Season 03 • Episode 16 • The Enigma machine

Season 03 • Episode 16 • The Enigma machine

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The Enigma machine

Season 03

Episode 16 Time frame 2 periods

Prerequisites :

^Mainryptographitehniques

Objectives :

•

^{Disover the workings of the Enigma mahine.}

•

^{Count the numberof} possibilitiesoered by the mahine.

Materials :

• 6

opiesof eah fat sheet.

• 6 × 3 × 3 = 54

opies of the Enigma mahine setup page.

• 6 × 4 = 24

opiesof the rotors page.

1 – Expert teams ^{25 mins}

The lassisdividedin6groups.Eahgroupisgivenafatsheetabout oneof theaspets

of the Enigmamahine. They have 25minutes tounderstand the explanation and nd a

partial formulafor the numberof possibilities oered by their part of the mahine.

2 – Mixing the teams 30 mins

The lass is one again divided in 6 groups, with one memberfrom eah of the 6 expert

groups.They have30minutestoommuniateandunderstandthe globalworkingsofthe

Enigma mahine, and ompute the total number of possibilities.

3 – Coding and decoding messages ^{1 period}

Eah group has to ode and deode some messages and gets mark depending on the

numberof orret odings and deodings.

The overall design of Enigma ^{Episode 16}

Document Fact sheet 1

An Enigma mahine is aneletro-mehanialrotor ma-

hines that was used for the enryption and deryption

of seret messages by the German army during World

WarII.Likeother rotormahines, theEnigma mahine

is a ombination of mehanial and eletrial subsys-

tems.

The mehanialsubsystem onsistsof akeyboard;aset

of rotatingdisksalledrotorsarranged adjaentlyalong

a spindle; and one of various stepping omponents to

turn one or more of the rotors with eahkey press.

Themehanialpartsatinsuhawayastoformavaryingeletrialiruit.Whenaletter

key ispressed, the iruitis ompleted;urrent ows through the various omponentsin

their urrent onguration and ultimately lightsone of the display lamps, indiatingthe

outputletter.Forexample,when enrypting amessagestartingwiththe lettersANX...,

the operator would rst press the A key, and the Zlamp might light, so Z would be the

rst letter of the iphertext. The operator would next press N, and then X in the same

fashion, and so on.

To illustrate the detailed operation of

Enigma, please refer to the wiring diagram

ontheleft.Tosimplifytheexample,onlyfour

omponents of a omplete Enigma mahine

are shown. Inreality,thereare 26lampsand

keys, several plugs (varied with model) and

rotor wiringsinsidethe rotors(atleastthree

were installed).

Current ows from the battery (1) through

a depressed bi-diretional letter-swith on a

keyboard (2)tothe plugboard(3).Theur-

rent winds through the (unused in this ins-

tane, so shown losed) plug (3), then via

the entry wheel (4) through the wiring of

the three installedrotors(5),and enters the

reetor (6). The reetor returns the ur-

rent, via an entirely dierent path, through

the rotors (5) and entry wheel (4), proee-

ding throughplug 'S'onnetedwith aable

(8) to plug 'D', and another bi-diretional

Season 03 • Episode 16 • The Enigma machine

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In German military usage, ommuniations were divided up into a number of dierent

networks, all using dierent settings for their Enigma mahines. Eah unit operating on

a network was assigned asettings listfor its Enigma for a periodof time. Fora message

to be orretly enrypted and derypted, both sender and reeiver had to set up their

Enigma in the same way; the rotor seletion and order, the starting position and the

plugboard onnetions must be idential. All these settings (together the key in modern

terms) must have been established beforehand, and were distributedin odebooks.

An Enigma mahine's initialstate, the ryptographi key, has several aspets :

•

^{Wheel order (Walzenlage) :the hoie ofrotors and the order inwhihthey are tted.}

•

^{Initialposition of the rotors : hosen by the operator,dierent foreah message.}

•

^{Ring settings} (Ringstellung) : the position of the alphabet ring relative to the rotor wiring.

•

^{Plug settings} (Stekerverbindungen) : the onnetionsof the plugs inthe plugboard.

In fat, the Enigma iphermahine onsists of ve variable features :

1

^{. a plugboard whihan ontain fromzero tothirteen dual-wired ables;}

2

^{. three ordered (left to right) rotors whih wire twenty-six input ontat points to}

twenty-six output ontat pointspositionedonalternate faes of a disk;

3

^{. twenty-six serrations around the periphery of the rotors whih allow the operator}

to speify aninitialrotationalposition for the rotors;

4

^{. a moveable ring oneah of the rotors whih ontrols the rotationalbehaviorof the}

rotor immediatelyto the leftby means of anoth;

5

^{. a reetor half-rotor (whih do not in fat rotate) to fold inputs and outputsbak}

onto the same fae of ontat points.

Your task :

^{Understand the overallworkings of the Enigmamahineand beready toput}

The plugboard ^{Episode 16}

Document Fact sheet 2

An Enigma mahine is an eletro-mehanial rotor mahines

that was used for the enryption and deryption of seret

messages by the German army during World War II. Like

other rotor mahines, the Enigma mahine is a ombination

of mehanial and eletrialsubsystems.

The rst variable omponent was the plugboard. Twenty-six

(A to Z) dual-holed sokets were on the front panel of the

mahine.Adual-wiredplugboardableouldbeinserted ma-

king a onnetion between any pair of letters. Enigma ryp-

tographers had a hoie of how many dierent ables ould

be inserted (from zero to thirteen) and whih letters were

onneted.

A able plaed onto the plugboard onneted letters up in pairs; for example, E and Q

mightbeaonneted pair.The eet wastoswapthoselettersbeforeand afterthe main

rotor srambling unit. For example,when anoperator presses E, the signal was diverted

to Q before entering the rotors. Several suh stekered pairs, up to13, mightbe used at

one time. However, normally only10 pairs were used atany one time.

Theplugboardontributedagreatdealtothestrengthofthemahine'senryption:more

thananextrarotorwouldhavedone.Enigmawithoutaplugboard(known asunstekered

Enigma)anbesolved relativelystraightforwardlyusinghandmethods;these tehniques

are generally defeated by the addition of a plugboard, and Alliedryptanalysts resorted

to speial mahines tosolve it.

Your task :

^{Understandtheworkingsoftheplugboardandndoutthenumberofdierent}

settings therewere, depending onthe number

p

^{ofplugs used. Youwillbethe plugboard}

Rotors inner circuitry

Season 03

Episode 16

Document Fact sheet 3

An Enigma mahine is an eletro-mehanial rotor mahines

that was used for the enryption and deryption of seret

messages by the German army during World War II. Like

other rotor mahines, the Enigma mahine is a ombination

of mehanial and eletrialsubsystems.

The seondvariableomponentwasthe threeordered(leftto

right)rotorswhihonnetedtwenty-six inputontatpoints

to twenty-six output ontat points positioned on alternate

faes of adis.

The rotors (alternatively wheels or drums, Walzen in German) formed the heart of an

Enigma mahine. Eah rotor was a dis approximately 10 m (3.9 in) in diameter with

brass spring-loaded pins on one fae arranged in a irle; on the other side are a or-

responding number of irular eletrial ontats. The pins and ontats represent the

alphabet typially the 26 letters A to Z. When the rotors were mounted side-by-side

on the spindle,the pins of one rotor rest against the ontats of the neighbouring rotor,

forming an eletrial onnetion. Inside the body of the rotor, 26 wires onneted eah

pin on one side to a ontat onthe other in a omplex pattern. Mostof the rotors were

identied by Romannumeralsand eahissued opy ofrotor I waswiredidentiallytoall

other rotors I.

Byitself,arotorwillperformonlyaverysimpletypeofenryptionasimplesubstitution

ipher. Forexample, the pin orresponding tothe letter Emightbewired tothe ontat

for letterTonthe opposite fae,and soon. TheEnigma'somplexity,and ryptographi

seurity, amefrom usingseveral rotorsinseries (usually three)and the regularstepping

movement of the rotors, thus implementinga poly-alphabetisubstitution ipher.

Your task :

^{Understand the inner workings of the rotors and nd out the number of}

dierentsettingstherewereforeahdisk,and forthree onseutive disks.Youwillbethe

inner rotors speialist inyour team.

Rotors positioning ^{Episode 16}

Document Fact sheet 4

An Enigma mahine is an eletro-mehanial rotor mahines

that was used for the enryption and deryption of seret

messages by the German army during World War II. Like

other rotor mahines, the Enigma mahine is a ombination

of mehanial and eletrialsubsystems.

The thirdvariableomponentofEnigma wasthe initialrota-

tional position of the three rotors ontaining the wired diss.

This was speied by the ryptographers and set by the ma-

hine operatorsby means of twenty-six serrations around the

rotor periphery.

The rotors (alternatively wheels or drums, Walzen in German) formed the heart of an

Enigmamahine. Byitself,arotorwillperform onlyaverysimpletypeof enryption a

simple substitution ipher. For example, the pin orresponding to the letter E might be

wiredtotheontatforletterTontheoppositefae,andsoon.TheEnigma'somplexity,

andryptographiseurity,amefromusingseveral rotorsinseries(usuallythreeorfour)

and the regular stepping movement of the rotors, thus implementing a poly-alphabeti

substitution ipher.

When plaed in anEnigma, eah rotor an be set to one of 26 possible positions. When

inserted, it an be turned by hand using the grooved nger-wheel whih protrudes from

theinternalEnigmaoverwhenlosed.Sothattheoperatoranknowtherotor'sposition,

eah had an alphabettyre (orletter ring) attahed tothe outsideof the rotor disk,with

26 haraters (typially letters); one of these ould be seen through the window, thus

indiatingthe rotationalpositionof the rotor.

The Army and Air Fore Enigmas were used with several rotors. From Deember 1938,

therewereve,fromwhihthreewere hosenforinsertioninthemahinefora partiular

operating session. Rotors were marked with Roman numeralsto distinguish them : I, II,

III, IV and V.

Your task :

^{Understand rotors} positioning and nd out the number of dierent settings therewerefor eahdisk,and forthreeonseutivediskshosenamongve possibledisks.

Stepping motion

Season 03

Episode 16

Document Fact sheet 5

An Enigma mahine is an eletro-mehanial rotor mahines

that was used for the enryption and deryption of seret

messages by the German army during World War II. Like

other rotor mahines, the Enigma mahine is a ombination

of mehanial and eletrialsubsystems.

Thefourthvariableomponentofthemahinewasamoveable

ring on eah of the rotors; eah ring ontained a noth in a

spei loation. The purpose of the noth was to fore a

rotation of the rotor immediatelyto the left when the noth

was in apartiular position

The rotors (alternatively wheels or drums,

Walzen in German) formed the heart of an

Enigma mahine. By itself, a rotor will per-

form only a very simple type of enryption

a simple substitution ipher. For example,

the pin orresponding to the letter E might

be wired to the ontat for letter T on the

opposite fae, and soon.

Toavoidmerely implementingasimple(and

easily breakable) substitution ipher, every

key press aused one or more rotors to step

beforethe eletrial onnetions were made,

and so hanged the substitution alphabet

used for enryption. This ensured that the

ryptographisubstitutionwouldbedierent

at eah new rotor position, produing a

more formidablepolyalphabeti substitution

ipher.

Therightmostrotorrotatedeverytimeakeywaspressed.The

rightmost rotor's noth fored a rotation of the middle rotor

one every twenty-six keystrokes. The middle rotor's noth

fored a rotation of the leftmost rotor one every 26 X 26

keystrokes. Sine there were no more rotors, the leftmost ro-

tor's noth had absolutelyno eet whatsoever.

Your task :

^{Understand the rotorsstepping motion and nd out the number of dierent}

settingsthere were forthe positionof the nothes for threeonseutivedisks. Youwillbe

the stepping motionspeialistin your team.

The reflector ^{Episode 16}

Document Fact sheet 6

An Enigma mahine is an eletro-mehanial rotor mahines

that was used for the enryption and deryption of seret

messages by the German army during World War II. Like

other rotor mahines, the Enigma mahine is a ombination

of mehanial and eletrialsubsystems.

The fth and nal variable omponent of Enigma was the

reetor. The reetor had twenty-six ontat points like a

rotor, but only onone fae.

Thereetoronnetedoutputsofthelastrotorinpairs,rediretingurrentbakthrough

the rotors by a dierent route. The reetor ensured that Enigma is self-reiproal :

onveniently, enryption was the same as deryption. However, the reetor also gave

Enigma the property thatno letterever enrypted toitself.This wasasevere oneptual

aw and a ryptologial mistake subsequently exploited by odebreakers.

Thirteen wires internally onneted the twenty-six ontat points together in a series of

pairssothataonnetionomingintothereetorfromtherotorswassentbakthrough

the rotors a seond time by a dierent route. The internal wiring ould be onstruted

in the following fashion. When one end of the rst wire was onneted to ontat point

#1, the other side of the wire had twenty-ve dierent ontat points to whih it ould

beonneted.

Thustherstwireonsumedtwoontatpointsandhadtwenty-vedierentpossibilities.

The seond wire also onsumed two ontat points, and had only twenty-three dierent

onnetion possibilities remaining from the unonsumed ontat points. The third wire

onsumed twomore ontat pointsand had twenty-one possibilitiesfor onnetion.

Your task :

^{Understand therole and workingsof the reetorand nd outthe number of}

Coding and decoding with Enigma

Season 03

Episode 16 Document Exercises

Foreahofthefollowingexerises,youwillhavetosetup apaperEnigmamahinewith:

•

^{a hoie of up to 10plugs, eahone withing twoletters;}

•

^{three rotors from the ve available for pratial purposes you will rst have to ut}

them out and tape two opies of eah rotor side by side;

•

^{the initialposition for eahrotor;}

•

^{the positionofthenothforthe rsttworotors,that isthepositionwhih,wereahed,}

willmake the next rotor move.

Forthe rst twoexerises,the setup willbe given andyouwillhave todeode amessage.

For the lasttwo, you will have to agree on a setup with another group, ode a message,

send it tothe other groupand deode their message. Eahexerise is worth 5 points.

Wewillagreethatthe rstrotorstartsmovingtothe leftafterthe rstletterisoded(or

deoded),and that westart bakfrom theinitialpositionatthe beginningof aeahnew

message. Alsorememberthat the odingand deoding proesses are exatly the same.

Exercise 1 – A simple message with a simple setup

•

^{Use noables.}

•

^{Pik disks I, II III, inthat order.}

•

^{Set the startingpositions as1, 1,1.}

•

^{Set the nothes positionsat 26,26,26.}

•

^{Deode the message NZAZLHICGI NF.}

Exercise 2 – A simple message with a more complicated setup

•

^{Look up the ongurationfor the day 31 onthe overall design sheet.}

•

^{Set up the Enigma mahine aordingly.}

•

^{Deode the message JMFLR PBDBT ZDJH}

Exercise 3 – Coding and decoding a short message

•

^{Agree on a omplete setup with another group, then ode a short message, with less}

than 20haraters.

•

^{Send the iphered message tothe othergroup through the teaher.}

•

^{Deipher the message reeived fromthe othergroup.}

Exercise 4 – Coding and decoding a longer message

•

^{Agree on a omplete setup with another group, then ode a message with at least 60}

haraters.

•

^{Send the iphered message tothe othergroup through the teaher.}

•

^{Deipher the message reeived fromthe othergroup.}

Coding and decoding with Enigma ^{Episode 16}

Document Setup

Disks used :

^{I II III IV V}

Starting position and notch for disk 1 :

^and

Starting position and notch for disk 2 :

^and

Starting position and notch for disk 3 :

^and

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Season 03 • Episode 16 • The Enigma machine

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Document 1

^Rotors

Rotor I

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Rotor II

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Rotor III

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Rotor IV

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Rotor V

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