n mn hc: An ton v bo mt thng tin Nhm 2

n mn hc: An ton v bo mt thng tin Nhm 2

B GIO DC V O TO

I HC NNG

N MN HC AN TON V BO MT THNG TIN ti:

GIAO THC PHN PHI V THA THUN KHA DIFFIE - HELLMANGing vin:Hc vin:

TS. Nguyn Tn Khi1. Phan Trng

2. Dng Hng Vinh

Nng, thng 03 nm 2015MC LC3LI M U

4CHNG I. GII THIU CHUNG

42.1.M ha thng tin, d liu.

42.1.1.M ha l g?

42.1.2.Cc yu cu i vi m ha.

42.1.3.Phn loi m ha.

52.1.4.Ti sao cn phi m ha?

52.2.M ha cng khai

52.2.1.Gii thiu

62.2.2.Ti sao m ha cng khai ra i

72.2.3.Nguyn tc cu to ca h m ha cng khai.

72.2.4.Cc c im ca h m ha cng khai

82.2.5.Phn bit m ha cng khai vi m ha i xng

82.2.6.ng dng ca h m ha cng khai

9CHNG II. GIAO THC THA THUN KHA DIFFIE HELLMAN.

92.1.Gii thiu.

112.2.Giao thc tha thun kha Diffie Hellman

112.2.1.Khi nim tha thun kha.

112.2.2.Giao thc tha thun kha Diffie - Hellman.

112.2.3.Cch thit lp giao thc tha thun kha Diffie - Hellman.

152.2.4.Cc c im c trng ca giao thc tho thun kha Diffie - Hellman.

172.2.5.Giao thc cho nhm nhiu hn 2 ngi.

19KT LUN

LI M UT xa n nay, trao i thng tin lun l nhu cu cn thit ca con ngi. c bit l trong cuc sng hin i ngy nay, nhu cu trao i thng tin c nng ln mt tm cao mi khi m mng my tnh v Internet pht trin mt cch mnh m v gi vai tr quan trng trong mi lnh vc ca i sng x hi nh: chnh tr, qun s, hc tp, mua sm, kinh doanh, Tt c nhng thng tin c trao i ngy nay u c cc h thng thng tin qun l v truyn i trn h thng mng. i vi nhng thng tin bnh thng th khng ai ch n, nhng i vi nhng thng tin mang tnh cht sng cn i vi mt c nhn hay mt t chc th vn an ton v bo mt thng tin l rt quan trng v c t ln hng u. Chnh v vy nn rt nhiu t chc, c nhn nghin cu, tm kim v a ra rt nhiu gii php bo mt thng tin. Trong m ha d liu v m ha kha cng khai ang t ra rt thch hp rt trong truyn thng tin d liu v c tnh bo mt kh cao. Mt trong nhng vn quan trng ca vic m ha thng tin l qun l cc kha sao cho m bo s b mt v an ton ca d liu c m ha. Ngay t thi k ban u xut hin nhu cu m ha thng tin v cc k thut m ha thng tin, vn bo mt kha c quan tm. Song song vi s pht trin ca cc k thut m ha thng tin, cc k thut qun l kha cng c nhng bc pht trin mnh. Ngy nay, c nhiu k thut m ha d liu rt phc tp, em n hiu qu bo mt thng tin rt cao, bn cnh cng c nhng phng php qun l, phn phi v tha thun kha mang n hiu qu bo mt kha rt cao. Mt trong s cc k thut qun l kha l giao thc phn phi v tha thun kha Diffie-Hellman. S ra i ca giao thc ny l mt bc nhy vt trong s pht trin ca cc k thut m ha thng tin. Nhn thy y l mt k thut nn tng quan trng, nhm quyt nh nghin cu su giao thc phn phi v tha thun kha Diffie Hellman. Trong qu trnh hc tp v nghin cu, nhm nhn c nhiu kin thc qu bu v s h tr t ging vin. Song, mc d tm hiu nhiu ti liu nhng kt qu tm hiu khng trnh khi sai st, rt mong thy v cc anh ch trong lp gp nhm c th hon thin hn qu trnh nghin cu.CHNG I. GII THIU CHUNG2.1. M ha thng tin, d liu.

2.1.1. M ha l g?

Ni n m ha tc l ni n vic che du thng tin bng cch s dng thut ton. Che du y khng phi l lm cho thng tin bin mt m l cch thc chuyn t dngc th c hiu cthnh dngc nhng khng th hiu c. Mt thut ton l mt tp hp ca cc cu lnh m theo chng trnh s bit phi lm th no xo trn hay phc hi li d liu.2.1.2. Cc yu cu i vi m ha.

Confidentiality (Tnh b mt) :m bo cho d liu c truyn i mt cch an ton v khng th b l thng tin nu nh c ai c tnh mun c c ni dung ca d liu gc ban u. Ch nhng ngi c ch nh mi c kh nng c c ni dung thng tin ban u.

Authentication (Tnh xc thc) :Gip cho ngi nhn d liu xc nh c chn chn d liu m h nhn l d liu gc ban u.K gi mo khng th c kh nng gi dng nh l mt ngi khc hay ni cch khc l khng th mo danh gi d liu. Ngi nhn c kh nng kim tra ngun gc thng tin m h nhn c.

Integrity (Tnh ton vn):Gip cho ngi nhn d liu kim tra c rng d liu khng b thay i trong qu trnh truyn i. K gi mo khng th c kh nng thay th d liu ban u bng d liu gi mo.

Non-repudation (Tnh khng th chi b):Ngi gi hay ngi nhn khng th chi b sau khi gi hoc nhn thng tin.

2.1.3. Phn loi m ha.

Phn loi theo cc phng php: M ha c in (Classical cryptography) M ha i xng (Symmetric cryptography). M ha bt i xng (Asymmetric cryptography). Hm bm mt chiu (Hash function)

Phn lai theo s lng kha: M ha kha b mt (Private-key Cryptography) M ha kha cng khai (Public-key Cryptography2.1.4. Ti sao cn phi m ha?

Ngy nay, khi mng Internet kt ni cc my tnh khp ni trn th gii li vi nhau, th vn bo v my tnh khi s thm nhp ph hoi t bn ngoi l mt iu cn thit. Thng qua mng Internet, cc hacker c th truy cp vo cc my tnh trong mt t chc (dng telnet chng hn), ly trm cc d liu quan trng nh mt khu, th tn dng, ti liu Hoc n gin ch l ph hoi, gy trc trc h thng m t chc phi tn nhiu chi ph khi phc li tnh trng hot ng bnh thng.

y l mt phng php h tr rt tt trong vic chng li nhng truy cp bt hp php ti cc thng tin c truyn i trn mng, p dng m ha s khin cho ni dung thng tin c truyn i di dng khng th c c i vi bt k ai c tnh mun ly thng tin .

Tt nhin khng phi ai cng phi dng m ha. Nhu cu v s dng m ha xut hin khi cc bn giao tip mun bo v cc ti liu quan trng hay truyn chng mt cch an ton. Cc ti liu quan trng c th l: ti liu qun s, ti chnh, kinh doanh hoc n gin l mt thng tin no m mang tnh ring t.

2.2. M ha cng khai

2.2.1. Gii thiuM ha kha cng khai (Public Key Cryptography) c thit k sao cho kha s dng trong qu trnh m ha khc bit vi kha c s dng trong qu trnh gii m. Hn th na, kha dng trong qu trnh gii m khng th c tnh ton hay suy lun t kha dng m ha v ngc li, tc l hai kha ny c quan h vi nhau v mt ton hc nhng khng th suy din c ra nhau. Thut ton ny c gi lPublic-Keybi v kha dng cho vic m ha c cng khai cho tt c mi ngi.Mt ngi han ton xa l c th dng kha ny m ha d liu nhng ch duy nht ngi m c kha gii m tng ng mi c th c c d liu m thi. Hnh 1: Cch thc m ha cng khai

2.2.2. Ti sao m ha cng khai ra i

M ha i xng d rng pht trin t c in n hin i, vn tn ti hai im yu sau:

Vn trao i kha gia ngi gi v ngi nhn: Cn phi c mt knh an ton trao i kha sao cho kha phi c gi b mt ch c ngi gi v ngi nhn bit. iu ny t ra khng hp l khi m ngy nay, khi lng thng tin lun chuyn trn khp th gii l rt ln. Vic thit lp mt knh an ton nh vy s tn km v mt chi ph v chm tr v mt thi gian.

Tnh b mt ca kha: khng c c s quy trch nhim nu kha b tit l. Vo nm 1976 Whitfield Diffie v Martin Hellman tm ra mt phng php m ha khc m c th gii quyt c hai vn trn, l m ha kha cng khai (public key cryptography) hay cn gi l m ha cng khai (asymetric cryptography). y c th xem l mt bc t ph quan trng nht trong lnh vc m ha.2.2.3. Nguyn tc cu to ca h m ha cng khai.

M ha kha cng khai ra i gii quyt c vn m m ha ring thiu xt. Trong h thng m ha ny th mi mt ngi s dng khi tham gia vo u c cp 2 kha :

Mt kha dng cho vic m ha d liu (Public key)

V mt kha dng cho vic gii m d liu (Private key),

Trong Public keyc a ra cho tt c mi ngi cng bit, cnPrivate keyphi c gi kn mt cch tuyt i.Gi s hai pha mun truyn tin cho nhau th qu trnh truyn s dng m ha kha cng khai c thc hin nh sau :

- Sender yu cu cung cp hoc t tm kho cng khai ca Receiver trn mt Server chu trch nhim qun l kho cng khai.- Sau hai pha thng nht thut ton dng m ha d liu, Sender s dng kha cng khai ca Receiver cng vi thut ton thng nht m ha thng tin b mt.- Thng tin sau khi m ha c gi ti Receiver, lc ny chnh Sender cng khng th no gii m c thng tin m anh ta m ha (khc vi m ha kha ring).- Khi nhn c thng tin m ha, Receiver s s dng kha b mt ca mnh gii m v ly ra thng tin ban u.

C nhiu phng php m ha thuc loi m ha kha cng khai. l cc phng php Knapsack, RSA, Elgaman, v phng php ng cong elliptic ECC. Mi phng php c cch thc ng dng hm mt chiu khc nhau.2.2.4. Cc c im ca h m ha cng khaiThng thng, cc k thut mt m ha kha cng khai i hi khi lng tnh ton nhiu hn cc k thutm ha kha i xngnhng nhng li im m chng mang li khin cho chng c p dng trong nhiu ng dng. Vy l vi s ra i ca M ha kha cng khai th kha c qun l mt cch linh hot v hiu qu hn. Ngi s dng ch cn bo v kha Private key.H thng ny an ton hn nhiu so vi m ha kha ring, ngi m ha khng th gii m c d liu m ha bng kha cng khai ca ngi khc. Tuy nhin nhc im ca m ha kha cng khai nm tc thc hin, n chm hn m ha kha ring.2.2.5. Phn bit m ha cng khai vi m ha i xng

iu kin cn ca nhng gii thut ny l:

1. Khi mt ngi no c c mt hay nhiu chui bt c m ha, ngi cng khng c cch no gii m c mu tin ban u, tr khi ngi bit c secret key dng cho m ha.

2. Secret key phi trao i mt cch an ton gia hai party tham gia vo qu trnh m ha.

M ha bt i xng l nhng gii thut m ha s dng 2 kha : public key v private-key. Hai kha ny c mt mi lin h ton hc vi nhau. M ha bng kha ny th ch c th gii m bng kha kia. C hai ng dng ca loi m ha ny : M ha bt i xng v ch k in t ( digital signature ).Trong ng dng m ha bt i xng ( v d gii thut RSA )mi bn A, B s c mt public key (PU) private key (PR) ring mnh. A to ra PUA v PRA.B to ra PUB v PRB. PUA s c A gi cho B v khi B mun truyn d liu cho A th B s m ha bng PUA. A s gii m bng PRA. Ngc li nu A mun truyn cho B th A s m ha bng PUB v B gii m bng PRB. PRA v PRB khng bao gi c truyn i v ch c gi ring cho mi bn .

Trong ng dng ch k in t th A s m ha mu tin bng PRA. Bi v ch c A l bit c PRA nn khi mt party no nhn c mu tin ny , party c th bit c mu tin xut pht t A ch khng phi mt ai khc. ng nhin gii m , party cn c PUA.2.2.6. ng dng ca h m ha cng khaiM haEmail hocxc thcngi gi Email (OpenPGPorS/MIME).M ha hoc nhn thc vn bn (Cc tiu chunCh k XML*hocm ha XML*khi vn bn c th hin di dngXML).

Xc thc ngi dng ng dng (ng nhp bng ththng minh, nhn thc ngi dng trongSSL).

Ccgiao thctruyn thng an ton dng k thutBootstrapping(IKE,SSL): trao i kha bng kha bt i xng, cn m ha bng kha i xng.

CHNG II. GIAO THC THA THUN KHA DIFFIE HELLMAN.2.3. Gii thiu.

Hnh 2. Gio s Martin Hellman (gia) cng ng nghip l Whitfield Diffie (phi) khm ph ra mt m kha cng khai Diffie-Hellman.Nm 1976, mt s t ph thay i nn tng c bn trong cch lm vic ca cc h thng mt m ha. chnh l vic cng b ca bi vit phng hng mi trong mt m hc (New Directions in Cryptography) ca Whitfield Diffie v Martin Hellman. Bi vit gii thiu mt phng php hon ton mi v cch thc phn phi cc kha mt m. L h thng u tin s dng "public-key" hoc cc kha mt m "khng i xng", v n c gi l trao i kha Diffie-Hellman (Diffie-Hellman key exchange). Bi vit cn kch thch s pht trin gn nht tc thi ca mt lp cc thut ton mt m ha mi, cc thut ton cha kha bt i xng (asymmetric key algorithms).

Trao i kha Diffie-Hellman b co buc rng n uc pht minh ra mt cch c lp mt vi nm trc trong Tr s Truyn Thng Chnh ph Anh (GCHQ) bi Malcolm J .Williamson). Vo nm 2002, Hellman a ra thut ton c gi chung l trao i kha DiffieHellmanMerkle cng nhn s ng gp ca c Ralph Merkle, ngi pht minh ra thut ton m ha cng khai.

Trc thi k ny, hu ht cc thut ton mt m ha hin i u l nhng thut ton kh i xng (symmetric key gorithms), trong c ngi gi v ngi nhn phi dng chung mt kha, tc kha dng trong thut ton mt m, v c hai ngi u phi gi b mt v kha ny. Tt c cc my in c dng trong th chin II, k c m Caesar v m Atbash, v v bn cht m ni, k c hu ht cc h thng m c dng trong sut qu trnh lch s na u thuc v loi ny. ng nhin, kha ca mt m chnh l sch m (codebook), v l ci cng phi c phn phi v gi gn mt cch b mt tng t.

Do nhu cu an ninh, kha cho mi mt h thng nh vy nht thit phi c trao i gia cc bn giao thng lin lc bng mt phng thc an ton no y, trc khi h s dng h thng (thut ng thng c dng l 'thng qua mt knh an ton'), v d nh bng vic s dng mt ngi a th ng tin cy vi mt cp ti liu c kha vo c tay bng mt cp kha tay, hoc bng cuc gp g mt i mt, hay bng mt con chim b cu a th trung thnh Vn ny cha bao gi c xem l d thc hin, v n nhanh chng tr nn mt vic gn nh khng th qun l c khi s lng ngi tham gia tng ln, hay khi ngi ta khng cn cc knh an ton trao i kha na, hoc lc h phi lin tc thay i cc cha kha-mt thi quen nn thc hin trong khi lm vic vi mt m. C th l mi mt cp truyn thng cn phi c mt kha ring nu, theo nh thit k ca h thng mt m, khng mt ngi th ba no, k c khi ngi y l mt ngi dng, c php gii m cc thng ip. Mt h thng thuc loi ny c gi l mt h thng dng cha kha mt, hoc mt h thng mt m ha dng kha i xng. H thng trao i kha Diffie-Hellman (cng nhng phin bn c nng cp k tip hay cc bin th ca n) to iu kin cho cc hot ng ny trong cc h thng tr nn d dng hn rt nhiu, ng thi cng an ton hn, hn tt c nhng g c th lm trc y.

Mc d, bn thn thut ton l mt giao thc chn kha nc danh (khng cn thng qua xc thc) nhng n cung cp ra mt c s cho cc giao thc xc thc khc nhau kh hon ho.

2.4. Giao thc tha thun kha Diffie Hellman

2.4.1. Khi nim tha thun kha.

Tho thun kho: vic trao i kho gia cc ch th trong mt cng ng no c th c thit lp mt cch t do gia bt c hai ngi no khi c nhu cu trao i thng tin.

2.4.2. Giao thc tha thun kha Diffie - Hellman.

- Trao i kha Diffie Hellman l thit lp mt kha chia s b mt c s dng cho thng tin lin lc b mt bng cch trao i d liu thng qua mng cng cng. y m mt trong s nhiu phng thc dng trao i kha trong ngnh mt m hc.

- Phng php ny khng cn c s can thip ca mt TA ( c quan y thc) lm nhim v iu hnh hoc phn phi kha.

- Phng php ny cho php nhng ngi s dng c th cng nhau to ra mt kha b mt thng qua mt knh truyn thng khng m bo v bo mt. Kha b mt ny s c dng ngi s dng trao i thng tin vi nhau. Tnh hung:

Alice v Bob mun chia s thng tin bo mt cho nhau nhng phng tin truyn thng duy nht ca h l khng an ton. Tt c cc thng tin m h trao i c quan st bi Eve k th ca h.

Lm th no Alice v Bob chia s thng tin bo mt cho nhau m khng lm cho Eve bit c?

Thot nhn ta thy Alice v Bob phi i mt vi mt nhim v khng th. 2.4.3. Cch thit lp giao thc tha thun kha Diffie - Hellman. Gii quyt tnh hung trn: tng c bn:

im ch cht ca tng ny l Alice v Bob trao i mu sn b mt thng qua hn hp sn.

u tin Alice v Bob trn mu bit chung (mu vng) vi mu b mt ring ca mi ngi.

Sau , mi ngi chuyn hn hp ca mnh ti ngi kia thng qua mt knh vn chuyn cng cng.

Khi nhn c hn hp ca ngi kia, mi ngi s trn thm vi mu b mt ca ring mnh v nhn c hn hp cui cng.

Hn hp sn cui cng l hon ton ging nhau cho c hai ngi v ch c ring hai ngi bit. Mu cht y l i vi mt ngi ngoi s rt kh (v mt tnh ton) cho h tm ra c b mt chung ca hai ngi (ngha l hn hp cui cng). Alice v Bob s s dng b mt chung ny m ha v gii m d liu truyn trn knh cng cng. Lu , mu sn u tin (mu vng) c th ty la chn, nhng c tha thun trc gia Alice v Bob. Mu sn ny cng c th c gi s l khng b mt i vi ngi th ba m khng lm l b mt chung cui cng ca Alice v Bob.

tng gii quyt tnh hung trn c th c m t thng qua s sau:

Hnh 3: S giao thc tha thun kha Diffie Hellman s ny, ta thy: u tin, Alice v Bob thng nht v mu sn chung (mu vng), Alice v Bob trao i mu sc c trn ca h. Cui cng, iu ny to ra mt mu b mt ging ht nhau m k khc khng c kh nng to c ra ging vy. K t y, Alice v Bob s trao i bng cch m ha v gii m s dng kha b mt (th hin bng mu sn b mt cui cng). M t giao thc:

Giao thc c th c m t khi quc nh sau:

Thit lp kha:

Alice v Bob tha thun s dng chung mt nhm cyclic hu hn G v mt phn t sinh g ca G. Phn t sinh g cng khai vi tt c mi ngi, k c k tn cng. Di y chng ta gi s nhm G l nhm nhn.

Giao thc s dng nhm nhn s nguyn modulo p, trong p s nguyn t, v g l cn nguyn thy mod p. Khi Alice v Bob mun truyn thng tin bo mt cho nhau c th cng thc hin theo giao thc sau trao i:1. Alice chon ngu nhin s aA (0 aA p-2) b mt, tnh

v gi bA cho Bob

2. Tng t, Bob chn ngu nhin s aB (0 aB p-2) b mt, tnh v gi bB cho Alice.

3. Alice tnh c kha:

4. Bob tnh c kha:

+ By gi Alice v Bob c cng kha chung l:

M ha:

Thng ip m trc khi c gi i bi Alice (hoc Bob) s c m ha thnh mgab. Gii m gii m thng ip m, gi di dng mgab, Bob (hoc Alice) phi tnh c gi tr (gab)-1. Gi tr (gab)-1 c tnh nh sau: V Bob bit |G|, b, v ga, mt khc theo nh l Lagrange trong l thuyt nhm ta c x|G| = 1 vi mi x thuc G, nn Bob tnh c (ga)|G|-b = ga(|G|-b) = ga|G|-ab = ga|G|g-ab = (g|G|)ag-ab=1ag-ab=g-ab=(gab)-1.

Vic gii m by gi tr nn d dng: Bob s dng (gab)-1 tnh v phc hi thng ip nguyn thy bng cch tnh: mgab(gab)-1 = m(1) = m. V d minh ha:

Ta xt v d minh ha sau nm r hn. Trong v d ny, cc gi tr b mt c vit bng mu , cc gi tr khng b mt c vit bng mu xanh1. Alice v Bob thng nht vi nhau chn s nguyn t p = 37 v g = 5. 2. Alice chn mt gi tr ngu nhin bt k aA = 7 v b mt aA. Alice tnh bA = 57 mod 37 = 18. Sau Alice gi bA = 18 cho Bob.

3. Bob chn mt gi tr ngu nhin bt k aB = 5 v b mt aB

Bob tnh bB = 55 mod 37 = 17. Sau Bob gi bB = 17 cho Alice.

4. Bob nhn c bA = 18 v tnh kha chung: KB = 185 mod 37=15, v b mt KB 5. Alice nhn c bB =17 v tnh kha chung: KA = 177 mod 37=15, v b mt KA6. Nh vy Alice v Bob cng chia s b mt chung l s15

Ch l ch c aA, aB v KA, KB l c gi b mt. Tt c cc gi tr cn li nh p, g, bA, bB, u cng khai. Mt khi Alice v Bob tnh c kha b mt dng chung, h c th dng n lm kha m ha ch h bit gi cc thng ip qua cng knh giao tip m. ng nhin, m bo an ton, cc gi tr aA, aB v p cn c ly ln, g khng cn ly gi tr qu ln. Thc t th g thng ly gi tr 2 hoc 5.M t v d trn bng bng sau:AliceBob

B mtCng khaiTnhGiTnhCng khaiB mt

a =7p = 37, g = 5p,gb = 5

a = 7p = 37 g = 5bA = 18bA = gamod p = 18bA p = 37, g = 5b = 5

a = 7p = 37 g = 5bA = 18bBbB = gbmod p = 17p = 37 g = 5bA = 18bB = 17b = 5

a =7,s = 15p, g, bA, bBs = bBamod p = 15s = bAbmod p = 15p, g, bA, bBb = 5,s = 15

2.4.4. Cc c im c trng ca giao thc tho thun kha Diffie - Hellman.

2.4.4.1. Giao thc l an ton i vi vic tn cng th ngGiao thc l an ton i vi vic t n c ng th ng, ngha l mt ngi th b d bit bA v bB s kh m bit c KA,B.

Quay li v d xt. Eve l mt k nghe trm c ta theo di nhng g Alice v Bob gi cho nhau nhng khng th thay i ni dung cc cuc lin lc.

Eve mun ti thit li nhng thng tin bo mt m Alice v Bob chia s cho nhau. Eve s phi i mt vi mt nhim v thc s kh khn.Di y l bng gip xc nh ai bit c gi tr no. (Eve l mt k nghe trm.)

AliceBobEve

B mtCng khaiTnhGiTnhCng khaiB mtBitKhng bit

a =7p = 37, g = 5p,gb = 5p = 37, g = 5a,b

a = 7p = 37 g = 5bA = 18bA = gamod p = 18bA p = 37, g = 5b = 5bA = 5amod 37 = 18

a = 7p = 37 g = 5bA = 18bBbB = gbmod p = 17p = 37 g = 5bA = 18bB = 17b = 5bB = 5bmod 37 = 17

a =7,s = 15p, g, bA, bBs = bBamod p = 15s = bAbmod p = 15p, g, bA, bBb = 5,s = 15s = bBamod p = bAbmod ps

Ta thy Eve ri vo tnh th tin thoi lng nam. C y bit c gi tr ca bA, bB v vy c y bit c , . C y cng bit nhng gi tr ca g v p, nhng li khng bit c cc gi tr ca aA, aB v KA,B

y chnh l bi ton Diffie - Hellman m khi bit bA, bB tm KA,B, bi ton ny tng ng vi bi ton ph m ElGammal. By gi ta i chng minh iu ny. - Php mt m ElGammal vi kho K = (p, g, a, ), trong = ga mod p cho t t mt bn r x v mt s ngu nhin k Zp-1 lp c mt m eK(x, k) = (y1, y2) vi y1 = gk mod p, y2 = xk mod p. V php gii m c cho bi y1 = gk mod p. Gi s ta c thut ton A gii bi ton Diffie-Hellman. Ta s dng A ph m ElGammal nh sau:Cho mt m (y1, y2). Trc tin, dng A cho y1 = gk mod p v = ga mod p ta c A(y1,B) = gka = k mod p. Sau , ta thu c bn r x t k v y2 nh sau:

x = y2(k)-1 mod p.

Ngc li, gi s c mt thut ton khc l B dng ph m EllGamml , tc l .p dng B cho = bA, y1 = bB, y2=1, ta c mod p tc gii c bi ton Diffie Hellman.

Trn thc t cc gi tr ca p, aA, aB l rt ln. Nu p l s nguyn t c t nht 300 ch s, aA v aB c t nht 100 ch s th thm ch ngay c thut ton tt nht c bit n hin nay cng khng th gii uc nu ch bit g, p, bA, bB k c khi s dng tt c kh nng tnh ton ca nhn loi. Bi ton ny cn c bit n vi tn gi bi ton logarit ri rc. Bi ton logarit ri rc vn cn ang gy rt nhiu tranh ci v cha c thut gii c th no.2.4.4.2. Giao thc l khng an ton i vi vic tn cng ch ng.

Giao thc l khng an ton i vi vic tn cng ch ng bng cch nh tro gia ng. Ngha l mt ngi th ba Eve c th nh tro cc thng tin trao i gia Alice v Bob.Chng hn, Eve thay m Alice nh gi cho Bob bi v thay m Bob nh gi cho Alice bi . Nh vy, sau khi thc hin giao thc trao i kho, Alice lp mt kho chung vi Eve m vn tng l vi Bob; ng thi Bob cng lp mt kho chung vi Eve m vn tng l vi Alice. Eve c th gii m mi thng bo m Alice tng nhm l mnh gi n Bob cng nh mi thng bo m Bob tng nhm l mnh gi n Alice.Mt cch khc phc kiu tn cng ny l lm sao Alice v Bob c kim th xc nhn tnh ng n ca cc kho cng khai bA v bB. Ngi ta a vo giao thc trao i kho Diffie-Hellman thm vai tr iu phi ca mt TA c mt h phn phi kho Diffie-Hellman nh mt cch khc phc nhc im ny. Trong h phn phi kho Diffie-Hellman, s can thip ca TA l rt yu, thc ra TA ch lm mi vic l cp chng ch xc nhn kho cng khai cho tng ngi dng ch khng i hi bit thm bt c mt b mt no ca ngi dng. Tuy nhin, nu cha tho mn vi vai tr hn ch ca TA th c th cho TA mt vai tr xc nhn yu hn, khng lin quan g n kho, chng hn nh xc nhn thut ton kim th ch k ca ngi dng, cn bn thn cc thng tin v kho (c b mt ln cng khai) th do cc ngi dng trao i trc tip vi nhau.

2.4.5. Giao thc cho nhm nhiu hn 2 ngi.Giao thc Diffie-Hellman khng gii hn vic tha thun kha ch cho hai bn tham gia. Bt k s lng ngi s dng no cng c th tham gia vo giao thc to kha b mt chung bng cch thc hin lp li cc bc trao i thng tin v tnh ton trong giao thc.

Trc tin xt v d Alice, Bob v Carol cng tham gia giao thc Diffie-Hellman nh sau (tt c tnh ton di y da trn modulo):

Cc bn tha thun trc v cc tham sv.

Mi bn t to kha ring t, gi tn l,, v.

Alice tnhv gi cho Bob.

Bob tnhv gi cho Carol.

Carol tnhv s dng gi tr lm kha b mt chia s.

Bob tnhv gi cho Carol.

Carol tnhv gi cho Alice.

Alice tnhv s dng gi tr lm kha b mt chia s.

Carol tnhv gi cho Alice.

Alice tnhv gi cho Bob.

Bob tnhv s dng gi tr lm kha b mt chia s.

Mt k nghe ln c th quan st c,,,,, v, nhng khng th tn dng c bt c t hp no ca nhng gi tr ny tnh ra c.

C ch ny c th c m rng chongi da vo hai nguyn tc c bn sau:

Bt u giao thc vi mt kha "rng" ch cha. B mt mi bn c to ra bng cch tnh ly tha ca gi tr hin ti lu ti mi bn vi phn ring t ca mi bn (ly tha ca lt u tin chnh l kha cng khai ca mi bn). Nguyn tc ny c th c thc hin theo bt k th t no.

Bt k gi tr tm thi no (vi s lt tnh ttr xung, trong l s lng ngi trong nhm) u c th truyn cng khai, ngoi tr gi tr cui cng ( tnh htlt ly tha) s to thnh b mt chia s (v vy khng c l gi tr ca lt cui cng). Do , mi ngi phi tnh b mt chia s chung bng cch p dng kha ring t ca mnh sau cng (nu khng s khng c cch no cho ngi cui cng truyn c kha cui cng cho ngi nhn, v ngi cui cng s bin kha thnh kha b mt m c nhm mun bo v).2.5. ng dng ca giao thc trao i kha Diffie Hellman

2.3.1. Tha thun kha bng xc thc mt khu chia s mt khu, Alice v Bob c th s dng dngtrao i kha bng xc thc mt khu(PAKE) ca giao thc DiffieHellman phngtn cng ngi ng gia. Mt cch n gin l s dng phn t sinhglm mt khu. c im ca cch ny l k tn cng ch c th th mt mt khu duy nht trong mi ln tng tc vi mt bn, do h thng ny c th cung cp kh nng bo mt tt ngay c vi mt mt khu tng i yu. Gii php ny c m t trong tiu chunX.1035caITU-Tv c s dng trong chun mng my tnh trong nhG.hn.

2.3.2. Kha cng khai

Ngi ta cng c th s dng DiffieHellman nh l mt phn cah tng kha cng khai. Mt cch n gin, kha cng khai ca Alice c t l. gi mt thng ip ti Alice, Bob chn mt s ngu nhinbv gi Alice(khng m ha) cng vi thng ip c m ha vi kha i xng. Ch c Alice mi c th gii m thng ip v ch c c mi c kha ring ta. chng tn cng ngi ng gia, ngi ta c th s dng mt kha cng khai c chia s trc.

Trong thc t, DiffieHellman khng c s dng theo cch ny v thc raRSAl thut ton m ha kha cng khai c dng ph bin nht. L do chnh l do yu t lch s v thng mi, c th lcng ty bo mt RSAto nnnh cung cp chng thc sdng choch k s, sau ny tr thnhVerisign. DiffieHellman khng th dng k chng thc. Tuy nhin, thut tonElGamalvDSAc mi lin h ton hc vi ch k s, cng nh lMQV,STSv thnh phnIKEca b giao thcIPsecdng m bo an ton thng tin chogiao thc Internet.

KT LUN

Sau mt thi gian nghin cu giao thc phn phi v tha thun kha Diffie Hellman. Nhm nm c mt s ni dung quan trng. Vic nng cao bo mt, an ton thng tin l tt yu trong thi i thng tin ngy nay. Cc k thut m ha thng tin khng ngng c pht trin, t k thut m ha c in, n cc k thut m ha i xng v bt i xng. Song song vi s pht trin ca cc k thut m ha l cc k thut qun l, phn phi, tha thun kha gip m bo tnh b mt, an ton ca kha. Giao thc trao i kha Diffie Hellman l k thut nn tng cho nhiu loi giao thc xc thc sau ny. Bn cnh nhng ng dng c bn phn phi v tha thun kha, giao thc Diffie Hellman cn c ng dng trong cc lnh vc tha thun kha bng xc thc mt khu, c s h tng kha cng khai,Qua qu trnh nghin cu, nhm tm hiu c nhiu ni dung. Nhng vn khng trnh khi sai st do cn hn ch v thi gian v chuyn mn. Nhm rt mong nhn c s gp ca thy v cc anh ch nhm c th hon thin bi nghin cu.

Chn thnh cm n.

Trang 20

_1487839714.unknown

_1487839718.unknown

_1487839722.unknown

_1487839724.unknown

_1487839725.unknown

_1487839726.unknown

_1487839723.unknown

_1487839720.unknown

_1487839721.unknown

_1487839719.unknown

_1487839716.unknown

_1487839717.unknown

_1487839715.unknown

_1487839712.unknown

_1487839713.unknown

_1487839711.unknown