
noonn-commutative cryptography

cryptographic aadimangal, reethikal, samvidaanangal enniva ardhagrooppukal, grouppukal, valayangal thudangiya paraspara virudhamaaya beejaganita gadanakale adisthaanamaakkiyulla cryptology mekhalayaanu noonn-commutative cryptography. cryptographic aavasyangalkkaayi oru noonn-commutative beejaganita gadanayude aadyakaala prayogangalilonnu cryptographic protocolukal vikasippikkunnathin braid grouppukalude upayogamaayirunnu. pinneedu thompson grouppukal, polycyclic grouppukal, grigorchukk grouppukal, matricks grouppukal thudangiya mattu niravadhi noonn-commutative gadanakal cryptographic aaplikkeshanukalkkulla saadhyathayulla sthaanaarthikalaayi thiricharinju. noonn-commutative cryptography ninnu vyathyasthamayi, nilavil vyaapakamaayi upayogikkunna rsa cryptosistom, defy-hellman qee exchange, eliptik karvu cryptography thudangiya public-qee cryptosistangal nambar sidhaanthathe adisthaanamaakkiyullathaanu, athinaal commutative beejaganita gadanakale aasrayichirikkunnu.
qee exchange, encryption-decryption, praamaaneekaranam thudangiya vividha cryptographic prasnangal pariharikkunnathin noonn-commutative cryptographic protocolukal vikasippicheduthittundu. eee protocolukal commutative kesil anubandha protocolukalumaayi valare saamyamullathaan.
chila noonn-commutative cryptographic protocolukal.
eee protocolukalil "jii" oru abeel ithara grouppaanennu anumaanikkappedum. w", "a" enniva "g" yude gadakangalaanenkil "w" a "enna notteshan" a − 1wa "enna moolakathe soochippikkum.
qee ekschenchinulla protocolukal.
qoo, liie muthalaayava kaaranam protocol..
qoo, liie muthalaayava kaaranam inipparayunna protocol., alis, bob ennivaykkaayi oru pothu rahasya qee "keey" sthaapikkunnu.
anshell-anshell-goldfeld protocol.
ithu oru noonn-abeeli group "jii" upayogikkunna oru pradhana exchange protocolaanu. qoo, liie muthalaayava kaaranam protocolinte kaaryatthilennapole ithinu "eiii", "bii" ennee rund commuting subgroupukal aavasyamillaathathinaal ithu pradhaanamaan.
stikkalinte qee exchange protocol.
eee protocolinte yadhaartha roopeekaranathil oru parimithamaaya feeldil invertible maatriksukalude grooppaayirunnu group upayogichirunnathu.
encryption decryption vendiyulla protocolukal.
oru rahasya sandesham engane encrypt cheyyaamennum thudarnnu oru noonn-commutative group upayogichu decrypt cheyyaamennum eee protocol vivarikkunnu. bobinu "emm" enna oru rahasya sandesham ayaykkaan alice agrahikkatte.
aadhikaarikathaykkulla protocolukal.
oru sandesham ayachayaal sarikkum alis aano ennu bob parisodhikkatte.
protocolukalude suraksha adisthaanam.
mukalil avatharippicha vividha protocolukalude surakshayudeyum shakthiyudeyum adisthaanam inipparayunna rund prashnangalude budhimuttaanu
konjugasi serch prashnam pariharikkan oru algorithavum ariyillengil, "x" → "u" x "enna functione vann-way functionaayi kanakkakkaam.
plaattphom grouppukal.
oru prathyeka cryptographic protocolil upayogikkunna oru noonn-commutative groupine aaa protocolinte plaattphom group ennu vilikkunnu. chila savisheshathakalulla grouppukale maathrame noonn-commutative cryptographic protocolukal nadappakkunnathinulla plaattphom grouppukalaayi upayogikkaan kazhiyoo. oru prathyeka noonn-commutative cryptographic systethinaayi oru plaattphom groupaayi nirddeshikkappetta oru groupaayi "jii" maaratte. g" ll ninnu prathekshikkunna gunangalude oru pattikayaanu thaazhe koduthirikkunnathu.
plaattphom grouppukalude udaaharanagal.
braid grouppukal.
n" oru positteev poornnasamkhyayaayirikkate. x" 1 ", x" 2 ", ennivayaal srishtikkappedunna oru grouppaanu" b "n" enna braid group. . . , x" "n"-1 thaazhepparayunna avatharanam undu
thompsante samgham.
thaazhepparayunna ananthamaaya avatharanamulla "eph" enna ananthamaaya grouppaanu thompsons groupa
grigorchukkinte samgham.
tii" ennathu ananthamaaya verukalulla bainari treay soochippikkatte. ellah parimithamaaya bainari sequenceukaludeyum koottamaanu varkttisukalude "vii". a" ("t") ennathu "t" yude ellah automorphisangaludeyum koottatthe soochippikkatte. ("tii" ennathinte oru automorphism, connectans nilanirthunna vakkukalude vakkukalaanu.) grigorchukkinte group γ ennathu thaazhepparayunna reethiyil nirvachichirikkunna "a", "b", "c", "d" ennee automorphisangal srishtikkunna "a" ("t") nte upavibhagamaananu
artin group.
oru artin group "a" (γ) inipparayunna avatharanamulla oru grouppaanu
ivide formula _ 12 (formula _ 13 gadakangal), formula _ 14 enniva undu.
matricks grouppukal.
f" oru parimithamaaya feeld ayirikkatte. f" nuu mukalilulla maatriksukalude grouppukal chila noonn-commutative cryptographic protocolukalude plaattphom grouppukalaayi upayogichittundu.

