Military Cryptanalysis

204 Pages·1941·14.787 MB·English

by  Friedman W.F.

0
61
YRATILIM SISYLANATPYRC
(‘ _
-VITRAp:
Transposition and Fractionating Systems
Transposition Syhema
(Numbers in parenthe& refer to paragraph numbers in thie text
bY
William F. Friedman
W From Aegean Park Press
Page 1
MILITARY CRYPTANALYSIS PART IV............................... 1
Transposition and Fractionating Systems......................... 1
SECTION I............................................................................ 6
GENERAL ........................................................................ 6
SECTION II ........................................................................... 8
SOLUTION OF SIMPLE TRANSPOSITION CIPHERS ... 8
SECTION III .......................................................................... 23
INCOMPLETELY-FILLED RECTANGLES ....................... 23
SECTION IV.......................................................................... 42
OPPORTUNITIES AFFORDED BY STUDYING............... 42
SECTION V........................................................................... 45
SPECIAL SOLUTIONS FOR TRANSPOSITION .............. 45
SECTION VI.......................................................................... 85
PRINCIPLES OF MATRIX RECONSTRUCTION ............ 85
SECTION VII......................................................................... 91
SOLUTION OF GRILLES.................................................. 91
SECTION VIII........................................................................ 100
COMBINED SUBSTITUTIOX-TRANSPOSITION............. 100
SECTION IX.......................................................................... 103
SOLUTION OF THE ADFGVX SYSTEM ......................... 103
SECTION X........................................................................... 150
SOLUTION OF BIFID FRACTIONATING SYSTEMS ...... 150
ANALYTICAL KEY FOR MILITARY CRYPTANALYSIS,.... 198
INDEX .................................................................................. 199
MILITARY CRYPTANALYSIS
Part IV
TRANSPOSITION AND FRACTIONATING SYSTEMS
BY
WILLIAM F. FRIEDMAN
Page 2
This is a quality reproduction of a U.S. Military
text, originally published in 1941 - declassified
from CONFIDENTIAL in December 1992.
ISBN: O-89412-198-7 (soft cover)
AEGEAN PARK PRESS
P.O. Box 2837
Laguna Hills, California 92654
(714) 586-8811
FAX [phone]
Manufactured in the United States of America
Page 3
The Golden Guess
Is Morning-Star to the full round of Truth.
-Tennyson.
Page 4
MILITARY CRYPTANALYSIS, PART IV.
TRANSPOSITION AND FRACTIONATING SYSTEMS
CONTENTS
Section Paragraphs Pages
I. General ___________________________________________________________________________ 1-3 l-2
II. Solution of simple transposition ciphers ______________________________________ 4-11 3-17
III. Incompletely-filled rectangles _________________________________________________________ 12-16 18-36
IV. Opportunities afforded by studying errors and blunders made by enemy cryptographers- 17-19 37-39
V. Special solutions for transposition ciphers ______________________________________ 20-29 40-79
VI. Principles of matrix reconstruction ______________________________________ 30-31 8O-84
VII.Solution of grilles ________________________________________ 32-34 85-93
VIII. Combined substitution-transposition systems ________________________________________-------------- 35-36 94-96
IX. Solution of the ADFGVX system _________________________________--------------- 37-43 97-143
.X noituloS fo difib gnitanoitcarf smetsys --------------________________________________________ 65-44 481-441
XI. Analytical key -______-________________________________---------------------------------------------------------- 57 185
Index ________________________________________--------------------------------------------------------------- 186-188
Page 5
NOITCES I
LARENEG
yrotcudortnI skramer gninrecnoc noitisopsnart srehpic .._ ..~..~..~~~..~ ~.~~~~~~~..~ .__._.__......... .._........ 1
cisaB msinahcem of noitisopsnart srehpic _................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .._ 2
esahponoM dna esahpylop _noitisopsnart _..... ~~~ .~ ..~.. . . . ..____._.._. ..___..____.._.....__.. __________ 3
.1 yrotcudortnI skramer gninrecnoc noitisopsnart .a--.srehpic s4- detats ni a suoiverp ,txet
noitisopsnart srehpic era ylhguor suogolana ot wasgij“ ”selzzup ni taht lla eht seceip of hcihw
eht lanigiro si desopmoc era tneserp tub era ylerem .degnarrasid ehT seceip otni hcihw eht
erutcip gnimrof eht sisab of a wasgij elzzup yam eb dedivid era yllausu etiuq ralugerri ni ezis
dna ;epahs eht retaerg eht tnuoma of ,ytiralugerri sa a ,elur eht retaerg eht ytluciffid ni -saer
gnilbmes eht secoip ni reporp .redro nI siht ,tcepser ,oot noitisopsnart srehpic era suogolana ot
wasgij ,selzzup rof eht retaerg eht tnuoma of noitrotsid ot hcihw eht nialp txet si de,tcejbus ni
eht noitisopsnart ,ssecorp eht erom tluciffid semoceb eht .noitulos
.b nI wasgij selzzup ereht si yllausu on ytiraluger tuoba eht ezis of eht laudividni seceip
otni hcihw eht lanigiro erutcip sah neeb ,tuc dna siht ,erutaef of ,esruoc yllairetam setubirtnoc
ot eht ytluciffid ni gnitcurtsnocer eht .erutcip erehT ,era ot eb ,erus stimil detatcid( yb -noc
snoitaredis of )ytilibacitcarp hcihw evres ot tneverp eht seceip gnieb edam oot ,llams rof neht
yeht dluow emoceb ;elbaeganamnu no eht rehto ,dnah ereht era osla stimil hcihw tsum eb -bo
devres ni tcepser ot eht reppu edutingam of eht ,seceip rof fi yeht era edam oot egral eht elzzup
semoceb oot ysae ot .evlos esehT serutaef of wasgij selzzup osla evah rieht seigolana ni -snart
noitisop .sdohtem nI eht ,rettal fi eht lau.txet stinu ot eb detcejbus ot noitisopsnart era edam
etiuq ,egral yas eritne ,secnetnes eh.t seitluciffid a tsylanatpyrc lliw evah ni gnitcurtsnocer eht
txet era yllacitcarp ;lin no eht rehto ,dnah fi eseht lautxet stinu era edam etiuq ,llams neve
rellams naht elgnis ’,srettel neht eht noitcurtsnocer of eht noitisopsnart txet yb a tsylanatpyrc
netfo semoceb a yrev tluciffid .rettam nI neewteb eseht owt semertxe ereht yam eb suoirav
seerged of ,noitatnemgarf detimil ylno yb snoitaredisnoc of .ytilibacitcarp
.c tI si ,etanutrof ,revewoh taht eht .tsylanatpyrc seod ,ton sa a ,elur evah ot dnetnoc htiw
smelborp ni hcihw eht ezis of eht lautxet stinu seirav nihtiw eht emas ,egassem sa si eht esac ni
wasgij .selzzup tI si spahrep elbissop ot esived a noitisopsnart metsys ni hcihw eht txet si
dedivid pu ni hcus a rennam taht eritne ,secnetnes elohw ,sdrow ,selballys laudividni ,srettel dna
snoitcarf of srettel form eht stinu rof ;noitisopsnart tub ti si ton tluciffid ot enigami woh -carpmi
lacit hcus a emehcs dluow eb rof raluger ,noitacinummoc dna ti yam eb nekat rof detnarg taht
hcus ytiralugerri ni ezis of lautxet stinu lliw ton eb deretnuocne ni lacitcarp .noitacinummoc
.d ehT syad nehw eht elpmis sdohtem of drow noitisopsnart erew tneiciffus rof yratilim
sesoprup evah gnol ecnis dessap ,yb dna ti si yldrah ot eb detcepxe taht smargotpyrc of hcus
lautceffeni erutan lliw eb deretnuocne ni eht yratilim snoitacinummoc of neve eht rellams seimra
of .yadot ,revewoH ni emit of ,ycnegreme nehw a eganoipse-retnuoc pihsrosnec si desicrexe revo
lanretni ,snoitacinummoc ti si elbissop taht detalosi secnatsni of elpmis drow noitisopsnart yam
eb .deretnuocne ehT noitulos of hcus sesac dluohs tneserp on ,seitlucEid sselnu suoremun edoc
seman dna sllun era osla desu ni eht .smargotpyrc ereM noitatnemirepxe htiw eht ,smargotpyrc
gniyrt suoirav sepyt dna sezis of ,selgnatcer lliw yllausu esolcsid eht terces .txet fI edoc seman
1 ecnerefeR si ereh edam to dellac-os gnitanoitcarf .smetsys eeS laicepS txeT .oN 166, decnaodA yratiliM
,yhpargotpyrC .ces .IX
)1(
Page 6
2
era desu dna eht txetnoc sevig on rulc ot eht ytitnedi of eht snosrep ro secalp ,denoitnem ti Fnnr
eb yrassecen ot tiaw litnu lanoitidda segassem emoceb ,elbaliava ,ro gnikcal hcus a ,ytilibissop
ereht si yllausu tneiciffus ,noitacifitsuj rednu eht seicnegixe of ,raw ot lepmoc eht stnednopserroc
ot laever eht gninaem of eseht edoc .seman
.e hguohtlA noitisopsnart ,srehpic sa a lareneg ,elur era hcum ssel xelpmoc ni rieht scinahcem
naht era noitutitsbus ,srehpic eht tsylanatpyrc yllausu secneirepxe a gnileef of etsatsid dna
yamsid nehw detnorfnoc htiw nwonknu srehpic of siht .yrogetac erehT era lareves snosaer rof
sih ekilsid rof .meht nI eht tsrif ,ecalp hguohtla noi,tisopsnart srehpic era yldettimda ssel etacirtni
naht noitutitsbus ,srehpic sa a lareneg elur ereht era ton ylraen os ynam citylanatpyrc sloo’t dna
”skcirt“ ot eb desu ni eht noitulos of eht remrof sa ereht era ni eht ,rettal dna erofereht eht
latnem sulumits dna noi,tcafsi’tas hcihw eht tsylanatpyrc yllausu sevired dna sdrager sa trap of eht
drawer rof sih drah robal ni gnivlos a rehpic si netfo gnissim ni eht esac of noi,tisopsnart .srehpic
nI eht dnoces ,ecalp etipsed rieht kcal of ,ytix.elpmoc eht noitulos of noitisopsnart srehpic netfo
sevlovni a suodnemert tnuoma of emit dna robal tsom of hcihw ylnommoc snrut tuo ot eb
sseltiurf .noitatnemirepxe ,yldrihT ni nredom yratilim ,noitacinummoc noitisopsnart sdohtem
era yllausu ton deyolpme enola tub ni noitcnujnoc htiw noitutitsbus dna-sdohtem neht eht
smelborp yam emoceb tluciffid ,deedni rof yllausu erofeb eht noitutitsbus nac eb dekcatta ti si
yrassecen tsrif ot revocnu eht .noitisopsnart ,yllaniF ni gnikrow htiw noitisopsnart srehpic a
hcum rehgih eerged of ycarucca ni erem lacinahcem snoitarepo si deriuqer naht ni gnikrow htiw
noitutitsbus ,srehpic esuaceb eht latnedicca noissimo ro noitidda of a elgnis rettel lliw yllausu
etatissecen gnitirwer eht krow steehs gniylppa ot eritne segassem dna gnitrats .hserfa ,suhT
siht tros of krow sllac rof a tnatsnoc etats of detartnecnoc ,noitnetta htiw sti gnitluser etats of
lacigolohcysp ,noisnet hcihw sekat sti llot ni latnem raew dna .raet
.2 cisaB msinahcem of noitisopsnart .+.srehpic ,yllacisaB lla noitisopsnart srehpic evlovni
ta tsael owt :sessecorp )1( gnitirW eht txet-nialp stinu yllausu( elgnis )srettel nihtiw a cificeps
raluger ro ralugerri lanoisnemid-owt ngised dellac a ”,xirtam“ ”,egac“ ”,emarf“ ”,elgnatcer“
,.cte ni hcus a degnarraerp rennam taht eht dias stinu era detubirtsid ylraluger ro ylralugerri
tuohguorht eht suoirav sllec ro snoitcesbus of taht ;ngised )2‘( gnivomer eht txet-nialp stinu
from eht ngised ni hcus a degnarraerp rennam sa ot egnahc eht lanigiro ecneuqes ni hcihw yeht
dewollof eno rehtona ni eht nialp ,txet suht gnicudorp rehpic .txet ecniS eht tsrif ssecorp stsisnoc
of gnibircsni eht txet nihtiw eht ,ngised ti si yllacinhcet derrefer ot sa eht ssecorp of :noitpircsni
dna ecnis eht dnoces ssecorp stsisnoc of gnibircsnart eht txet from eht ,ngised ti si yllacinhcet
derrefer ot sa taht of .noitpircsnart rehtiE ro htob sessecorp yam eb ,evititeper yb -egnarraerp
tnem of ,esruoc ni hcihw esac eht etaidemretni spets yam eb derrefer ot sa sessecorp of ,noitpircser
ro evitpircser .sessecorp
.b tI si yldrah yrassecen ta siht tniop ot evig eht tneduts yna snoitacidni sa ot woh ot
etaitnereffid a noitisopsnart from a noitutitsbus .rehpic fI a weiver si ,yrassecen ,revewoh eh
si derrefer ot noitceS VI of yratiliM ,sisylanatpyrC traP .I
.3 esahponodll dna esahpylop .u-.noitisopsnart sA yam eb derrefni from eht gniogerof
,snoitinifed nehw a noitisopsnart metsys sevlovni tub a elgnis ssecorp of ,noitpircsni dewollof yb
a elgnis ssecorp of ,noitpircsnart eht metsys yam eb derrefer ot sa esuhponom ,noitisopsnart
ylnommoc dellac elgnis .no&sops.nart nehW eno ro erom evitpircser sessecorp enevretni neewteb
eht lanigiro noitpircsni dna eht lanif noitpircsnart eht metsys yam eb derrefer ot sa esahpylop
.noitisopsnart sA a lareneg ,elur eht noitulos of eht rettal epyt si hcum erom tluciffid naht eht
,remrof yllaicepse nehw eht evisseccus snoitisopsnart era yllaciteroeht tcerroc ni .elpicnirp
.b ynA metsys hcihw si detius rof esahponom noitisopsnart si osla yllausu detius rof esahpylop
,noitisopsnart eht sessecorp of ,noitpircsni noitpircser dna noitpircsnart gnieb dehsilpmocca
htiw eht emas ro htiw tnereffid .syek
Page 7
NOITCES II
NOITULOS FO ELPMIS NOITISOPSNART SREHPIC
hpargaraP
elpmiS sepyt of noit4opsnart . .._..__________. ..~~ ~~.~~~ .~~ . . . . ..__.._......_..........._ .__....._ 4
ehT s.e1picnirp of noitulos of laretilinu lloitieopsnart-etuor srehjlic .._________ ___.______.__. -- .____________...____ 5
deyeK ranmuloc noitiq.opsnart htiw dellif-yletelpmoc selgnatcer ..____________...._..________________ _ _______.. ..___ .___ 6
elpmaxE of noitulos .--_. _ ._-.--_.__.______-----.-------------------.---.--.----------~-- _ ______: __.__.._.___________---..-------..____ 7
ehT drow-elbaborp dohtem of noi,tulos __.________ _ _____ _ ____________________--.----------- ____ ___________.._.._.___________...___ 8
lareneG skramer on noitulos ______________._________________________ _ ________________ -- ____________________________ ___.__.____ ____ 9
noitcurtsnoceR of laretil yek ____________________.---.----.--------------------------- ___...._____________-----------------.. -_ ..__ _ 10
nmuloC dna wor .noitisopsnart _______________.__..____________________- _ _________________........---------------.----------....___ 11
.4 elpmiS sepyt of .a--.noitisopsnart ehT elpmis sesac of desrever ,gnitirw lacitrev ,gnitirw
ro liar ecnef gnitirw yldrah eriuqer suoires ,noitnetta ecnis yeht yam eb devlos tsomla yb -cepsni
.noit esehT sdohtem era dedulcni ereh ylno esuaceb yeht yam eb deretnuocne ni pihsrosnec
.snoitarepo
.b ehT wol eerged of cihpargotpyrc ytiruces dedroffa yb eseht sdohtem yam eb desaercni ot
a thgils eerged yb gnidda sllun ro yb gnisiugsid eht lanigiro drow ,shtgnel dna gnipuorger otni
eslaf sdrow ro otni spuorg of raluger .htgnel
.c emoS selpmaxe of eseht tselpmis sepyt of noitisopsnart .wollof teL eht egassem :eb
EGDIRB DEYORTSED TA NEVELE .MP
)1( gnisreveR ylno eht sdrow dna gniniater lanigiro drow :shtgnel
M
---rehpiC E G D I R B D E Y 0 R T S E D T A N E V E L E P
)2( gnisreveR ylno eht sdrow dna gnipuorger otni eslaf drow :shtgnel
BRIDGE--rehpiC TROYED, ATDES EVEN PMEL
)3( gnisreveR eht elohw txet dna gnipuorger otni :sevif
M
---rehpiC P N E V E L E T ,A D E Y 0 R T S E D E G D I R B
)4( gnisreveR eht elohw ,txet gnipuorger otni ,sevif dna gnitresni a llun ni yreve htfif :noitisop
..--rehpiC T R I M M P N E V P E L E T A A D E Y R 0 R .T S L
UGEDE MBRID
)5( gnitirW eht txet yllacitrev ni owt snmuloc dna gnikat eht gnitluser B S .RB
shpargid rof eht rehpic ,txet sa nwohs ta eht .edis ehT rehpic -sem R T I D
egas :semoceb RI EG
OD ED
YG TS
ITRSB YGODR ro,EDDEE EE OR
SDGIB DRDYR EOTEE DD EY
E D
esehT elpmis sepyt nac eb devlos ylerem yb .noitcepsni
.5 ehT selpicnirp of noitulos of laretilinn noitisopsnart-etuor .a--.srehpic ehT dellac-os
laretilinu noitisopsnart-etuor sdohtem era txen ot eb .denimaxe ehT noi,tulos of smargotpyrc
derehpicne yb eseht sdohtem si a rettam of gnitnemirepxe htiw cirtemoeg ,serugif yllausu -cer
(3)
Page 8
4
,selgnat of suoirav snoisnemid detseggus yb eht latot rebmun of srettel ni eht ,egassem neht
gnitcepsni eseht ,selgnatcer gnihcraes rof elohw sdrow ro eht stnemarf of sdrow yb gnidaer
,yllatnoziroh ,yllanogaid ,yllacitrev ,yllarips dna os ’.no eeS( laicepS tseT .oS ,561 yratnemelE
yratiliM ,yhpargotpyrC ,5391 .srap ,02 ).12
.b ehT tnuoma of noitatnemirepxe taht tsum eb demrofrep ni eht noitulos of srehpic of siht
epyt yam eb yllairetam denetrohs yb snaem of ealumrof dna selbat detcurtsnoc rof eht .esoprup
tuB esuaceb srehpic of siht epy,t era of tneuqerfni ecnerrucco ,yadot eseht ealumrof dna selbat
era ylno yllanoisacco lufesu dna ecneh yeht evah ton neeb dedulcni ni siht txet ’.
.6 deyeK ranmuloc noitisopsnart htiw dellif-yletelpmoc .a-.selgnatcer nI lacitcarp -pyrc
,yhpargot eht snoisnemid of eht noitisopsnart ,elgnatcer sa a lareneg ,elur tonnac yrav neewteb
egral ;stimil taht ,si ti nac eb demussa ni ecitcarp taht selgnatcer desab nopu senil of gnitirw
gniniatnoc ssel naht 5 srettel ro erom naht 52 srettel lliw ton ylnommoc eb .deretnuocne fI eht
,htdiw taht ,si eht rebmun of ,snmuloc si denimreted yb a ,yek neh,t eht rebmun of swor semoceb
a noitcnuf of eht htgnel of eht egassem ot eb .derehpicne fI eht rettal si yrev ,gnol regnol naht
nac eb yltneinevnoc deldnah tuohtiw oot ynam ,srorre ti si a nommoc ecitcarp ot kaerb pu a
egassem otni owt ro erom strap dna taert hcae trap sa hguoht ti erew a etarapes .noitacinummoc
hcuS strap era ylnommoc demret .snoitces
.b nehW eht tsal wor of a noitisopsnart elgnatcer si yletelpmoc ,dellif eht noitulos of eht
gnitluser margotpyrc si ylbaredisnoc erom elpmis naht nehw siht si ton eht 3.esac -esnoC
,yltneuq siht lliw eht etutitsnoc tsrif esac ot eb .deiduts
1 It si gnitseretni to evresbo taht ,leinaD of lacilbiB ,emaf saw yltnerappa eht firat tsylanatpyrc ni yrotsih
sa( llew sa eno of eht tseilrae sreterpretni of ,)smaerd for eh devlos eht margotpyrc ni eht gnitirwdnah“ on eht
”,llaw gniniatbo sa sih tnemrehpiced sdrow hcihw eh deterpretni sa gnitciderp eht llafnwod of razzahGlcB dna
sih ytsanyd leinaD( :V l-28). ehT gniwollof laitrap tnuocca of eht edosipe si ,ton sa gninethgilne sa eno thgim
,hsiw tub ti si ylbaborp eht tseb noitanalpxe .elbaliava It, si nekat from .rD xaM s’nhoFpileS elcitra on eht -bus
tcej ni ehT hsiueJ ,aidepolcycnE .lov 8, .pp 490-491 (1925): .ENE%‘ m, ,LEKET NISRAHPU lD~O~( np3 22X WD)
Words nettirw yb a suoiretsym dnah on eht sllaw of s’razzahsleB ,ecalap dna deterpretni yb leinaD sa gnitciderp
eht doom of eht gniK dna sih .ytsanyd ehT tnedicni si debircsed sa follows: ecnO nehw gniK razzahsleB saw
gniteuqnab htiw sih sdrol dna gniknird eniw from eht nedlog 5lessev of eht elpmet of ,HWHT a s’nam dnah saw
nees gnitirw on eht llaw niatrec suoiretsym .sdrow denethgirF yb eht ,noitirappa eht gniK deredro :sih -lortsa
srego to nialpxe eht ;noitpircsni tub yeht erew elbanu to daer .ti leinaD saw neht denommus to eht layoR
,ecalaP dna eht gniK desimorp mih yltsoc stneserp if eh dluoc rehpiced eht .noitpircsni leinaD daer ti “ ,eneM
,enem ,leket ”,nisrahpu dna denialpxe ti to naem taht doG dah ”derebmun“ eht modgniK of razzahsleB dna
thguorb ,ti to na ;dne taht eht gniK dah neeb dehgiew dna found ;gnitnaw dna taht sih modgniK saw dedivid
dna nevig to eht sedelh dna .snaisreP
ehT first noitseuq hcihw stneserp flesti to eht ,citirc ,yleman yhw dluoc eht noitpircsni eb detchpiced yb
leinaD degagne-ylno eht noitnetta of eht ,stsidumlaT ohw decnavda suoirav .srewsna niatreC of meht
dedulcnoc taht eht werbeH gnitirw dah neeb degnahc ni eht emit of ,arzE os taht neve eht sweJ taht erew
found ni eht layor court dluoc not daer na noitpircsni nettirw ni ciahcra .sretcarahc tuB esoht ohw dewollof
.R noenriS ni gniniatniam taht eht gnitirw dah not degnahc found rehto snoitulos for eh.t ;melborp .e II. ti saw
nettirw ni eht cihpargotpyrc noitanibmoc m m, hcae rettel of hcae riap gnieb detutitsbus yb sti ,noinapmoc
.e 9. naa X1 xtt M ;’Un or eht sdrow erew nettirw :suht ~~~ llpD‘ ,OJIIVP eno evoba eht ,rehto gnivah to eb
daer ;yllacitrev ro 9OWl 5pn MB ,“ hcae drow ;drawkcab ro ,niaga VW Pn5 Xm PX eht first owt srettel of
hcae drow gnieb desopsnart .hnaS( 22~). It si tnedive taht eht rohtua of eht kooB of leinaD tnaem taht eht
noitpircsni saw nettirw ni sretcarahc railimaf to eht gniK dna esiw nem of ,nolybaB tub ,taht sa often sneppah
htiw tneicna ,snoitpircsni eht noitisopsnart of niatrec srettel delffab yreve tpmetta to rehpiced .meht . . .”
’ eeS ,rhoL xoneL .R dna ,namdeirF mailliW F., rofealumroF eht noitulos of noitisopsnart .srehpic knabreviR
noitacilbuP .oN 19, ,aveneG ,sionillI 1918.
* eeS laicepS txeT .oN 165, yratnemelE yratiliM ,yhpargotpyrC 1935, .ceS .V In siht txet eht mret -snart“
noitisop ”elgnatcer Iliw eb desu ot etangised eh,t matrix, frame, ,egac or ngised sseldrager of rehtehw eht rettal
si yletelpmoc dellif or not,.
Page 9