turing

randaam lokamahaayudhasamayathu blechli paarkkile britiish gavanment coode aandu saifar schoolil ganithashaasthranjanum cryptaanaalistumaaya alaan turing 1942 joolaiyil aavishkaricha oru maanuval coode breaking reethiyaanu turingery allengil turing reethi (peettar eriksan, peettar hilton, donald michi ennivar turingismus ennu kaliyaayi visheshippikkunnu). jarmmankaarude "geheimscriber" (rahasya ezhuthukaaran) yanthrangalilonnaaya essed 40, essed 42 teleprinter rotter stream siffer mesheenukal nirmmicha laurence sifarinte cryptanalysinu ithu upayogichirunnu. britishukaar noonn-mozhs traafikkinu "fish" ennum eee yanthrathil ninnu "tunny" (tyoona malsyathinulla mattoru vaakk) ennum coode namakaranam cheythu.
oru tunie sandesham vaayikkunnathin aadyam sisttathinte yukthisahamaya ghadana ariyappedanam, randaamathaayi chakrangalile sajeevamaaya kaamukalude kaalaakaalangalil marria paatten uruthirinjathaanu, moonnaamathaayi eee sandeshathinulla scrambler chakrangalude prarambha sthaanangal-sandesha qee-sthaapikkappettu. 1942 januvariyil avasaanicha maasangalolam vilyam tute sahapravarthakarum tuniyude yukthisahamaya ghadana thayyarakkiyirunnu. sandesha qee nedunnathine blechli parkkil "setting" ennu vilichirunnu, ennaal kyaam paattenukalude uthbhavamayirunnu-ithu "wheel breaking" ennariyappettirunnu-athaanu turingeryude lakshyam.
ore qee upayogichu onniladhikam sandeshangal kaimaarunnathile jarmman oopparettar pishakukal, oru "depth" srishtikkunnathu, aaa keeyude derivation anuvadichu. kyaam krameekaranangal labhikkunnathin atharam oru pradhana streamilake turingery prayogichu.
sz40 umm sz42 umm.
blechli paarkk cryptaanaalistukal oru yanthram kaanunnathin munbu tunie samvidaanathinte yukthisahamaya pravartthanam nannayi pravarthichirunnu-ithu 1945 ll maathramaan sambhavichathu, europile sakhyakakshikalude vijayathin thottumunbu.
oru vernam stream siffer nadappilaakkiya 12-wheel rotter siffer mesheenukalaayirunnu ezz. isad mesheenukal. avaa saadhaarana laurence teleprintharukalumaayi inn-lainil gadippichirunnu. sandesha aksharangal 5-bitt anthaaraashtra telegraph aksharamaalayilaan encode cheythath. 2 (aii. tii. eiii. 2). ganithashaasthra notteshanil soochippikkunna "exclusive" allengil (soar) function upayogichu inputt pratheekangalumaayi oru syoodoraandam caractor-bye-caractor qee stream samyojippichaan outtputtu seifertext pratheekangal srishtikkappettathu. playin tekst, siffer tekst, cryptographic qee enniva thammilulla bandham ithaanu
athupole, manassilaakkunnathin, playin tekst nalkunnathinu siffer tekst athe keeyumaayi samyojippichu
ore krameekaranangalulla ore mesheene enciferinginum desiferinginum upayogikkaan anuvadikkunnathinulla avashya parasparabandham ithu srishtikkunnu.
oro pratheekatthinum keeyude anchu bittukalil oronnum mesheente rund bhaagangalile prasakthamaaya chakrangal srishtichu. ivaye "chii" (formula _ 3) chakrangal ennum "psi" (formula _ 4) chakrangal ennum vilichirunnu. chii" chakrangal oro pratheekatthinum oru sthaanathu neengi. psi" chakrangalum orumichu neengi, pakshe oro pratheekatthinum sesham allah. rund "myoo" (formula _ 5) allengil "motor" chakrangalaanu avarude chalanathe niyanthrichirunnathu.
essed mesheenukal srishtikkunna qee stream oru "chii" gadakavum oru "psi" gadakavum soar functionumaayi samyojippichu. athinaal, enciferinginulla playin tekstumaayi samyojippicha qee-allengil desiferinginulla siffer tekstumaayi-inipparayunna reethiyil prathinidheekarikkam.
pratheekaathmakamaayi
panthrand chakrangalkk chuttum oru koottam camerakal (allengil "pinnukal") undaayirunnu. eee kaamukal uyarthappettatho thaazhnnatho aaya sthaanathu sajjeekarikkam. uyarnna sthaanathu avar blechli parkkil "×" ennum bainari akkam 1 nuu thulyamaayum ezhuthiya oru "maarkk" srishtichu, thaazhethattil avar "·" ennum bainari akkam 0 nuu thulyamaayum ezhuthiya oru "space" srishtichu. oro chakratthileyum kaamukalude ennam avaye poornna bhramanam poortthiyaakkaan aavashyamaaya preranakalude ennathinu thulyamaayirunnu. eee samkhyakalellaam parasparam qoo-praimaan, ithu paatten aavarthikkunnathin munbu saadhyamaaya ettavum dairkhyameriya samayam nalkunnu. motham 501 kaamukalulla ithu 2501 nuu thulyamaanu, athaayath ekadesham 10151, jyothishaasthraparamaayi oru valia samkhya. ennirunnaalum, anchu preranakale swathanthramaayi kanakkaakkukayaanenkil, samkhyakal kooduthal niyanthrikkaavunnavayaan. eathenkilum jody "chii" chakrangalude bhramana kaalayalavinte gunanaphalam 41 × 31 = 1271 num 26 × 23 = 598 num edayilulla samkhyakal nalkunnu.
vyathyastatha.
cryptaanaalisisil palappozhum pradhana saadhyathakalude oru shreni illaathaakkunnathinulla oru maargam nalkunna eathenkilum tharatthilulla paattenukal kandethunnathu ulppedunnu. blechli parkkil keeyilo seifertextilo aduthulla rund aksharangalude moolyangalude soar samyojanathe vyathyasam ennu vilikkunnu (greak aksharamaaya "deltta" formula _ 8 pratheekappeduthunnu) kaaranam soar modulo 2 kuraykkunnathinu thulyamaanu ("kadam vaangaathe")-koodaathe, aakasmikamaayi, modulo 2 kootticherkkal ("kyaari" illaathe). athinaal, qee (keey) yile pratheekangalkk, vyathyasam formula _ 9 thaazhepparayunna reethiyil labhichu, avide adivarayidunnathu thudarnnulla pratheekatthe soochippikkunnu
(playin tekst, siffer tekst, keeyude rund gadakangal ennivaykku samaanamaayi).
avar thammilulla bandham avar vyathyastharaakumbol baadhakamaan. udaaharanathinu, athupole
ithaanu cases
playin teksttine p umm sipper teksttine z umm prathinidheekarikkunnunde, inipparayunnavayum sariyaanu
oppam
deferencing tuniyilekku oru vazhi nalkiyathinte kaaranam, seifertextile pratheekangalude aavruthi vitharanam kramarahithamaya streamil ninnu verthirichariyaan kazhinjillengilum, keeyude "chii" ghadakam neekkam cheytha seifertexinte oru pathippin ithu shariyalla ennathaanu. kaaranam, plaintextil aavarthichulla aksharavum "psi" chakrangal neengaathathum vyathyasthamaaya "psi" aksharam (formula _ 15) nall pratheekamaayirikkum ("······" allengil 00000), allengil, blechley paarkk padaavaliyil "/". eathenkilum aksharathodoppam soar-edii cheyyumbol, eee shoonyamaaya aksharathinu oru falavumilla, athinaal eee saahacharyangalil, plaintextile formula _ 16. aavarthichulla aksharangal kooduthal pathivaayirunnu, kaaranam jarmman swabhaavasavisheshathakal (ee, tt, ll, ss enniva thaarathamyena saadhaaranamaanu), koodaathe oru saadhaarana telegraph sandeshathile nashtam kaaranam telegraph vidagdhar palappozhum figure-shift, lettar-shift pratheekangal aavarthikkunnath giberishilekku nayichekkaam.
tanniyekkurichulla pothuvaaya report udharikkaan ippol formula _ 9 ennu vilikkappedunna onnil vyathyasthamaaya keeykku saadhaarana keeyil ninnu nedaan kazhiyaatha vivarangal nalkaan kazhiyumenna thathwam turingery avatharippichu. eee soothravaakyam-8 thathwam chakram thakarkkunnathinum krameekaranatthinumulla mikkavarum ellah stattistikkal reethikaludeyum adisthaana adisthaanamaayirikkanam.
bitt level vyathyasam.
aii. tii. eiii. 2 kodinte poornnamaaya 5-bitt pratheekangalil vyathyastatha prayogikkunnathinoppam, ithu vyakthigatha impulsukalilum (bittukal) prayogichu. athinaal, chakrangalude formula _ 19, formula _ 20 ennivayaal encaif cheytha aadyathe impulsinu, onnil vyathyaasamund
randaamathe aavegathinu
angane.
oro impulsinum (aadyathethinu yathaakramam 41 umm 43 umm) "chii", "psi" chakrangalude periodicity athinte formula 9-nte paattenil prathifalikkunnuvennath sradhikkendathaanu. ennirunnaalum, "chii" chakrangal cheythathupole "psi" chakrangal oro inputt pratheekatthinum munneraathathinaal, ithu formula 24-nulla oro 41x43 = 1763 pratheekangalilum paatten aavarthikkuka mathramalla, kooduthal sankeernamaaya oru kramam mathramaayirunnu.
turinginte reethi.
1942 joolaiyil turing gaveshana vibhaagathil eathaanum aazhchakal chelavazhichu. aazhathil ninnu labhicha thacol thakarkkunna prashnatthil addehathinu thaalpparyamundaayirunnu. joolaiyil, thacol neelatthil ninnu kyaam krameekaranangal nedunnathinulla reethi addeham vikasippichu. athil oru aavarthana, eathaandu pareekshanavum pishakumaan prakriya ulppettirunnathu. vyathyasthamaaya "psi" aksharam shoonyamaaya aksharamaayirikkumbol ("······" allengil 00000), allengil mattethenkilum pratheekathodoppam ithu mattilla enna vasthuthaye ithu aasrayichirikkunnu. angane deltta qee caractor anchu "chii" chakrangalude (i.iii. formula _ 16).
deltta "psi" aksharam sharashari samayathinte pakuthiyolam shoonya aksharamayirunnathinaal, formula _ 26 nuu sariyaavaanulla 50 sathamaanam saadhyathayund. oru prathyeka formula _ 9 pratheekatthe aaa sthaanathinte δformula _ 3 aayi kanakkakkiyaanu prakriya aarambhichath. oro "chii" chakratthinum ×, · ennivayude falamaayundaakunna oohaathmaka bitt paatten, keeyil aksharangal ullathra nirakalum formulayude anchu aavegangale prathinidheekarikkunna anchu varikalum adangiya oru paper sheettil rekhappeduthiyittundu. tyoottinte pravartthanatthil ninnulla arivu, oro chakrangaludeyum aanukaalikatha, ithu eee moolyangal backie keeyile uchithamaaya sthaanangalil pracharippikkan anuvadichu.
oro chii chakrangalkkum oronnaayi anchu sheettukalude oru koottavum thayyarakki. ivayil uchithamaaya "chii" chakrathinaayulla kaamukalude ennavumaayi bandhapetta oru koottam nirakal adangiyirunnu, avaye 'kej' ennu vilikkunnu. athinaal 30 enna formulakku atharam 29 nirakalundaayirunnu. formula _ 29 moolyangalude thudarchayaaya 'oohangal' kooduthal anumaanathmaka kyaam avastha moolyangal srishtichu. iva muun anumaanangalodu yojikkukayo viyojikkukayo cheythekkaam, koodaathe eee sheettukalil karaarukaludeyum viyojippukaludeyum ennam rekhappeduthiyittundu. abhiprayavyathyaasangal kararukalekkaal ganyamaayi kooduthalaayirunnuvenkil, soothravaakyam _ 15 aksharam "/" enna shoonya aksharamallenn anumanikkappettu, athinaal prasakthamaaya anumaanam thallikkalanju. kramena, "chii" chakrangalude ellah kyaam krameekaranangalum avayil ninnu "psi", motor wheel kyaam krameekaranangalum kanakkakki.
eee reethi vikasippicheduthappol, yadhaartha 500 allengil athil kooduthal pratheekangalekkaal valare kuranja dairkhyamulla qee upayogichu upayogikkaan anuvadikkunna mechappeduthalukal varuthi.

