Hebern 1 rotor cipher machine, the Bible

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Introduction

In 1917, the American Hebern invented an encryption machine, the encryption element of which was a rotor.

In 1996, Donald A. Dawson wrote a book: "Cryptanalysis of the single rotor cipher machine", which describes, as the title indicates, the cryptanalysis of Hebern's 1 rotor machine.

It was thanks to Dawson's book that I learned to resolve messages encrypted by Hebern's machine. Unfortunately, this book is difficult to obtain. Fortunately, my website (partly) supplants this book. Likewise, Randy Nichols (LANAKI) former president of the ACA wrote a white paper (lesson 22) on the cryptanalysis of the Hebern machine. This text is largely based on Dawson's book. Unfortunately, it does not contain any exercises. In Dawson's book, the exercises are very useful for testing our understanding. This is why I decided to publish on this web page a booklet (named "The Bible") which contains exercises very similar to those of Dawson. But with a notable improvement: I give the solutions to the problems.

Note: The challenge page is similar to this page, but with one difference: I do not give the solutions to the problems of my challenge.

WARNING! Many of the problems given can be solved with pencil and paper. For others, although you can use paper and pencil, a computer program is useful. For example you can use the software I created (link). More specifically use software based on Dawson algorithms (dawson.py, tb_pln_cry.py, etc.).

Part A: The Hebern machine use only one rotor (no other permutations)

Chapter 1: We know everything (rotor wiring)

FTQ wiring 
PI = F T Q J V A X M W D S N H L R U C O K B P E I G Z Y
Pi = PI inverse
Table for ciphering and deciphering:
  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A F T Q J V A X M W D S N H L R U C O K B P E I G Z Y
B S P I U Z W L V C R M G K Q T B N J A O D H F Y X E
C O H T Y V K U B Q L F J P S A M I Z N C G E X W D R
D G S X U J T A P K E I O R Z L H Y M B F D W V C Q N
E R W T I S Z O J D H N Q Y K G X L A E C V U B P M F
F V S H R Y N I C G M P X J F W K Z D B U T A O L E Q
G R G Q X M H B F L O W I E V J Y C A T S Z N K D P U
H F P W L G A E K N V H D U I X B Z S R Y M J C O T Q
I O V K F Z D J M U G C T H W A Y R Q X L I B N S P E
J U J E Y C I L T F B S G V Z X Q P W K H A M R O D N
K I D X B H K S E A R F U Y W P O V J G Z L Q N C M T
L C W A G J R D Z Q E T X V O N U I F Y K P M B L S H
M V Z F I Q C Y P D S W U N M T H E X J O L A K R G B
N Y E H P B X O C R V T M L S G D W I N K Z J Q F A U
O D G O A W N B Q U S L K R F C V H M J Y I P E Z T X
P F N Z V M A P T R K J Q E B U G L I X H O D Y S W C
Q M Y U L Z O S Q J I P D A T F K H W G N C X R V B E
R X T K Y N R P I H O C Z S E J G V F M B W Q U A D L
S S J X M Q O H G N B Y R D I F U E L A V P T Z C K W
T I W L P N G F M A X Q C H E T D K Z U O S Y B J V R
U V K O M F E L Z W P B G D S C J Y T N R X A I U Q H
V J N L E D K Y V O A F C R B I X S M Q W Z H T P G U
W M K D C J X U N Z E B Q A H W R L P V Y G S O F T I
X J C B I W T M Y D A P Z G V Q K O U X F R N E S H L
Y B A H V S L X C Z O Y F U P J N T W E Q M D R G K I
Z Z G U R K W B Y N X E T O I M S V D P L C Q F J H A
OBC wiring 
PI = O B C L J A T D I U Z X S W R H N Y E V M G K F Q P
Table for ciphering:
  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A O B C L J A T D I U Z X S W R H N Y E V M G K F Q P
B A B K I Z S C H T Y W R V Q G M X D U L F J E P O N
C A J H Y R B G S X V Q U P F L W C T K E I D O N M Z
D I G X Q A F R W U P T O E K V B S J D H C N M L Y Z
E F W P Z E Q V T O S N D J U A R I C G B M L K X Y H
F V O Y D P U S N R M C I T Z Q H B F A L K J W X G E
G N X C O T R M Q L B H S Y P G A E Z K J I V W F D U
H W B N S Q L P K A G R X O F Z D Y J I H U V E C T M
I A M R P K O J Z F Q W N E Y C X I H G T U D B S L V
J L Q O J N I Y E P V M D X B W H G F S T C A R K U Z
K P N I M H X D O U L C W A V G F E R S B Z Q J T Y K
L M H L G W C N T K B V Z U F E D Q R A Y P I S X J O
M G K F V B M S J A U Y T E D C P Q Z X O H R W I N L
N J E U A L R I Z T X S D C B O P Y W N G Q V H M K F
O D T Z K Q H Y S W R C B A N O X V M F P U G L J E I
P S Y J P G X R V Q B A Z M N W U L E O T F K I D H C
Q X I O F W Q U P A Z Y L M V T K D N S E J H C G B R
R H N E V P T O Z Y X K L U S J C M R D I G B F A Q W
S M D U O S N Y X W J K T R I B L Q C H F A E Z P V G
T C T N R M X W V I J S Q H A K P B G E Z D Y O U F L
U S M Q L W V U H I R P G Z J O A F D Y C X N T E K B
V L P K V U T G H Q O F Y I N Z E C X B W M S D J A R
W O J U T S F G P N E X H M Y D B W A V L R C I Z Q K
X I T S R E F O M D W G L X C A V Z U K Q B H Y P J N
Y S R Q D E N L C V F K W B Z U Y T J P A G X O I M H
Z Q P C D M K B U E J V A Y T X S I O Z F W N H L G R

Table for deciphering:
  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A F B C H S X V P I E W D U Q A Z Y O M G J T N L R K
B A B G R W U O H D V C T P Z Y X N L F I S M K Q J E
C A F Q V T N G C U B S O Y X W M K E H R L J P I D Z
D E P U S M F B T A R N X W V L J D G Q K I O H C Y Z
E O T R L E A S Z Q M W V U K I C F P J H N G B X Y D
F S Q K D Z R Y P L V U T J H B E O I G M F A W X C N
G P J C Y Q X O K U T S I G A D N H F L E Z V W B M R
H I B X P W N J T S R H F Z C M G E K D Y U V A L Q O
I A W O V M I S R Q G E Y B L F D J C X T U Z K P N H
J V N U L H R Q P F D X A K E C I B W S T Y J O M G Z
K M T K G Q P O E C W Z J D B H A V R S X I N L F Y U
L S J F P O N D B V Y I C A G Z U Q R W H M K E X T L
M I E O N M C A U X H B Z F Y T P Q V G L J D W S K R
N D N M L B Z T W G A Y E X S O P U F K I C V R J Q H
O M L K A Y S V F Z X D W R N O T E J H B U Q I P G C
P K J Z X R U E Y W C V Q M N S D I G A T P H O F B L
Q I Y W Q T D X V B U P L M R C H F Z S O G N E A K J
R X V P S C W U A T O K L Q B G E Y R N F M D Z J I H
S U O R B V T Z S N J K P A F D X Q M E L C Y I H G W
T N Q A U S Y R M I J O Z E C W P L D K B X H G F V T
U P Z T R X Q L H I N Y D B V O K C J A W G F E U S M
V Y S Q W P K G H M X C A U N J B I Z V F E D T R L O
W R P V O J F G L W B Z T M I A H Y U E D C S Q K N X
X O U N I E F K V A Y S L H Z G X T D C B R P J M W Q
Y T M H D E J U Z X R K G Y F W S C B A Q O I L V P N
Z L G C D I T Y W Q J F X E V R B A Z P N H K U O M S

1. Decipher the following messages. You can use the tables given.

a) First message
Key: Rotor FTQ, Extern key: Z, cipher mode, clockwise, cryptogram: 
         BTHJG DVXLH PWQ
b) Second message
Key : Rotor OBC, Extern Key : Z, decipher mode, clockwise, cryptogram: 
         FTUOE DDJQS TOLIY GOAUC PWJOD XIYX

2. Same, but we use mathematical formulas

a) First message
Key : Rotor FTQ, extern key: Z, cipher mode, clockwise, cryptogram: 
         JZJFR
b) Second message
Key : Rotor OBC, External Key: G, cipher mode, clockwise, cryptogram: 
         XAXNGG

3. Decipher the following message

Key: Rotor OBC, External key: B, cipher mode, clockwise, Cryptogram : 
         XWFJT GUSBR BGUEV POXDZ MIXEE TEHAT DXABM ZCWKT PPHKG QLIJG
         WZXRT OGUHT OMOTF VXLTT WWAAG PXZYM OLQIT WFYJT FQSES GCLNC
         WGOBR IMLLL UDIEH BPEB
Note : the cryptogram is long, I suggest you write on a software to decipher it.

4. Trigonometric direction

Key : rotor : FTQ, Extern Key : D, cipher mode, Trigonometric direction Cryptogram : 
         OGUYB

Chapter 2: We know the cryptogram and the plain text

In the following problem, we know the cryptogram and the plain text. The objective is to find the rotor wiring. 

Cryptogram:
      CPCKA TIEHT EIDDZ HVZDC ZRQXS MZIMA KEINJ UQAMO GDXIY VNOZU
      XLZLY PGSJO NCXQQ PCQXE QWOKD RFKKD YKGCF TVMAJ UUMBD NWUKE
      GJMLP TUKUK KBHBT YLDFC SVSAL FIGRK NWIFF JCKWG ENDCV CSIDU
      MQDXO CKYGL LDKBN CAJRP ZJXNW FTJYU RAEWS SMHUH HVXWN DJFWN
      MEPFG INLLT IK
Plain text (From Galileo Galilei) :
      AFTER SEVERAL ATTEMPTS CONSIDERING NEITHER LABOR NOR EXPENSE 
      I MANAGED TO CONSTRUCT AN INSTRUMENT WHICH ENLARGES OBJECTS 
      MORE THAN EIGHT TIMES Z DOT Z TO THE PROFOUND AMAZEMENT OF 
      HIS LORDSHIP AND THE ENTIRE SENATE OF VENICE I DEMONSTRATED 
      MY TELESCOPE

Chapter 3: We only have the cryptogram

Here is a cryptogram. The text is in English. The Lampboard and keyboard permutations are equal to the Identity permutation.

We suggest using the diagonal fusion method presented in Dawson's work. 

      EHDXF GCFOU VIIIP GICBI HYBNN DOJDE YBZJZ ITLCA DYUNC NCEUH
      ADOQL EAJBU ZOFXG XOGYK UYUWV TXAPK VWBFG OONOM IHSPY ZPQJI
      GNHHB DEKHF ZVBIP JIXSA PHEXJ NEBAB SWEIL KETOP JQYAS GBCOG
      UYGDF GBDEZ JSVMD UDKIP LGYCC RKJLZ TYBTW TLRCX QPYXY EMABH
      CIMYV TWUUW WBYHJ NBOFM ZHAEY EENAL WYMJO SVCSW HBBLQ SJTZM
      CHOTE SXNHP CFZLD HUAJY UMVTO NVCEN DEZNA GJMFT BWGXB EILYA
      LFNWV OJGED TKSYE KSSGD WYPRI BTHCK PIMJY FAMHA EDLEU FBOEF
      WTMKY QIJVY ZZZYV MVWJG MNNOC NVHXA UHEYP CEWAD EWEKF XAMSQ
      HFYSY IUOBI ZDBSN AZQFT MOXOZ UDKGT OUUHK NNNWT SPCMF MOGZD
      JCYYZ XAKJW NDKNR OMPCK RNRWX GHCSM XQWGF TBIVQ EPFDS ALXOY
      SBBNC NZXOJ DWVCE NDPLR VJLNB LRDHG PRZXO ZVLOE DNDUN NJJDE
      AZCMJ WTSXH RWCJU QXREL IACDW AAOQK WYYTF QUJVJ OHIFE EAMIH
      FXYHZ THLYA ZFAHR MTLKN DUNPC GRWLR UIQWH KGTZM XWQWP NAYNC
      JKLNY XXHFA PRXTA HNCCX UYZWA NXGLC GOASW FTAWU KKOVS TTRZE
      AAXDS ZYYRJ MOOHP KACVA EDEZV UXAXG DEAZC MJWTS GWRKD UIYME    
      SSXBD STKCS UASOT MKKGZ YONVW EMINA ZQFWB FITQH PQCSZ MKNCX
      DEHNS DOJIL IOZGH EYSYE NPZWO HJNWP FBJUI LRKJH JCYNY UUJVC
      KHEWE LLCCQ ZPFYU WLOPD ZSDQV BVYVS ZUCYZ JVKVZ BNG

Part B: The wiring of the rotor and keyboard are unknown

Chapter 1: We know the cryptogram and the plain text

We know the plain text and the cryptogram. Lampboard and rotor permutations are unknown. The objective is to reconstitute them.

Plain text (John Locke): 

  Slavery is so vile and miserable an Estate of Man and so directly
  opposite to the generous Temper and Courage of our Nation that it
  is hardly to be conceived that an Englishman much less a Gentleman
  should plead for it z dot z And truly I should have taken Sir
  Robert Filmer quote s Patriarcha as any other Treatise which would
  persuade all men that they are slave, and ought to be so
Cryptogram: 
      ZOIFN OUUVE RKQPY DXLCZ UKGLA NQESV YGKBO BXTRE IOQUR YGLOU
      YNRLX SETEB OLRUB UPWXR HKQZH EXGQM IUHZO LEPSI JCSTU FMFGB
      LQWVA HCRYL KAMQC UJBYV IFDBG XOZYY XSIUN FTDRE ZTREX TLNVB
      UZTOB QAOAO VFLVX KLZKP YDQGR CGOJZ VTVES JIOQD WMMSJ YKBDC
      LBXQP ENCPM UMOEY BLMLT SHNTI PWPVQ HBOVD VZYVT KSWBN SSHLQ
      ZCKZU KVROE FRJGQ KWGEE UYPUI CTXWH XUTQY YQIIP NTZZC JHRPD
      BYDPK KBKBD

Chapter 2: We only have the cryptogram

We only know the cryptogram. On the other hand, the wiring of the rotor and the keyboard permutation are unknown. The lampboard permutation matches the identity. 

ZAOCF XWHKT JFWHR WCSBY MSBUV YXEBN QFGYX SBCWA EXBWZ CFPOU
SULCY BAFVQ HAKKW NXCFY KEMPG RVEHM SMFMS VKZSD KCKNI KFBZA
TTWHD KIPSJ AYTVM ISBDT BURHP UBRUM DYZQX MZLNJ IQKWI XXHXJ
CFRGV NQMRR LHCVQ NAOZB CXDHZ LOPDG BHZYR BMRZL CUIRW XVJRP
TUKPY WAEAP BAKXK ESFXN ENECR DRKTL MWIHD KSMFJ RUYCK KFCTZ
CQRLP BMJAV CPKWB LWYXZ RZKAA TSUOG VOCUV YTUZM QRYZB UYZKA
ACNWG OJYNG TSHDO WXLWF GMRLT BCXZX THJSE MLNBR NPCPM FQTRQ
KCKZV NWYPS PUSEG PDBZA MHNPY TIVTX RBTUK UCNBN FSAXB FFFUA
KKWNX CFYKE BFASA WMYKB MIOOE XRTYC KWWKG OPWMW QNXMR RLHLY
UPYTI VKZNU RUKPY WZMMZ KKVDE UCJYZ KVATR RZLBO CGTBB USKAH
RWQTI GKVEZ XKRUN RUEBM EUKKM WRUQV TOKUU RFXPY BWNTI GKMAN
HERYX PXIIR EWWHX HDSMA CHECD NJMCP HJUFN PJTVL DKGAM OKMYU
XKXPO JHSBT ZURMU WPANR ETILH PSXXP OHCRZ XDBCX RURON UVOZG
YUXKX PMZLY ZZNDT ACHXC UPNPT PASBN QFGUQ PXQAD XAHJG LAYBL
TELZP KVXZB STSLJ LRGIC PYKSD JHVAP AJZUM NCJIW IBKZV VOMOE
BFLNY CDQPU BLQTC CBDHC NYIHV WNKAN RYDBE MEYUV TOQDN XSPHL
ECMWZ CHSSQ PHRBU SUSMJ AGHQH CMVRX VHHSS WKLWU YUXNL WQWYG
PWIAM GHKDY NPFYK EWDJT JRVBI WTSNR CRVHM CPKQH EQQFB ZNDKQ
CPZXW FYPWZ APTNJ MZEWD SDSBU CVUOR CFNKA WTACK KPOBS AKKWN
XCFYK EJUEG HKDYA FBERJ QXSDS RWUDM BLPFW IAEFU NRCMY FNSYR
WXVJY QEBBA DUDHG BRAQH BJKUB RWBCX WKTEP EQLZG ZGRAS RCVYE
XYJYU XVWKM OEBFZ EGFZB QAEVK ZJFNX JWHET DCKRQ SHECB TQUZU
HJBIK CTAIE KEVEV TDWHD BPOPM FQTLO WIRXV AJOPS DMIWA RXBBI
RLISU OQTZG IKDUV KNGTE LUAPU RLHID KEIYV JBUEL MPCXV HHSSW
KLWFN JUFDV IOICP UVYQM LGAVR QGURI LCMMW HUUSK EJVVB TTETZ
DGBER XXJSC JASIH EJQJR ELHYD ZYLAL EYTQY KYBRR FPZOM RJMBO
ARUNS RWFST MTFXT URHXF JEVJQ MBZZW AHLYU VTOKU KQCPZ CCYRW
ABSYI QPRZA KJLQI NECRD

References

  • Cryptanalysis of the single rotor cipher machine, by Donald A. Dawson, Aegean Park Press, 1996.

Web Links

  • Classical Cryptography Course, par LANAKI, Lecture 22 (Cipher Machines II). (link).