Breaking The Enigma - Speaker Deck

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Turing Breaking)The)Enigma

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Early&Life

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Turing's)fond)of)the)football)ﬁeld, for)geometric)problems)the) touchlines)yield

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For,%of%course,%the%body%is%a% machine.%It%is%a%vastly%complex% machine,%many,%many%:mes%more% complicated%than%any%machine%ever% made%with%hands;%but%s:ll%a=er%all%a% machine

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Personally*I*think*that*spirit*is*really* eternally*connected*with*ma5er*but* certainly*not*always*by*the*same* kind*of*body...

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...I#did#believe#it#possible#for#a#spirit# at#death#to#go#to#a#universe#en5rely# separate#from#our#own,#but#I#now# consider#that#ma;er#and#spirit#are#so# connected#that#this#would#be#a# contradic5on#in#terms

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Theory'Of'Computa0on

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Any$eﬀec(vely$generated$theory$ capable$of$expressing$elementary$ arithme(c$cannot$be$both$ consistent$and$complete

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The$behaviour$of$the$computer$at$ any$moment$is$determined$by$the$ symbols$which$he$is$observing,$and$ his$'state$of$mind'$at$that$moment...

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...We$will$also$suppose$that$the$ number$of$states$of$mind$which$ need$to$be$taken$into$account$is$ ﬁnite

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A"machine"which"can"read"a" character"at"a"known"point,"and" op2onally"change"state

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A"machine"which"can"write"a" character"at"a"known"point," op1onally"change"state

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A"machine"which"can"move"to"any" known"point"on"a"tape

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$automaton = new Automaton( 1, // initial state [2], // acceptable, final states new Rulebook([ new Rule(1, "a", 1), new Rule(1, "b", 2), new Rule(2, "b", 2), new Rule(2, "a", 1), ]) )

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assertFalse( $automaton->hasAcceptableState() ); $automaton->readCharacter("a")->readCharacter("b"); assertTrue( $automaton->hasAcceptableState() );

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github.com/turingphp

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new Rulebook([ new Rule(1, "a", 1), new Rule(1, "b", 2), new Rule(2, "b", 2), new Rule(2, "a", 1), ]) Given&the&sequence&ababb: Start%in%state%1 Read%a%and%stay%in%state%1 Read%b%and%move%to%state%2 Read%a%and%move%to%state%1 Read%b%and%move%to%state%2 Read%b%and%stay%in%state%2

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All#complex#machines#can#be# deﬁned#in#terms#of#the#simplest# Determinis6c#Finite#Automaton

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Understanding+Computa1on, by+Tom+Stuart

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Enigma

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$machine = new Machine( [ new Rotor( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "EKMFLGDQVZNTOWYHXUSPAIBRCJ", 0 ), new Rotor( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "AJDKSIRUXBLHWTMCQGZNPYFVOE", 0 ), new Rotor( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "BDFHJLCPRTXVZNYEIWGAKMUSQO", 0 ) ], new Reflector( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "FVPJIAOYEDRZXWGCTKUQSBNMHL" ) );

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// first rotor new Rotor( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "EKMFLGDQVZNTOWYHXUSPAIBRCJ", 0 )

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EKMFLG...IBRCJ-→-KMFLG...BRCJE

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// second rotor new Rotor( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "AJDKSIRUXBLHWTMCQGZNPYFVOE", 0 )

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// third rotor new Rotor( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "BDFHJLCPRTXVZNYEIWGAKMUSQO", 0 )

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new Reflector( "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "FVPJIAOYEDRZXWGCTKUQSBNMHL" )

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And$the$return$trip: B"→"A"→"A"→"T So#we#press#A#and#T#lights#up...

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A!→!K!→!L!→!V!→!B!→!A!→!A!→!T T!→!A!→!A!→!B!→!V!→!L!→!K!→!A