OXACE6_U]CD^g$EYk

[d”,c\Z2ZEGFfFAC`OXF6Z2cd_g7EFf]aZ2ZE2FXFe”•]ChhbTžpVEYOfEGZÇOfEGpœ

JI]Ckf`b_Cƒ.OfAaEsE¡VE2ZY]VOf`b[\_V–EsZYc\_pV`FeOf`b_Cƒ\]C`FfAOXACkXEYEM”·cdD#`bh`bE2FK[\”Z2c\ZtACED#`bFXFfE2FKc\Z2Z[>kXpV`b_Cƒ‚Of[

(

y21)M

Z[\hpFWOtcdkfOD#`FfFfE2F2V–KAC`ZtAc\kf`FfEI”•[>kOfACE (7kXFeOKkfEY”•EYkXEY_aZYEIOX[c.pac‹OXc

ZYcdq7c\Z`OWTD#`bFXFfE2F2V–KAC`bZtA[VZYZY]CkK`“”OfAaEFe`bšYEs[\”~OfAaEpCc‹Otc.c\kfktc&T#E¡CZE2E2pCFOXACEFf`š2EM[\”OXACEZYc>ZtACE

Z[\_!a`bZOD#`FfFfE2F26–KAC`ZtA Dc&T£AacdqCq$EY_ [\_ChbT `“”.c\ZYZYE2FXFeEGFžZ2cd_ qCkX[‹|\[> \E›OXACE!E2|U`bZOf`b[\_ [\”^kfEGZE2_>OXhT

c\ZYZYE2FXFeEGpžpCcdOXcaœ

;’_ OXACE›kfEGFWO.[d”IOfACEqacdq$EYkGl–E–K`bhbhK[\_ChbT Z[>_aFe`pVE2k.ZY[\hp FeOXcdkfO#[\k#Z[\_!a`bZO.D#`FfFfE2F2œ @AC`F#ZtAC[\`ZE`bF

D#[dOX`|‹c‹OXE2p g'T™OXACEž”·c>ZÇO‚OfAacdO#FfTUD.D#EYOfkX`bZžEY_aZYkfTUqVOX`[>_ cdhbƒ\[>kf`OfACDF‚cdkXEpVEGFe`bƒ\_CEGp—Of[™c\ZtAC`bEY|>Ežc;kXEYhc‹OX`|>E

AC`bƒ\A+Ffq$EYE2pœn@ACEYkXE”•[>kfE>7c\hh[\q$EYktc‹OX`[>_aFKD^]7FWOMg7E‚`D#qChbEYD#EY_'OXE2pŸgUT›h[U[> ']aq›OXcdgahEGF6–KAC['FeEsOX[dOtcdhFe`bšYE^pC[

_C[\O6E¡CZE2E2pžOfACEZ2c\ZtACEZYc\qac\ZY`“OWT>œ

+6_7pVEYkKOXACEsqCkXEY|U`b[\]aFKc>FfFf]CD#qVOf`b[\_~UOfACEg$EYA7c&|'`b[\]ak[\”OXACE^Z2c\ZtACED#EYD#[\kXTžpV]akf`b_Cƒ†cd_EY_7ZkXT'qCOf`b[\_ #•[>k

pVEGZkXT'qCOf`b[\_ %pVE2q7E2_apCF,g$[dOXA[\_.OfAaE6ZYc\ZtAaEK`_C`Of`cdh7FWOtc‹OfE6c\_ap.[\_.OfAaEnFeEGi']CEY_aZYE[d”9D.E2D#[\kXT‚c\Z2ZEGFfFfE2F–KAC`ZtA

cdkXEq7E2ke”•[>kfD#EGpœ,@ACEc\FXFe]aD.qCOf`b[\_aFDc\pCEMgUTOXACEc‹OfOXc>Zt \EYk[>_OXACEZYc>ZtACEM`_C`Of`cdhFWOtc‹OfEsDc&T†Aa`ƒ>AChTž|&c\kfT

c\Z2Z[>kXpV`b_CƒžOf[OfACE.OtcdkXƒ\EOXE2p!ZkXT'qCOf[\ƒ>kXc\qCAC`Z^pVE2|U`bZYE\œ.PV`_aZYE.OfACE2T+FWOXkf[>_Cƒ\hbTŸZ[>_apV`Of`b[\_!OfACE#qCktc\ZOf`ZYcdga`hb`“OWT

[d”OfACEcdOeOtc\Zt 9U–oEsZtAC[U[>FfE6OX[Zhc\FXFe`”•TžZYc>ZtACEc‹OeOtc\Zt VFc\Z2Z[\ktpV`b_CƒOX[.OfACEsZ[>kfkXE2Ffq$[\_apV`b_Cƒ.kfEGi']C`kXEYD#E2_>OtFŽ[>_

OfAaEs`_C`Of`cdhFWOtc‹OfE[\”OXACEZYc>ZtACEM

C 1 MOfACEGFeE†cdOeOXc>Zt VFIkXE2i']C`bkXE‚OXAac‹O_a[OtcdgChbE#`_U|>[\hb|\E2p+`_™OXACEEY_V‘

ZkXT'qCOf`b[\_;cdhbƒ\[>kf`OfAaD g$E.ZY[\_'OXc\`_aE2p›`b_;OfAaE.Z2c\ZtACEg$E”•[>kfE.cd_UT[\gaFfEYkX|‹c‹Of`b[\_~œI@AC`FIZYhbc>FfFn[d”ŽcdOeOXc>Zt VF

`bFDcd`b_ChbT†gac>FeEGpž[>_OXACEs[\g7FeE2kf|‹c‹OX`[>_ž[\”Z[>hbpFeOXcdkfOKD#`bFXFeEGFYœ

(9)

C= C* M`_!OfAaE2FfE.cdOeOXc>Zt VFnOXACEc\pV|>EYktFfc\kfTD^]7FWOsg$E#c\gChbE^OX[

OfkX`ƒ>ƒ\EYkMOXACE†ZYc>ZtACE#`_'Of[Ÿc U_C[‹–K_—FWOtc‹OfEg$E”•[>kfE.OXACEEY_aZYkfTUqVOX`[>_œ†@AC`FsD#E2c\_aFMOfAacdOsOfACE†cdOeOtc\Zt \E2k

–K`hbhƒ\E2_CEYktc‹OXEc#ZtAC['FeE2_ž_U]CD‚g7E2k6[d”Z[\hpFWOtcdkfOD#`FfFfE2F2œ

*$C> B B* MOfAaE†ZYc\ZtAaE.c\hkXE2c>pVTŸAC[\hpCFsc\hhOXACE.OXcdgahEGF`_V‘

|\[\hb|\EGp†`b_OfACEsE2_aZkXTUqVOf`b[\_cdhbƒ\[\kX`OfACD›œ

¤6[‹– OXACEYkXEsOfAakfE2EAUT'q$[dOXACE2Ff`F6kXE2cdhb`FWOX`bZ2cdhbhTcdqCqChbTOf[pC`9EYkXEY_'O6OWTUq$E2FI[d”lZkXTUqVOf[>ƒ\ktcdqCAC`ZspVE2|'`ZEGF6–K`bhh

g$EpV`bFXZ]7FfFfE2p`_OXACEs_CE¡UOnFfE2ZOf`b[\_aF2œ

,C[>k‚cŸƒ>`|>EY_˜`b_C`Of`cdhFWOtc‹OfE>OfACEFeEGi>]aEY_aZYE†[d”6D#EYD#[>kfT™c\ZYZYE2FXFeEGFsq$EYkf”•[\kXD.EGp pV]CkX`b_CƒŸOfAaEžEY_7ZkXT'qCOf`b[\_

ZYc\_g$Es[\g7FeE2kf|>E2pgUTOX`D#`b_Cƒ†cd_ac\hTVFf`bF[>kgUT†q$[‹–EYk6cd_7cdhbTUFf`Fc>FFe]Cƒ>ƒ\EGFWOXE2p†`b_

(

y>y)­œl@ACEq7[‹–EYkKcd_7cdhbTUFf`F

cdhbhb[‹–6FsOfAaEc‹OfOXc>Zt \EYkOf[+[>gaFfEYkX|\E#OfAaEžEY_7ZkXT'qCOf`b[\_ c\Z2ZEGFfF^g'T˜c>ZYZEGFfF–KACEYkXE2c>F^cŸOX`D#`b_Cƒ!cdOeOtc\Zt ™ƒ\`b|\E2F^c

ƒ\hb[\g7cdhD#E2c\Ff]CkXE^[\”ŽOfAaE.E2|\E2_>OtFIOfAacdO[VZ2Z]CkspV]CkX`b_CƒžOXACE#EY_aZYkfTUqVOX`[>_œ‚zIFscžkXE2Ff]ChO2~cq$[‹–oE2kc\_acdhbTVFe`FI[d”

OfAaEZYc\ZtAaEMD#E2D.[>kfT–K`bhbh[\gU|U`[>]aFfhTƒ>`|>EMD#[>kfEM`_C”•[\kXD#cdOf`b[\_OfAac\_Of`bD.`b_Cƒ7œ

z6_a[dOfAaEYkIZYhbc>FfFn[d”lc‹OfOXc>Zt UFnAac\Fng7E2EY_;qakf[>q7['FeEGpgUT;JMFe|U`b  CGD`_

(

y*)4œn¤nEYkXE\7OfACE.c‹OfOXc\Zt >EYk6`Fnc\gChbE

Of[pV`bkfEGZÇOfhbTŸ[\g7FeE2kf|>EsOfACE#Z[>_'OfEY_'OM[d”,OfAaE.Z2c\ZtACE‚–K`“OXA!cžFf[d”³OW–cdkXEqCkX[\g$E\œ ;’_;qakXc>ZÇOf`ZE>$OfAC`FM`_V”•[>kfDcdOf`b[\_

`F6Dcd`b_ChbTž[\gCOXcd`b_CEGpgUT]aFf`_Cƒ`b_'OfE2kXc>ZÇOf`b[\_7Fg7EYOW–oE2EY_›OW–[†pCc‹Otc.OXcdgahEGFOfAacdOIFfAacdkXEOfACE‚Ffc\D.EZ2c\ZtACEM,OfAaE

(aktFWOc\kfktc&T –K`bhh,g$E.OfACEhb[U[\ U]Cq;OtcdgChbE#`_U|>[\hb|\E2p+`_!OfAaE.E2_aZkXTUqVOf`b[\_—cdhbƒ\[>kf`OfAaD OfACEFfE2Z[>_ap+c\kfktc&T

`F6Z[>_>OXkf[>hhbE2pžgUT†OfAaEc‹OeOtc\Zt >EYkGœOJI]CkX`_Cƒ#OXACEsEY_7ZkXT'qCOf`b[\_OfACEcdOeOXc>Zt \E2kq$EYkf”•[\kXDFKcFeEGi']CEY_aZYE[d”,c\ZYZYE2FXFeEGF

Of[ Ÿœ@ACEGFeEc>ZYZEGFfFfE2FIDc&T+Ff]$E2k”•kf[>D Z[>_a`ZÇOsD#`bFXFfE2FpV]CE#OX[OtcdgChbE.œ@ACEYkXE”•[>kfE>g'T+q7E2ke”•[>kfD#`b_Cƒ

ZtAC['FeE2_#c>ZYZYE2FXFeEGFOf[;\OXACEnc‹OfOXc>Zt \EYk,`FŽc\gChbEKOf[ƒ>EY_CE2kXcdOfE6Ff[\D#EnZY[\_a`ZÇOoD.`FXFeEGF,–KAC`ZtA†cdkXEKkfE2hbcdOfE2p.OX[sOfAaE

FfE2ZkXEO, >EYT\œ@AC`F, U`_7p‚[\”9cdOeOtc\Zt VFZYcd_#[>_ChT^g7E6D#[>]C_'OfE2p‚[\_#D‚]Ch“OX`“‘4OfAakfEGc\pVEGp^qCkX[VZEGFfFf[\ktF

(

}\€1)7Ff]aZtA.c>FOfAaE

jEY_'Of`b]CD Hž¤I@œ@~[žZ2cdkXkfT›Ff]aZtA;cd_+cdOeOtc\Zt OfACE#c‹OfOXc\Zt >EYk6D‚]aFeOIg$E.c\gChEOf[žkXE2c>pŸcd_apŸOfkX`ƒ>ƒ\EYknOfACE.ZYc>ZtACE

EY`OfAaEYkng$[dOXAŸg7EY”•[\kXEcd_apŸcd”³OfE2kKOfACE^EY_aZYkfTUqVOX`[>_[>knpV]CkX`b_Cƒ#OfACE^EY_aZYkfTUqVOX`[>_œ-;’_›OXAC`FnFfEY_aFfE\VOXACEqCktc\ZOf`ZYc\h

cdqaqCh`ZYc\gC`bh`OWT†[d”OfACEGFeEcdOeOtc\Zt VF`bF6Ff`bD.`bhcdkOf[.OXACEs[\_CE[\””•[>kfƒ>E2pžFeOXcdOfEcdOeOXc>Zt VFYœ

!"$#&%'(*) +,).-/01243/+

@ACEZY[\D#qChbE¡V`“OWTž[d”kfEGFeEYOeOf`b_CƒcZYc>ZtACEMD.E2D#[\kXT?#•`4œE>œ7[d”,c#ZYc\ZtAaE 7]aFeA%pVEYq$EY_apaF6[\_OfAaEOXcdkXƒ\EYO6pVEY|U`ZE\œ

¢T^_acdOf]CkXE\'ZYc>ZtACEKD#EYD#[\kXT^`F,|\[>hbcdOf`bhE>œzIFlcZY[\_aFfE2i']CE2_aZE>\Fe`bD#qChbT‚kXEYD#[‹|U`_aƒIOXACE6|>[\hOXcdƒ>EFf]CqCqahT.[d”9OfAaE

pVE2|'`ZEn–K`hbh$ZYhEGcdkŽOfACEMZYc\ZtAaE\œ@AC`bFo`Fl[\_ahTc 9[\ktpCc\gChEK[>_EYD‚g7EGpCpVE2pžFeTVFeOfEYDF2\”•[>kŽ`b_aFeOXcd_7ZEn[>_#OfACEID#[>FeO

kXE2ZE2_'OIOWTUq$E2F[d”FeDc\keOsZYc\kXp+qCkf[VZYE2FXFe[>kXF

(

V,y

)l[>k[\_/JI`bƒ\`OXcdhŽPV`ƒ>_acdh,jlkX[VZEGFfFf[\ktFYœ#JI_+D#[\kXEZ[\D#qChbE¡

FfTUFeOfE2DF^hb` >EZY[\D#qC]VOXEYktFYOXACEŸc‹OeOtc\Zt >EYk_CE2E2pCF#c+]aFeE2k.c>ZYZY[\]C_'O‚[>_˜OfAaEžOtcdkXƒ\EOXE2p˜Aa[>FeO2œ˜zKZÇOX]acdhbhT>,OfAaE

ZYc>ZtACE`bFkXE2FfEOKgUTOXkf`bƒ\ƒ>EYkX`_Cƒ#cdhbhZYc>ZtACEgChb[UZt VF–K`OfA›Dcd_UT†D#EYD#[>kfT†c>ZYZEGFfFfE2Fg$E”•[>kfEc\_'T[>gaFfEYkX|&cdOf`b[\_œ

;’_›OfAa`bFIqacdkfOf`Z]ahbc\knZ[>_>OXE¡UO29c†Z2c\ZtACED#`FfFn[VZYZ]akXFn–KACEY_›OXACE‚c>ZYZEGFfFfE2p›E2hE2D#EY_'OIpV[UE2FI_C[\Ong7E2h[>_CƒOX[

c.gChb[UZt ž–KAC`bZtAŸc\hkXE2c>pVTh`bE2F`b_OfACEZ2c\ZtACE>œlPU`_7ZEc#ZYc>ZtACEgCh[VZt žZY[\_aFf`FWOtF[d”,c.FfEO6[\”E2hE2D.E2_'OXFK–K`OfAOfAaE

FXcdD#E"!$#&%')(6 .5

.12

:7,nD#['FWOŽFf`ƒ>_C`(7ZYc\_>O,gC`OXF2UcsZYc\ZtAaEKAC`“OZ[\kXkXE2Ffq7[>_apCFOf[^csZY[\hbh`Ff`[>_.[>_.OfACE !#% ' (6 .65

. 2 :-,6D#[>FeO

Ff`ƒ>_C`($ZYcd_'OMgC`“OtFM[d”,OfAaE‚`b_CqC]VOtFM[d”lOXACE^OtcdgChbE\œ ;’_ŸOXAC`FMFfEY_7FeE>9c\_!cdOeOXc>Zt FeOXc\keOX`_aƒ†”•kX[\D cd_;E2D#qVOWT;ZYc>ZtACE

ZYc\_—g7E†FfEYE2_—c>FscqacdkfOf`cdhlZY[\hbh`Fe`b[\_—c‹OfOXc>Zt 

(

}Cyd}\1)Ž[>_+OXACEžc\papVkfEGFfFf`b_Cƒž”•]a_aZÇOX`[>_™[\”cŸZ2c\ZtACE#D#EYD#[>kfT>œ

,C[>kn`b_aFeOXcd_7ZE\7[\_ŸjEY_'OX`]CD aCOfAaE^Fe`bšYE^[d”*ly^pac‹OXcžZYc\ZtAaEsgCh[VZt `bF 798 86aOfAU]aF2 Žy^ZYc>ZtACEsD#`bFXFeEGFK”•[>k

OfAaEz6¥oPhb['[> U]CqOXcdgahEGF`_U|\[>h|>EnOXACE^w‚D#[>FeOKFf`bƒ\_C`(7ZYc\_'Oga`“OtFK[d”E2c\ZtA \E2T†gUT'OfE\œ

@ACE (aktFeOqakXc>ZÇOf`ZYc\h`D#qChbEYD#E2_>Otc‹OX`[>_aFK[d”,Ff]aZtAŸc‹OeOtc\Zt VFAac&|\Eg$EYE2_;pVE2FXZkX`g$E2pcdƒ'cd`b_aFeOKL$;ePV@Q‚yc\_ap

JI¥oP˜gUT™jc\ƒ\E (y2x)c\_ap˜@Ff]C_C[U[ CGD (}>w*)4œ?;’_ (}>w*)K@Ff]C_C[U[ CGDq$[\`b_'O^[\]CO^OfA7c‹O.c;qacd`bk^[\”qahbc\`_V‘

OfEY¡UO ‹ZY`qaACEYkfOfEY¡'O†–KAa`bZtA hbE2c>pCF#Of[ c—AC`ƒ>A D#`bFXFktc‹Of`b[ #•`4œE\œbOf[ c˜hb[\_Cƒ˜E2_aZkXTUqVOf`b[\_£OX`D#E*%qCkf[‹|U`pVE2Fc\_

`bD.qakf[>gacdgChbEs|‹cdhb]CE”•[>kKOfAaE‚pV`$E2kfE2_aZE^g7EYOW–oE2EY_;Ff[\D#EgC`OXFn[d”,OfAaE (aktFWOIc\_apOfAaE^hc\FeOnkf[>]C_ap› >EYTVFYœKz6”³OfEYk

FfEY|\E2kXc\hŽ[>gaFeE2kf|‹cdOf`b[\_aF^OfACE›Z[>kfkXE2ZO‚qac\keOX`bc\hpC`9EYkXEY_aZYEZ2cd_ OfACE2_ g$E›pCE2pV]aZYE2p ”•kf[>D OfACE›hbE2c\FeO^”•kXE2i']CE2_'O

|‹cdhb]CE\œ@AC`F–[\kX ;cdhFe[›`bhhb]aFeOfktc‹OfEGFIOfACE`bD#qac\ZO[d”pac‹OXcDcdqaqC`_aƒ`b_'Of[OfAaE†ZYc\ZtAaE\œ Jn¥oP˜PVg7[&¡VE2FMAac&|>E

€H.`b_CqC]VOtF[d”ŽygUT'OfE\UgC]CO6g7EYOeOfE2kKq7E2ke”•[>kfDc\_aZEMZYcd_g7Esc>ZtAC`E2|\EGp†–KACE2_žE2c>ZtAžE2_>OXkfT`FKcdhb`bƒ\_CEGp†[\_Hd‘­gUT>OXE

g$[\]C_apacdkX`EGFYœ>+6_C”•[\kfOf]C_acdOfE2hT>>OXAC`FKpVE2ZYkfEGc\FfE2FŽOfACE_U]CD^g$EYk[\”PUg$[&¡†`_aqC]VOXFq$EYk6Z2c\ZtACEIgChb[UZt 9Vcd_7pž`O6Z[\_C‘

Ff`bpVE2kXc\gChbTžc 9E2ZOXFOXACE^ZkXTUqVOXc\_acdhbTVFe`Fc\FKq$[\`b_'OfEGp[>]VO6gUT

(

}H)­œo@Aa`bF6cdOeOtc\Zt c\hbFf[Fe]7ZYZEGFfFe”•]ChbhTcdqCqChb`bE2FOX[

L3;ePV@Q.ycd_apžOf[.OXACEz6¥oPœ

z6_a[dOfAaEYkžkXE2FfEO›ZYc>ZtACE+c‹OfOXc>Zt £pVEGpV`ZYc‹OXE2p OX[ E2D^g$E2pCpVEGp pVE2|'`ZEGF†Aac>Fžg$EYE2_ kXE2ZE2_'OfhbT£qakf[>q7['FeEGp gUT

~c\]Cktc\pV[>]V¡£`b_

(

y0H)4œ ;­O]aFfE2Fq$[‹–oE2kc\_acdhbTVFe`FžOf[£kfEGZ[‹|\E2k†hb`_CEGcdk›kXEYhc‹Of`b[\_7Fž[>_ OfACE—D#[>FeOŸFe`bƒ\_C`(7Z2cd_'O

gC`OXF[d”^c\hhMgUT>OXE2Fž[d”sOfAaE™zn¥oP FfE2ZYkfEYOž \E2T\œ @ACE™c‹OfOXc\Zt £–c\FžpCEYD#[\_aFeOfktc‹OXE2p c\ƒ>cd`b_aFeOpV`$E2kfE2_'Oz6¥P

(10)

`bD.qahE2D.E2_'OXc‹OX`[>_aFcd_7p `FFe`bD#`hcdk.Of[™OXACEOf`bD.`b_Cƒ˜c‹OfOXc>Zt ˜[d”

(

}H)4œ ;­OE¡VqChb[\`OXF.OfAaE”·c>ZÇO#OfA7c‹O#OfACE (aktFeO

`b_CqC]VOtFŽ[\”$OXACEMPVg7[&¡#h[U[> ']aq‚OtcdgChbE2FŽ`_z6¥oPc\kfEnƒ\`b|\EY_#gUT‚OfACEn¡U[>klg$EOW–EYEY_#OXACEnqahbc\`_'OfEY¡UOocd_ap.OXACEIFfE2ZYkfEYO

 \E2T\œ

!"$#&%'(*) ! "/!! ! + 2 3$+

;’_‚OfAC`FlZhc\FXF[d”9c‹OeOtc\Zt VF2&OfACE6c>pV|\E2kXFXcdkXTID‚]aFeOlg7EKcdgahEOf[`b_C`Of`cdhb`š2EFf[\D#EKZtAC['FeE2_‚ZYc>ZtACEgChb[UZt VF–K`OfApCc‹Otc

”•kX[\D OXACEhb[U[\ U]CqOXcdgahEGFYœ@AC`bFIZYc\_g$E^pV[>_CEsgUT a]aFfAC`b_Cƒ#OfAaE^ZYc>ZtACEsD#EYD#[\kXTžcd_7pžOXACEY_ŸgUTq7E2ke”•[>kfD#`b_Cƒ

”·cd >E›EY_aZYkfTUqVOX`[>_aF.–K`“OXA c™ U_C[‹–K_  \EYT `_£[\ktpVEYk.OX[™hb[>c>p ZYEYkfOXc\`_ OXc\gChE›gChb[VZt VF‚`b_'Of[™OfAaE;ZYc\ZtAaE\œ @AC`bF

kXE2i']C`bkfE2D.E2_'O‚hb`D#`OXF.OfAaE›FXZ[>q7E[d”nOfACEŸc‹OfOXc>Zt —Of[™D^]ChOf`‘4]7FeE2kXF#FfTUFeOfE2DF‚Ff`_7ZEŸcd_£c\ZYZYE2FXFOX[+OXACEŸZYc>ZtACE

D#EYD#[\kXTŸ`F_CEYEGpVE2pœ K `“OXA˜FeE2|\EYktcdhZtAC['FeE2_+`b_C`“OX`bc\h`bš2cdOf`b[\_aFc\_ap+Ff[\D#E#q7[‹–EYkIOfktc\ZYE2F2¢EYkfOf[\_a`' CGD

(

}1)

FfAC[‹– AC[‹– Of[#kXE2Z[‹|>EYkoOfACEsD#['FWO6Ff`ƒ>_C`($ZYcd_'OKgC`OXFK[\”EGc\ZtA \EYTžg'T'OXEs`_›z6¥oPœ

@AC`FZhc\FXFŽ[\”c‹OfOXc\Zt VFo`bFFf`D#`bhbc\kOf[‚OfACEc‹OfOXc\Zt VFŽOfAacdO6FWOtcdkfOo”•kX[\D cd_EYD#qVOWTžZ2c\ZtACEI`_OfAaEMFfEY_aFfEIOfAacdO

cdkXEžg7c\FfE2p˜[>_˜OfACE›cd_7cdhbTUFf`F[d”MZYc\ZtAaE†D#`bFXFeEGFYœ—@ACE[\_ChbT˜pV`$E2kfE2_aZE`bF^OfA7c‹O.OfACE2T˜]aFeEZ[>_a`ZÇO#D.`FXFeEGF

`b_aFWOXE2c>p[d”~ZY[\hp†FWOtcdkfOŽD#`bFXFfE2FŽOf[^ƒ'cd`b_†Fe[>D#E6`_C”•[\kXD#cdOf`b[\_†[>_OfAaEnD#[>FeOFf`ƒ>_C`(7ZYc\_>OogC`“OtF[d”OfAaEn \E2T‚gUT'OfEGFYœ

!"$#&%'(*) ( $+ 243/+

¢[dOXA†qCkXEY|U`[>]aFZhc\FXFeEGFl[d”c‹OeOtc\Zt VFZYcd_žg7EIOfAU–cdkfOfE2p†g'TFfTVFWOXEYDc‹OX`bZ2cdhbhT#hb[>c\pC`_CƒOfACEM–KAC[\hbEIOXcdgahEIg7EY”•[\kXE

cd_UT—EY_7ZkXT'qCOf`b[\_Žc>F^qakf[>q7['FeEGp˜`_

(

}CyH)­œ @AC`F.Ff`bD.qahE›Z[>]C_'OfEYkXD#E2c>Fe]CkXEžc&|>[\`pCFD#[>FeOZYc\ZtAaEžD#`bFXFfE2F2œ

¤6[‹–EY|>EYkG~OXAC`F.pC['EGF^_a[dO#`D#qChbT™OfAacdO#c\hhoOf`bD#`_Cƒ™|‹cdkX`bcdOf`b[\_aF^Aac&|\Ežg7E2EY_ kXEYD#[‹|>E2p,c\F^q7[>`_'OXE2p [>]VO‚gUT

¢EYkX_aFeOfEY`b_

(

yB)­œ ,C[>k`b_aFeOXcd_7ZE\ ,`ƒ>]CkfE@ FfAC[‹–6FžOfAacdOOX`D#`b_Cƒ |‹c\kf`c‹OX`[>_aFžFeOf`bhhsEY¡V`bFeOž”•[>kOXACE™[\kX`ƒ>`_ac\h

`bD.qahE2D.E2_'OXc‹OX`[>_ [\”Mz6¥P gUT ¢[>FXFeE2hbc\EYktFY,rK`mWD#EY_ cd_7p ¢cdkXkfEYOf[ ( )­Ž[>_ c!jEY_'Of`b]CD !–K`“OXA£c!hb[>c\pCE2p

ZYc>ZtACE`_a`“OX`bc\hFWOtc‹OfE>œ

0 500 1000 1500 2000 2500 3000

500 550 600 650 700 750 800 850

Plaintext number

Execution time (cycles)

,`ƒ>]CkXE M JI`FWOXkf`bgC]VOX`[>_£[\”nOX`D#`b_Cƒ™”•[\k#OfAaE[>kf`bƒ\`b_ac\hzn¥oP `D#qChbEYD#E2_>Otc‹OX`[>_ [>_£c™jEY_'Of`b]CD +”•[>k 8 (

qChcd`b_'OfE¡UOtF5#³OfAaEsq7EGcd ž[\”~OXACEpV`FWOXkf`bgC]VOX`[>_`FACE2kfEMOfkX]C_aZ2c‹OXE2pgC]VOnc\hD#[>FeOKkfEGc\ZtACEGF'8%

@ACEGFeEOX`D#`b_Cƒn|‹cdkX`c‹Of`b[\_7FDc&Tng$EopV]CElOf[6OXACE,”·c>ZÇO~OXAac‹O~OfACEZYc\ZtAaE,D.E2D#[\kXTn[\_Ff]Cq$EYktFfZ2cdhcdkqakf[VZEGFfFf[\ktF

`F^pVEGFe`bƒ\_CEGp!”•[\kAac\_apVhb`_aƒ;D#[\kXE#OfAacdO^[\_CE†c>ZYZYE2FXFsq7E2k‚ZYTUZYhE>œznD#[\_Cƒ;c\hhFe[>h]VOX`[>_aFs–KAC`ZtA˜`bD.qahE2D.E2_'O

OfAa`bF^”•E2cdOf]CkXE

(

}'} 1)­OfACE[\_CE†]7FeEGp—`_Mx\€›qCkX[VZEGFfFf[\ktFsZ[>_aFe`FeOXF`b_ FfqCh`OeOX`_aƒ;OfAaEžZYc>ZtACE†`b_>OX[+FfEY|\E2kXc\h

`b_apVEYq$EY_7pVEY_'OfhbT c>pCpVkXE2FXFeEGp gac\_C VFYœ @ACE2kfEY”•[\kXE\ŽD#E2D.[>kfT c>ZYZYE2FXFeEGF.Z2cd_ Fe]!$E2k#”•kf[>D Z[>_a`ZÇOq7E2_acdhOf`bE2F

–KACE2_ FeE2|\EYktcdhlFf`bD^]ChOXc\_CEY[>]aFsZ[>_aZ]CkXkXEY_'OkfEY”•EYkXEY_aZYE2FMOX[ŸOfACEFfc\D.Eg7cd_C ![UZ2Z]CkGœŸPU]aZtA—q7E2_acdhOf`bE2F‚c 9E2ZO

cd_7pc\kfEc 9E2ZOfE2pgUTOfAaEs–KAC[\hbED.`ZkX[d‘’cdktZtAC`OfEGZÇOf]akfE6[\”~OXACEsqCkX[UZYE2FXFe[>k #·`МE\œbCgUT†qC`bq$EYhb`_CE>aZ[>_a`ZÇOKgac\_C VF

pVEYOfE2ZOf`b[\_›hb[\ƒ\`ZdUhb[>c>p‹FeOf[>kfEi']CEY]CE>œYœ2œ%ǜ

(11)

;’_†Ff[\D#EnZYc>FeEGFY\OfACEI[\gaFfEYkX|\EGpOX`D#`b_Cƒ^|‹c\kf`c‹OX`[>_aF,Dc&T‚c\hbFf[g$EnpV]CEnOf[sOXACEnEY¡U`FeOfEY_7ZE6[\”Ff[\D#EnZY[\_7`bZO

D#`bFXFfE2F0MoE2|\EY_Ÿ`”,OfAaEOf[\OXc\hFf`š2E[d”,OXACE^hb[U[\ U]Cq›OXc\gChbE2FnpC['EGF6_C[\OnE¡CZYEYE2pOXACE‚Ff`bšYE[\”,OfACEly^Z2c\ZtACE>7Ff[\D#E

EYhbEYD#E2_>OtF†`b_ OfAaE;OXc\gChbE2F†Dc&T£g7E!EY|U`ZÇOfEGp ”•kX[\D OfACE™ZYc\ZtAaE;pV]CkX`_Cƒ OfACE!E¡VE2ZY]VOf`b[\_ `”OfAaEYT£h`bE+`b_ OfAaE

qac\keOX`bZY]Chbc\knFfEOIZtAC['FeE2_ŸgUT†OfAaE^kXEYqChc\ZYEYD#EY_'OIc\hƒ>[\kX`“OXACD›œPU]7ZtA+Z[>_a`ZÇOnD#`FfFfE2FKDc&Tq7[\OfE2_>OX`bc\hhbT›cdqCq$E2c\k

c\F‚Fe[U[>_ c\FsOXACE†OX[dOtcdhoFf`bšYEž[\”OfACEžOXcdgahEGFE¡CZYEYE2paFsOfAaEFfEO.Ff`bšYE\gC]CO^OfAaEYT—]aFf]acdhbhT™[VZYZY]Ck^–K`OfA c+_C[\_C‘

_CE2ƒ\hb`ƒ>`gChbE6qCkX[\g7cdgC`bh`OWT”•kX[\D Aac\h“”[\”OfACEMZYc\ZtAaE6Fe`bšYE>'c>Fl–E6–K`hbh9FeE2E6`_PUE2ZOf`b[\_wCœ@ACEIE¡V`FWOXEY_aZYE6[d”Ff]aZtA

Z[>_a`ZÇOMD.`FXFeEGF6OXACEY_+pCEYq$EY_apCFM[>_ŸOfACE.Fe`bšYE‚[d”,OXACE.Z2c\ZtACE>7ga]VOMc\hbFf[†[\_;OfACE#ZYc>ZtACE^c\FXFf[UZY`bcdOf`b|U`“OWTcd_apŸ[>_

OfAaEskfE2qChbc>ZE2D.E2_'OKc\hƒ>[\kX`“OXACD›œ

+,).(+ !) ! "$# 4

z6_£`b_>OXEYkXE2FeOf`b_Cƒ™E¡UOfE2_aFe`b[\_ [d”6OX`D#`b_Cƒ˜c‹OfOXc\Zt VF‚`bF.OXACEŸZhc\FXF^[\”IkXEYD#[dOXEžOX`D#`b_Cƒ˜c‹OfOXc\Zt VF2œ PU`b_aZEOf`bD#`_aƒ

c‹OfOXc>Zt UFc\qCqChbT›Of[›–oEGcd Ÿ`bD#qChE2D#EY_'OXcdOf`b[\_aF[\”cZkXT'qCOf[\ƒ>kXc\qCAC`Z^c\hƒ>[\kX`“OXACD›`“Os`Fq7['FfFf`gahE.Of[Ofktcd_7Feq$[>FfE

OfAaEYD OX[kXEYD#[\OfE#pVEY|U`ZE2F2œ^@ACEc>FfFf]CD#qVOf`b[\_7FIkXE2i']CEGFWOXE2p;Of[›D#[\]C_'OscžkXEYD#[dOXE^OX`D#`b_CƒŸc‹OfOXc\Zt ;c\kfE#Z[>D.‘

qChbEOXEYhbT!pV`$E2kfE2_'OspCEYq$EY_apV`b_CƒŸ[>_™–KAaEOfAaEYks–E#ZY[\_aFf`pVEYksqC]agCh`Z#[\ksFfE2ZYkfEYOe‘­ \EYT;c\hƒ>[\kX`“OXACDFYœ;’_™OfACE†Z2c\FfE

[d”qC]Cgah`ZǑ­ \E2T+ZkXTUqVOf[>ƒ\ktcdqCAUT\c>FfFf]CD#qVOX`[>_aFscdkXE#kfEGcdhbhT;–E2c\ 9œ#@AaE†c‹OeOtc\Zt U`b_Cƒ›D#c>ZtAC`b_CE3#•¥l|>E*%sFfEY_apaFsc

kXE2i']CE2FeOOX[ŸOfACEžOXc\kfƒ>EOfEGp˜FeE2kf|>EYkF#Ðz6hb`bZYE*%]aFe`b_Cƒ™z6hb`bZYE-FqC]Cgah`Z† >EYT #,`ƒ>]CkXEFH %œ;@ACEY_~,g'T™D#E2c>Fe]CkX`b_Cƒ

OfAaEOf`bD#EOf[ŸkXE2Ffq7[>_ap #·@K@Kr %~¥l|>EOfkX`bE2FOX[;pVE2pV]7ZEžznh`ZE1Fsqakf`b|‹c‹OfEž \EYT>œ@AC`FcdOeOXc>Zt +Aac>Fg7E2EY_ (aktFeO

E¡VqChb[\kXE2pgUTž¢kf]aD.hbEYTcd_ap¢[\_CE2Ac\ƒ>cd`b_aFeO6rnPVz

(

w*)4œ

TTR

Alice Network Eve

,`bƒ\]CkXE HM,rKE2D.[\OfEcdOeOXc>Zt †cdƒ'cd`b_aFWOKqC]agCh`Z \E2Tžcdhbƒ\[>kf`OfAaD#F

JI_ OXACEŸZ[>_>OXkXc\kfT>,FeEGZkXEOe‘­ \E2T˜cdhbƒ\[\kX`OfACDF.ZYcd_a_C[dO#g7EŸcdOeOXc>Zt \EGp˜`_ Ff]aZtA c!–c&T>œ ;’_apVE2E2pŽOfACE2kfE`bF

_C[qacdkfOf`Z]ahbc\knkXE2c\Ff[\_;Of[žAa[\q$E^OXAac‹OFf[\D#E‚pCcdOXcžEY_aZYkfTUqVOXE2p;–K`OfA+OfACEFfE2ZYkfEYOI \E2T c\kfE‚|\[\hb]C_'OXc\kf`bhbT

FfEY_'OgUT+z6hb`bZYE#Of[›¥l|>E†Fe`b_aZE¥Ž|\EpV[UE2Fs_a[dOs U_C[‹– OXACE†FeEGZkXEOs \E2T œ†@AaEYkXE”•[\kXE\Fe]aZtA—Z`bqCACE2keOXE¡UOXF

cdkXEc&|‹cd`bhbc\gChbEIOX[OfAaE^c‹OfOXc\Zt >EYk[\_ahT`“”OXACEYT›cdkXEsE2c&|>E2FXpVkf[>qCq$E2p†`b_›OfAaE^Z[>_>OXE¡UO6[d”lc#Dcd_C‘4`b_V‘4OfACEY‘4D#`pCpVhbE

c‹OfOXc>Zt  #,`bƒ\]akfEw%ǜ@,C[\k‚`_7FWOtcd_aZYE\¥l|\EZYc\_˜qCkf[>g7Ec;kX[\]VOX`_Cƒ+EYhbEYD#EY_'O‚[\”6c+Z[>D#D^]C_C`ZYcdOf`b[\_ ZtAac\_C_CE2h

g$EOW–EYEY_™z6hb`bZYEcd_ap!¢o[>gœ‚PUAaE.–K`bhbhD#[>_C`“OX[\kMOfAaE‚OXkXcI†Z^[>_;OfAa`bFZ[>D#D^]C_C`ZYcdOf`b[\_™ZtAacd_C_aEYhOf[D#E2c\Ff]CkXE

OfAaEskfEGFeq$[\_aFfEIOf`bD.Es[\”g$[dOXA›qacdkfOf`bE2F2œ

TTR

Alice Network Eve Bob

TTR

,`ƒ>]CkfEsw Mlr6EYD#[dOXEcdOeOtc\Zt žc\ƒ>cd`b_aFeOFfE2ZYkfEYOK \EYTcdhbƒ\[\kX`OfACDF

@ACE‚D.['FWOpV`GIZY]ChOIOtc\Ff `b_!c\hhkfE2D.[\OfE^Of`bD.`b_Cƒc‹OeOtc\Zt VF6`FnOf[žE2|‹cdhb]ac‹OXEOfAaE^EY_7ZkXT'qCOf`b[\_ŸOX`D#E.[d”,OfAaE

OXc\kfƒ>EO*MOfACEc‹OfOXc>Zt \EYkAac>FOX[IOtcd >EŽ`b_>OX[Mc>ZYZY[\]C_'O~OXACEOfktcd_aFfD#`bFXFf`[>_sOf`bD#Eo”•kX[\D OXACEoOXcdkXƒ\EYOOX[nOXACEc‹OeOtc\Zt U`b_Cƒ

Dc\ZtAC`b_CE>~gC]VOsOXACE†_C[>`bFfEc\pCpCE2p™gUT;OfAaE#Ofktcd_aFfD#`bFXFe`b[\_—pVE2hbc&TŸOX[›OfACEE2_aZkXTUqVOf`b[\_!Of`bD#E†`FZ[>_aFe`pVE2kXc\gChE>œ

@AacdOo`FŽ–KAUT#`_žqCkXc>ZÇOX`bZYEKOfACEI[\_ChbT# U_C[‹–K_kfE2D#[dOfEnOf`bD#`_Cƒ.c‹OfOXc\Zt 

(

w1)9–c>FlD#[\]C_'OXE2p[>_†chb[UZ2cdh$_CEOW–[\kX 9œ

@ACEncdOeOtc\Zt qCkXE2FfEY_'OXE2p.gUT‚¢EYkX_aFeOfEY`b_

(

y)7gUTUqac\FXFfE2FOfAa`bFŽqCkf[>gChbEYD Ff`b_aZEK`OocdqaqCh`bE2F,Of[^cqCkX[dOX[VZ[\hV`b_–KAC`ZtA

(12)

OfAaEFeE2kf|>EYkFŽOf`bD#E2FeOXcdD#q`bFKc\hbFf[‚Ofktcd_aFfD#`“OfOfE2p›c\_apc&|‹c\`hcdgChbE6OX[.OfACEcdOeOXc>Zt \E2k2œ@AC`F”•E2c‹OX]CkXEIOXACEY_Ÿc\hhb[‹–6F

OfAaE#cdOeOtc\Zt \E2k6OX[pV`bkXE2ZÇOXhT;c>ZYZYE2FXF6OXACE#EY_aZYkfTUqVOX`[>_ŸOf`bD#E.–K`OfAa[\]VOOfAaE‚_C[>`bFfE#c\pCpVEGp;gUT›OfAaE^OXkXc\_aFeD#`FfFf`b[\_

OfAakf[>]Cƒ\AOfACEs_aEOW–[\kX $œ@AC`F6Z[>_aFf`bpVE2kXc\gChbT–oEGcd \E2_aFoOfACEsFfE2ZY]Ckf`OWT†D#[VpVEYh~[d”~OXACEOXc\kfƒ>EOGœ

;­”l–E^–cd_'OnOX[žD#[\]C_'Oc†kXEYD#[dOXE‚ZYc>ZtACEsOX`D#`b_CƒcdOeOtc\Zt 9$c\_C[dOXACEYkI`D#q$[\kfOXc\_>OpV`GIZY]ChOWTŸ`bFnOf[Z[\_'OXkf[>h

OfAaE^FWOtc‹OXEs[d”OfACE‚ZYc\ZtAaEsg7EY”•[\kXEsE2c\ZtA›E2_aZkXTUqVOf`b[\_œzukXEYD#[dOXEs`_C`Of`cdhb`bš2c‹OX`[>_›[\k6kXE2FfEO6[\”OXACE^Z2c\ZtACEs`FK_C[\O

kXE2cdhb`FWOX`bZ\œzIFKcZ[>_aFeEGi']CEY_aZYE\'OfAaEs[\_ChbT†qCktc\ZOf`ZYcdhc>FfFf]CD#qVOf`b[\_`b_OXACEZ[>_'OfE¡UOK[d”kfE2D#[dOfEscdOeOXc>Zt `bFKOfAacdO

OfAaEZYc\ZtAaEM–c\Fhb[>c>pVE2pœ

4+$!6( 60 -/(*- (* + 243$+ 4 # !" 3/+9

@ACEqCkXEY|U`b[\]aFpV`FfZY]aFXFe`b[\_q7[>`_'OtF[\]VOOfA7c‹OKOfAaEcdqCqChb`ZYcdga`hb`“OWT[\”~OXACEpV`$E2kfE2_>O”·c\D.`bhb`EGFK[d”ZYc\ZtAaEMcdOeOXc>Zt VF

AC`bƒ\AChbTpCEYq$EY_apCFn[\_OfAaEsOWTUq7E[\”OXACEsOtcdkXƒ\EOXE2ppVEY|U`ZE>œ ,a[\kKEYD‚g7EGpCpVEGpŸpVEY|U`ZE2F<#•E\œƒaœŽ”•[\k JI`bƒ\`OXcdhPU`bƒ\_ac\h

jlkX[VZE2FXFf[\ktFY9D#`bZYkf[\‘­ZY[\_'OfkX[\hbhbEYktFYœbœœ%ǝ7OfAaE.D#['FWOs_acdOf]Cktcdh,Ff`“OX]ac‹OX`[>_+`Fscd_!cdOeOtc\Zt ;FeOXcdkfOf`b_Cƒ”•kf[>D cd_!EYD#qVOWT

ZYc>ZtACE\œ ,C[>kOfAC`FOWTUq$E.[\”oOtcdkXƒ\EYOXF2q7[‹–EYkscd_7cdhbTUFf`FI`F[\gU|U`b[\]aFfhTŸqakfEY”•EYkXkfEGp;OX[OX`D#`b_Cƒ;cd_7cdhbTUFf`FMFf`b_aZE#`O

EY_7cdgChbE2FOX[[\gaFfEYkX|\EIOfACEsD#E2D.[>kfTc\ZYZYE2FXFKFeEGi']CEY_aZYEsFWOXEYq›gUTFeOfEYq~œ ,C[>kK_C[\_V‘­EYD‚g7EGpCpVEGppCEY|U`bZYE2F5#·E\œƒaœ,”•[>k

jHF%ǝaOfACEFf`“OX]ac‹OX`[>_`FK|>EYkXTžpV`$E2kfE2_>OGœ ;’_C`Of`cdhb`šGc‹OX`[>_cdOeOXc>Zt VFKcdkXEI[>g'|U`b[\]aFfhbT†D^]aZtAD#[\kXEq7[‹–EYkf”•]ChgC]VO

OfAaEMZY[\kXkfEGFeq$[\_apC`_Cƒ (7EYhp†[d”~c\qCqChb`bZ2c‹OX`[>_aFŽ`Foh`bD#`“OXE2pOX[^D‚]Ch“OX`“‘­]aFfEYkFeTVFeOfE2D#F2œ>,C[>koFf`_Cƒ>hEI]aFfEYkf‘­FfTVFWOXEYDFl[>k

`b_OXACEZ[>_'OfE¡UOK[d”kfE2D#[dOfEMOX`D#`b_Cƒ†c‹OfOXc\Zt VF2UOfACEs[>_ChbT†kfEGcdhb`bFeOf`ZIA'TUq$[dOXACE2Ff`bF`F6c.hb[>c\pCE2p`_C`Of`cdhFWOtc‹OfE>œ

@ACEOWTUqC`bZ2cdhZYc>ZtACEcdOeOXc>Zt VF‚pVE2q7E2_apV`b_Cƒ™[\_ OXACEOWT'q$E[d”6OXACEOXcdkXƒ\EYOfEGp pVEY|U`ZE›cdkXEFf]CD#DcdkX`š2E2p˜`b_

@cdgChbE#y\œ

@oTUq7Es[\”pVE2|U`bZYE2F Hohc\FXF Hc>ZtACEsFWOtc‹OXE

E2D^g$E2pCpCE2p›pVEY|U`ZE q7[‹–EYk kfEGFeEYO

D^]ChOf`‘­]aFeE2kKFeTVFeOfEYD D#EYD#[\kXT `b_C`“OX`bc\h`bš2cdOf`b[\_

Ff`_Cƒ>hE]aFfEYk Of`bD.`b_Cƒ hb[>c>pVE2p

@c\gChbE.yM,@ŽTUqC`ZYc\hZYc\ZtAaEcdOeOtc\Zt VFpVEYq$EY_apC`_Cƒ[>_žOXACEOXc\kfƒ>EOXE2ppVEY|U`ZE

z6hbhUqCkXEY|U`[>]aFfhTMqCkX[\q$[>FfE2psZYc>ZtACEocdOeOtc\Zt VFc\ƒ>c\`_aFeOOXACEzn¥oP#•–K`OfA‚c^yG}\x‹‘­gC`“OFeEGZkXEO~ >EYT %cdkXEŽZ[>D.q7cdkXE2p

`b_™@cdgChbE†}Vg$[dOXA!`b_™OfE2kfDFM[d”EBI†Z`bEY_aZYT+cd_7p!c\qCqChb`bZ2cdgC`bh`OWT\œ#@ACE#hc\FeOZY[\hb]CD#_!`b_™OfACE.OXc\gChbE.ƒ>`|>E2FIOfAaE

_U]CD^g$EYks[\”`b_V”•[>kfDc‹OX`[>_!ga`“OtFs[\_!OfACEFeEGZkXEOs \E2T;kfEGZ[‹|>EYkXE2pŸ`b_™OfACE†cdOeOXc>Zt 9~c\FsFeOXcdOfE2p™gUTŸOXACE†cd]VOXAC[\ktF2œ

&6[\OfEoOfAacdOOfACEKc\FXFf]CD#qVOf`b[\_aF[>_OfAaEZ2c\ZtACEo`_a`“OX`bc\hCFWOtc‹OfEcdkXEŽ_a[dOlcdhb–c&TVFZhbE2cdkXhbTFeOXcdOfEGp \[>]Ck,Zhc\FXFe`(7ZYcdOf`b[\_

`FpCEYkX`|>E2p#”•kX[\D c.ZYc\kfEY”•]Ch$c\_acdhbTVFe`Fo[d”OXACE`_U|\[>h|>E2p†cdOeOtc\Zt VFYœ=,C[>ko`b_aFeOXc\_aZE>>OXACEsc‹OfOXc\Zt pVEGFfZYkf`bg$E2p†`b_

(

yB)

`FnFf]CqCq$[>FfE2pOf[†–[\kX ”•[>kncd_UTZ2c\ZtACEs`b_C`Of`cdhFWOtc‹OfE #ÐZhbE2c\knZYc>ZtACE\Chb[>c>pVE2p›Z2c\ZtACE>œYœYœ%ǜ¤6[‹–EY|\E2k2CcžZYcdkXE”•]ah

E¡Cc\D.`b_acdOf`b[\_;[\”,OfACE.qCkX[\ƒ\ktcdD cd_7p;Fe[>D#E‚Ff`D‚]ChbcdOf`b[\_aFMFfAC[‹– OfAacdOM`OXFMq$EYkf”•[\kXDcd_aZYEAC`bƒ\AChbTŸpVEYq$EY_apaFI[>_

OfAaEZYc\ZtAaEM`b_C`Of`cdhFeOXcdOfE\œl@Aa`bFK`b_a]aEY_aZYEM–K`bhbhg7EpC`bFXZ]aFXFfE2p`_;PUEGZÇOf`b[\_;wCœ

;’_ cdhbhOfACEGFeEŸc‹OfOXc>Zt UF2,OXACE›Of`bD#E;Z[\D#qChbE¡V`OWT˜kf[>]Cƒ\AahT ZY[\kXkfEGFeq$[\_apaFOX[!OXACEŸEY_7ZkXT'qCOf`b[\_ Z[>FeO#[d”Mc\hh

kXE2i']C`bkfEGp†qChcd`b_'OfE¡UOtFYCEY¡CZEYqCO”•[>k6¢EYkX_aFWOXEY`b_$FKc‹OeOtc\Zt –KAC`ZtA›q7E2ke”•[>kfDFKc.qCkXE2ZY[\D#qC]VOtc‹Of`b[\_7cdhFWOXEYq›–K`OfA›c

Ff`D#`bhbc\kOf`bD.EZY[\D#qChbE¡V`OWT\œ

zOeOtc\Zt  &Ic‹Of]akfE Hc\ZtAaEFeOXcdOfE Ho[\D#qChbE¡V`“OWT &EYTga`“OtF

(

y) @`bD#`_Cƒ 8

(

y

(

yH) j[‹–EYk ¥lD#qVOWT 8

2!

##" 8 0% $ !$#&%' ( 6

.12 :-,F#dw%

(

}H) @`bD#`_Cƒ ¥lD#qVOWT 8 9

% !$#&%' (6

.12 :-,F#·x\ %

(

}) j[‹–EYk ,C[\kXƒ\EGp 8

2 '&

8 ()

2!

##" 8+*

( % % !$#&%' ( 6

.12 :-,F#·x\ %

(

y*) L;EYD#[\kXT ,C[\kXƒ\EGp 8 -, y&}dx

@cdgChbEI} MlHo[\D#qac\kf`Ff[\_.g7EYOW–oE2EY_† U_C[‹–K_ZYc>ZtACEncdOeOXc>Zt VFlcdƒ'cd`b_aFWO,OXACEnzn¥oP$#•OfACEMFe`bšYE6[\”E2c\ZtA#hb[U[\ U]Cq#OXc\gChbE

`F 8 7 /. 810‚c\_apOXACEskXE2Ff]Ch“OtF`_gCktc\Zt \EYOXFZ[>kfkXE2Ffq7[>_apCFlOf[9 *7 8 8VU`4œE>œUOXACEgCh[VZt žFf`bšYEM[d”~OXACE lyZYc>ZtACE

[\_›c.jEY_'Of`b]CD %

Références

Documents relatifs

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334