Bài Tập Lớn Nhóm 10 - Copy

BI TP LN

CH K RSA

Li Cm n c c mt bi bo co b ch, hiu qu, hon chnh v t kt qu tt p trc ht nhm em xin gi ti ton th cc thy c khoa cng ngh thng tin li chc sc khe, li cho chn trng v li cm n su sc nht. Vi s quan tm, dy d ch bo tn tnh chu o ca cc thy c, s gip nhit tnh ca cc bn, n nay nhm em c th hon thnh bi bo co, ti: Ch K RSA. c c kt qu ny nhm em xin c bit gi li cm n chn thnh nht ti c gio b mn an ton bo mt thng tin quan tm gip , vch k hoch hng dn nhm em hon thnh mt cch tt nht bi bo co trong thi gian qua. Vi iu kin thi gian c hn cng nh kinh ghim cn hn ch ca mt sinh vin nn bi bo co s khng trnh khi nhng thiu st. Nhm em rt mong nhn c s ch bo, ng gp kin ca cc thy c cng ton th cc bn nhm em c iu kin b sung, nng cao thc ca mnh, phc v tt hn cng tc thc t sau ny.

Nhm 10: ng nh T Nguyn Trng Ti

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BI TP LN

CH K RSA

Mc LcLi m u................................................................................................3 Chng I: Tng quan v bo mt........................................................................4 I. Gii thiu chung v bo mt thng tin..........................................................................4 1. M u v bo mt thng tin......................................................................................................4 2. Nguy c v him ha i vi h thng thng tin.......................................................................6 3. Phn loi tn cng ph hoi an ton...........................................................................................6 II. Dch v c ch tn cng.............................................................................................7 1. Cc dch v an ton................................................................................................................. ..7 2. Cc c ch an ton................................................................................................................. ...7 3. Tn cng ph hoi an ninh.......................................................................................................8 III. Mc tiu v nguyn tc chung ca an ton bo mt......................................................................8 Chng II: Gii thiu v ngnh ch k in t.......................................................................................9 I. Gii thiu..................................................................................................................... .....................9 II. Lch s ngnh ch k in t.....................................................................................................11 III. Cc u im ca ch k in t................................................................................................12


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BI TP LN

CH K RSA

1. Kh nng xc nh ngun gc..............................................................................................12 2. Tnh ton vn................................................................................................................. ........13 3. Tnh khng th ph nhn.....................................................................................................13 IV. Thc hin ch k s kha cng khai........................................................................................13 V. Mt vi ch k in t................................................................................................................14 Chng III: Ch k RSA............................................................................................................15 I. Gii thiu ch k RSA.....................................................................................................15 II. Thut ton..................................................................................................................... ..............15 III. V d...................................................................................................................... ......................16 IV. Chun ch k s(bn ci tin ca ch k RSA)..........................................................18


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BI TP LN

CH K RSA

Li m uTrong mt m vn bo mt lun i i vi vn xc thc thng tin, c bit trong h thng m kho cng khai vn xc thc l v cng quan trng. gii quyt c vn xc thc ngi ta a ra mt cch va n gin va hiu qu l s dng ch k s. Vic s dng ch k s ngy cng c nhiu ng dng trong thc t, khng ch gii hn trong Ngnh Cng Ngh Thng Tin , Ngnh Mt M m cn c p dng trong mt s lnh vc khc nh trong lnh vc Ngn Hng xc thc ngi g, ngi nhn, lnh vc Vin thng s dng cc th thng minh. Vi mt m kho cng khai vic to ra ch k s v ng dng vo cc ti liu, cc vn bn in t l v cng quan trng. Ch k thng ( Ch k vit tay ) th c th gi mo c , vy th ch k s phi m bo nhng yu cu g c th to c s php l trong thi i Thng tin Tin hc ho. Ch k s phi c nhng tnh nng sau : 1. 2. 3. Ngi nhn vn bn k phi c th xc minh c bt k ch k hp l no ca ngi gi. Ch k khng th gi mo c Ngi k thng bo th khng th t chi ph nhn n v sau c

Mc ch ca bi bo co l gii thiu v ch k s Elgamal , y l mt trong nhng s mnh vo bc nht hin nay, v c nhiu nc trn th gii ng dng , c bit l ti M c bn ci tin ca s ny v c Vin tiu chun v Cng ngh quc gia M (NIST) chp nhn lm chun ch k s . im mnh v an ton ca s ch k s Elgamal l da trn tnh kh gii ca bi ton tm Logarithm ri rc trn trng hu hn Zp , y l mt bi ton m cho n nay cha c mt thut ton no gii n, song bi ton ngc ly lu tha li c th tnh ton hiu qu theo thut ton bnh phng v nhn. Ni cch khc , lu tha theo modulo p l hm mt chiu vi cc s nguyn t p thch hp.


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BI TP LN

CH K RSA

Chng ITNG QUAN V BO MTI. Gii thiu chung v bo mt thng tin 1. M u v bo mt thng tin Ngy nay vi s pht trin bng n ca cng ngh thng tin, hu ht cc thng tin ca doanh nghip nh chin lc kinh doanh, cc thng tin v khch hng, nh cung cp, ti chnh, mc lng nhn vin,u c lu tr trn h thng my tnh. Cng vi s pht trin ca doanh nghip l nhng i hi ngy cng cao ca mi trng kinh doanh yu cu doanh nghip cn phi chia s thng tin ca mnh cho nhiu i tng khc nhau qua Internet hay Intranet. Vic mt mt, r r thng tin c th nh hng nghim trng n ti chnh, danh ting ca cng ty v quan h vi khch hng. Cc phng thc tn cng thng qua mng ngy cng tinh vi, phc tp c th dn n mt mt thng tin, thm ch c th lm sp hon ton h thng thng tin ca doanh nghip. V vy an ton v bo mt thng tin l nhim v rt nng n v kh on trc c, nhng tu trung li gm ba hng chnh sau: - Bo m an ton thng tin ti my ch - Bo m an ton cho pha my trm - Bo mt thng tin trn ng truyn ng trc yu cu bo mt thng tin, ngoi vic xy dng cc phng thc bo mt thng tin th ngi ta a ra cc nguyn tc v bo v d liu nh sau: - Nguyn tc hp php trong lc thu thp v x l d liu. - Nguyn tc ng n. - Nguyn tc ph hp vi mc ch. - Nguyn tc cn xng. - Nguyn tc minh bch. - Nguyn tc c cng quyt nh cho tng c nhn v bo m quyn truy cp cho ngi lin quan. - Nguyn tc khng phn bit i x. - Nguyn tc an ton. - Nguyn tc c trch nim trc php lut. Nhm 10: ng nh T Nguyn Trng TiPage 5

BI TP LN

CH K RSA

- Nguyn tc gim st c lp v hnh pht theo php lut. - Nguyn tc mc bo v tng ng trong vn chuyn d liu xuyn bin gii. y chng ta s tp trung xem xt cc nhu cu an ninh v ra cc bin php an ton cng nh vn hnh cc c ch t c cc mc tiu . Nhu cu an ton thng tin: An ton thng tin thay i rt nhiu trong thi gian gn y. Trc kia hu nh ch c nhu cu bo mt thng tin, nay i hi thm nhiu yu cu mi nh an ninh my ch v trn mng. Cc phng php truyn thng c cung cp bi cc c ch hnh chnh v phng tin vt l nh ni lu tr bo v cc ti liu quan trng v cung cp giy php c quyn s dng cc ti liu mt . My tnh i hi cc phng php t ng bo v cc tp v cc thng tin lu tr. Nhu cu bo mt rt ln v rt a dng, c mt khp mi ni, mi lc. Do khng th khng ra cc qui trnh t ng h tr bo m an ton thng tin. Vic s dng mng v truyn thng i hi phi c cc phng tin bo v d liu khi truyn. Trong c c cc phng tin phn mm v phn cng, i hi c nhng nghin cu mi p ng cc bi ton thc tin t ra. Cc khi nim:

An ton my tnh: tp hp cc cng c c thit k bo v d liu v chng hacker.

An ton mng: cc phng tin bo v d liu khi truyn chng. An ton Internet: cc phng tin bo v d liu khi truyn chng trn tp cc mng lin kt vi nhau. Mc ch ca mn hc l tp trung vo an ton Internet gm cc phng tin bo v, chng, pht hin, v hiu chnh cc ph hoi an ton khi truyn v lu tr thng tin.

Nguy c v him ha i vi h thng thng tin Cc him ha i vi h thng c th c phn loi thnh him ha v tnh hay c , ch ng hay th ng.2.


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BI TP LN

CH K RSA

Him ha v tnh: khi ngi dng khi ng li h thng ch c quyn, h c th ty chnh sa h thng. Nhng sau khi hon thnh cng vic h khng chuyn h thng sang ch thng thng, v tnh k xu li dng. Him ha c : nh c tnh truy nhp h thng tri php. Him ha th ng: l him ha nhng cha hoc khng tc ng trc tip ln h thng, nh nghe trm cc gi tin trn ng truyn. Him ha ch ng: l vic sa i thng tin, thay i tnh trng hoc hot ng ca h thng. i vi mi h thng thng tin mi e da v hu qu tim n l rt ln, n c th xut pht t nhng nguyn nhn nh sau: T pha ngi s dng: xm nhp bt hp php, n cp ti sn c gi tr Trong kin trc h thng thng tin: t chc h thng k thut khng c cu trc hoc khng mnh bo v thng tin. Ngay trong chnh sch bo mt an ton thng tin: khng chp hnh cc chun an ton, khng xc nh r cc quyn trong vn hnh h thng. Thng tin trong h thng my tnh cng s d b xm nhp nu khng c cng c qun l, kim tra v iu khin h thng. Nguy c nm ngay trong cu trc phn cng ca cc thit b tin hc v trong phn mm h thng v ng dng do hng sn xut ci sn cc loi 'rp' in t theo nh trc, gi l bom in t. Nguy him nht i vi mng my tnh m l tin tc, t pha bn ti phm. 3. Phn loi tn cng ph hoi an ton: Cc h thng trn mng c th l i tng ca nhiu kiu tn cng: Tn cng gi mo l mt thc th tn cng gi danh mt thc th khc. Tn cng gi mo thng c kt hp vi cc dng tn cng khc nh tn cng chuyn tip v tn cng sa i thng bo. Tn cng chuyn tip xy ra khi mt thng bo, hoc mt phn thng bo c gi nhiu ln, gy ra cc tc ng tiu cc. Tn cng sa i thng bo xy ra khi ni dung ca mt thng bo b sa i nhng khng b pht hin. Tn cng t chi dch v xy ra khi mt thc th khng thc hin chc nng ca mnh, gy cn tr cho cc thc th khc thc hin chc nng ca chng. Tn cng t bn trong h thng xy ra khi ngi dng hp php c tnh hoc Nhm 10: ng nh T Nguyn Trng TiPage 7

BI TP LN

CH K RSA

v can thip h thng tri php. Cn tn cng t bn ngoi l nghe trm, thu chn, gi mo ngi dng hp php v vt quyn hoc lch qua cc c ch kim sot truy nhp. Tn cng b ng: Do thm, theo di ng truyn nhn c ni dung bn tin hoc theo di lung truyn tin. Tn cng ch ng: Thay i lung d liu gi mo mt ngi no , lp li bn tin trc, thay i ban tin khi truyn, t chi dch v. II. Dch v c ch tn cng Nhu cu thc tin dn n s cn thit c mt phng php h thng xc nh cc yu cu an ninh ca t chc. Trong cn c tip cn tng th xt c ba kha cnh ca an ton thng tin: bo v tn cng, c ch an ton v dch v an ton. Sau y chng ta xt chng theo trnh t ngc li: 1. Cc dch v an ton. y l cng c m bo an ton ca h thng x l thng tin v truyn thng tin trong t chc. Chng c thit lp chng li cc tn cng ph hoi. C th dng mt hay nhiu c ch an ton cung cp dch v. Thng thng ngi ta cn phi to ra cc lin kt vi cc ti liu vt l: nh c ch k, ngy thng, bo v cn thit chng khm ph, sa by, ph hoi, c cng chng, chng kin, c ghi nhn hoc c bn quyn. 2. Cc c ch an ton T cc cng vic thc t chng li cc ph hoi an ninh, ngi ta t h thng v sp xp li to thnh cc c ch an ninh khc nhau. y l c ch c thit k pht hin, bo v hoc khi phc do tn cng ph hoi. Khng c c ch n l no p ng c mi chc nng yu cu ca cng tc an ninh. Tuy nhin c mt thnh phn c bit nm trong mi c ch an ton l: k thut m ho. 3. Tn cng ph hoi an ninh Ta xc nh r th no l cc hnh ng tn cng ph hoi an ninh. l mi hnh ng chng li s an ton thng tin ca cc t chc. An ton thng tin l bn v bng cch no chng li tn cng vo h thng thng tin hoc pht hin ra chng. Trn thc t c rt nhiu cch v nhiu kiu tn cng khc nhau. Thng thut ng e do v tn cng c dng nh nhau. Cn tp trung chng mt s kiu tn cng chnh: th ng v ch ng. Nhm 10: ng nh T Nguyn Trng TiPage 8

BI TP LNIII.

CH K RSA

Mc tiu v nguyn tc chung ca an ton bo mt Ba mc tiu ca an ton bo mt thng tin: Tnh b mt: Tai san cua h thng ch c truy cp bi nhng ngi c thm quyn. Cac loai truy cp gm c: oc (reading), xem (viewing), in n (printing), s dung chng trinh, hoc hiu bit v s tn tai cua mt i tng trong t chc.Tinh bi mt c th c bao v nh vic kim soat truy cp (theo nhiu kiu khac nhau) hoc nh cac thut toan ma ha d liu. Kim soat truy cp chi co th c thc hin vi cac h thng phn cng vt ly. Cn i vi cac d liu cng cng th thng phng phap hiu qua la cac phng phap cua mt ma hoc.-

Tinh toan ven d liu: tai san cua h thng ch c thay i bi nhng ngi c thm quyn.-

Tinh sn dng: tai san lun sn sang c s dung bi nhng ngi c thm quyn. Hai nguyn tc cua an toan bao mt thng tin: Vic thm nh v bao mt pha i la kho va cn tinh ti tt ca cac tinh hung , kha nng tn cng c th c thc hin.-

Tai san c bao v cho ti khi ht gi tri s dung hoc ht y ngha bi mt.

Chng IIGii Thiu V Ngnh Ch K in TI. Gii thiu Hng ngy, chng ta vn thng hay dng ch k xc minh mt vn , hay xc nhn quyn ca mnh i vi mt vt thng nhng giy t hoc hp ng no . Chng hn nh tn mt bc in nhn tin t ngn hng, hay nhng hp ng Nhm 10: ng nh T Nguyn Trng TiPage 9

BI TP LN

CH K RSA

k kt mua bn, chuyn nhng Nhng ch k l ch k vit tay. Nhng yu t no lm nn sc thuyt phc ca n ? V mt l tng: - Ch k l bng chng th hin ngi k c ch nh k vn bn - Ch k th hin ch quyn , n lm cho ngi nhn vn bn bit rng ai ch th l ngi k vn bn - Ch k khng th ti s dng c , tc l n l phn ca vn bn m khng th sao chp sang vn bn khc - Vn bn k khng th thay i c - Ch k khng th gii mo v cng l th khng th chi b Trong cuc sng, mi th khng din ra theo ng m hnh l tng nu trn, nhng vi kh nng kim nh st sao th vic lm khc i khng phi l d. Chng ta c l do mang m hnh ny vo th gii my tnh, nhng c nhng kh khn hin nhin: cc dng thng tin trn my tnh c sao chp mt cch qu d dng, hnh nh ca ch k tay ca mt ngi no d kh bt chc ti u cng d dng sao chp t vn bn ny sang vn bn khc c cc c tnh nh m t trn , giao thc k trong th gii in t cn ti s h tr ca cng ngh m ha. l ch k in t(electronic signature) V cn bn, ch k in t cng ging nh ch vit tay. Chng ta dng n xc nhn li ha hay cam kt ca mnh v sau khng th rt li c. Ch k in t khng i hi phi s dng giy mc, n gn c im nhn dng ca ngi k vo mt bn cam kt no . C c mt bn chng nhn in t cng ging nh dng bng li xe xc nhn nhn dng ca mnh. Bn c th thi ly c bng li xe ti H Ni nhng n li cho php bn iu khin phng tin ti TP HCM. Tng t nh vy, bn chng nhn in t l vt khng nh nhn dng ca bn trn Internet vi nhng ngi chp nhn n. Nhm 10: ng nh T Nguyn Trng TiPage 10

BI TP LN

CH K RSA

Ch k in t (ting anh: electronic signature) l thng tin i km theo d liu (vn bn, hnh nh, video...) nhm mc ch xc nh ngi ch ca d liu . Ch k in t c s dng trong cc giao dch in t. Xut pht t thc t, ch k in t cng cn m bo cc chc nng: xc nh c ngi ch ca mt d liu no : vn bn, nh, video, ... d liu c b thay i hay khng. Hai khi nim ch k s (digital signature) v ch k in t (electronic signature) thng c dng thay th cho nhau mc d chng khng hon ton c cng ngha. Ch k s ch l mt tp con ca ch k in t (ch k in t bao hm ch k s) Tuy nhin cc ch k tha mn hai iu kin c bn sau: - Khng th gi mo. Nu P k thng bao M bng ch k S(P,M) th khng mt ai c th to c cp [M,S(M,P)] - Xc thc. Nu R nhn c cp [M,S(M,P)] c coi l ca R th R c th kim tra c rng ch k c thc s l ca P hay khng? Ch c P mi c th to ra c ch k ny v ch k c gn cht vi M. Hai yu cu u tin ny l nhng tr ngi chnh trong giao dch qua my tnh. Hai tnh cht b tr sau l nhng tnh cht mong mun i vi giao dch c hon tt nh ch k s: + khng th thay i. Sau khi c pht M khng th thay i bi S, R, hoc bi mt k thu trm no. +khng th s dng li. Mt thng bo trc c a ra s ngay lp tc b R pht hin. Mt s ch k s thng cha hai thnh phn: thut ton k v thut ton xc minh. Ngi A c th k bc in x dng thut ton an ton. Ch k Sig(x) nhn c c th kim tra bng thut ton xc minh cng khai Ver. Khi cho trc cp Nhm 10: ng nh T Nguyn Trng TiPage 11

BI TP LN

CH K RSA

(x,y) thut ton xc minh cho gi tr TRUE hay FALSE ty thuc vo vic ch k c xc minh nh th no. II. Lch s Ch k in t l thng tin i km theo d liu (vn bn, hnh nh, video...) nhm mc ch xc nh ngi ch ca d liu . Ta cng c th s dng nh ngha rng hn, bao hm c m nhn thc, hm bm v cc thit b bt in t. Ch k s kha cng khai (hay h tng kha cng khai) l m hnh s dng cc k thut mt m gn vi mi ngi s dng mt cp kha cng khai - b mt v qua c th k cc vn bn in t cng nh trao i cc thng tin mt. Kha cng khai thng c phn phi thng qua chng thc kha cng khai. Qu trnh s dng ch k s bao gm 2 qu trnh: to ch k v kim tra ch k. Khi nim ch k in t - mc d thng c s dng cng ngha vi ch k s nhng thc s c ngha rng hn. Ch k in t ch n bt k phng php no (khng nht thit l mt m) xc nh ngi ch ca vn bn in t. Ch k in t bao gm c a ch telex v ch k trn giy c truyn bng fax. Con ngi s dng cc hp ng di dng in t t hn 100 nm nay vi vic s dng m Morse v in tn. Vo nm 1889, ta n ti cao bang New Hampshire (Hoa k) ph chun tnh hiu lc ca ch k in t. Tuy nhin, ch vi nhng pht trin ca khoa hc k thut gn y th ch k in t mi i vo cuc sng mt cch rng ri. Vo thp k 1980, cc cng ty v mt s c nhn bt u s dng my fax truyn i cc ti liu quan trng. Mc d ch k trn cc ti liu ny vn th hin trn giy nhng qu trnh truyn v nhn chng hon ton da trn tn hiu in t. Hin nay, ch k in t c th bao hm cc cam kt gi bng email, nhp cc s nh dng c nhn (PIN) vo cc my ATM, k bng bt in t vi thit b mn hnh cm ng ti cc quy tnh tin, chp nhn cc iu khon ngi dng (EULA) khi ci t phn mm my tnh, k cc hp ng in t online. III. Cc u im ca ch k in t Nhm 10: ng nh T Nguyn Trng TiPage 12

BI TP LN1. Kh nng xc nh ngun gc

CH K RSA

Cc h thng mt m ha kha cng khai cho php mt m ha vn bn vi kha b mt m ch c ngi ch ca kha bit. s dng ch k s th vn bn cn phi c m ha bng hm bm (vn bn c "bm" ra thnh chui, thng c di c nh v ngn hn vn bn) sau dng kha b mt ca ngi ch kha m ha, khi ta c ch k s. Khi cn kim tra, bn nhn gii m (vi kha cng khai) ly li chui gc (c sinh ra qua hm bm ban u) v kim tra vi hm bm ca vn bn nhn c. Nu 2 gi tr (chui) ny khp nhau th bn nhn c th tin tng rng vn bn xut pht t ngi s hu kha b mt. Tt nhin l chng ta khng th m bo 100% l vn bn khng b gi mo v h thng vn c th b ph v. Vn nhn thc c bit quan trng i vi cc giao dch ti chnh. Chng hn mt chi nhnh ngn hng gi mt gi tin v trung tm di dng (a,b), trong a l s ti khon v b l s tin chuyn vo ti khon . Mt k la o c th gi mt s tin no ly ni dung gi tin v truyn li gi tin thu c nhiu ln thu li (tn cng truyn li gi tin). 2. Tnh ton vn C hai bn tham gia vo qu trnh thng tin u c th tin tng l vn bn khng b sa i trong khi truyn v nu vn bn b thay i th hm bm cng s thay i v lp tc b pht hin. Qu trnh m ha s n ni dung ca gi tin i vi bn th 3 nhng khng ngn cn c vic thay i ni dung ca n. Mt v d cho trng hp ny l tn cng ng hnh (homomorphism attack): tip tc v d nh trn, mt k la o gi 1.000.000 ng vo ti khon ca a, chn gi tin (a,b) m chi nhnh gi v trung tm ri gi gi tin (a,b3) thay th lp tc tr thnh triu ph!Nhng l vn bo mt ca chi nhnh i vi trung tm ngn hng khng hn lin quan n tnh ton vn ca thng tin gi t ngi gi ti chi nhnh, bi thng tin c bm v m ha gi n ng ch ca n tc chi nhnh, vn cn li vn bo mt ca chi nhnh ti trung tm ca n.3. Tnh khng th ph nhn

Trong giao dch, mt bn c th t chi nhn mt vn bn no l do mnh gi. ngn nga kh nng ny, bn nhn c th yu cu bn gi phi gi Nhm 10: ng nh T Nguyn Trng TiPage 13

BI TP LN

CH K RSA

km ch k s vi vn bn. Khi c tranh chp, bn nhn s dng ch k ny nh mt chng c bn th ba gii quyt. Tuy nhin, kha b mt vn c th b l v tnh khng th ph nhn cng khng th t c hon ton. IV. Thc hin ch k s kha cng khai Ch k s kha cng khai da trn nn tng mt m ha kha cng khai. c th trao i thng tin trong mi trng ny, mi ngi s dng c mt cp kha: mt cng khai v mt b mt. Kha cng khai c cng b rng ri cn kha b mt phi c gi kn v khng th tm c kha b mt nu ch bit kha cng khai. Ton b qu trnh gm 3 thut ton:

Thut ton to kha Thut ton to ch k s Thut ton kim tra ch k s

Xt v d sau: Bob mun gi thng tin cho Alice v mun Alice bit thng tin thc s do chnh Bob gi. Bob gi cho Alice bn tin km vi ch k s. Ch k ny c to ra vi kha b mt ca Bob. Khi nhn c bn tin, Alice kim tra s thng nht gia bn tin v ch k bng thut ton kim tra s dng kha cng cng ca Bob. Bn cht ca thut ton to ch k m bo nu ch cho trc bn tin, rt kh (gn nh khng th) to ra c ch k ca Bob nu khng bit kha b mt ca Bob. Nu php th cho kt qu ng th Alice c th tin tng rng bn tin thc s do Bob gi. Thng thng, Bob khng mt m ha ton b bn tin vi kha b mt m ch thc hin vi gi tr bm ca bn tin . iu ny khin vic k tr nn n gin hn v ch k ngn hn. Tuy nhin n cng lm ny sinh vn khi 2 bn tin khc nhau li cho ra cng mt gi tr bm. y l iu c th xy ra mc d xc sut rt thp. V. Mt vi ch k in t-

Full Domain Hash, RSA-PSS ..., da trn RSA. Chun ch k in t DSA.Page 14


BI TP LN-

CH K RSA

Ch k s ECDSA. H ch k in t ElGamal. Undeniable signature (ch k chng chi b). Ch k s SHA (thng thng l SHA-1). H ch k in t RSA.


Page 15

BI TP LN

CH K RSA

Chng IIICh k ELGAMALI. Gii thiu ch k ELGAMAL H ch ky ElGammal c a ra vao 1985. Mt phin ban sa i h nay c Hoc vin Quc gia tiu chun va ky thut (NIST) a ra nh mt chun cua ch ky in t. S ch k ElGama c thit k vi mc ch dnh ring cho ch k s, im mnh ca n l cng s nguyn t p trong cng mt s th vi R l ngu nhin nn ta c th c nhiu ch k s. iu ny c ngha l c nhiu ch k hp l trn bc in cho trc bt k. Thut ton xc minh phi c kh nng chp nhn bt k ch k hp l no khi xc thc ch k .

II. Thut ton Sinh kha: - chn mt s nguyn t ln p. - chn phn t sinh .-

chn ngu nhin Ks Zp v tnh Kp= Ks mod p

cng khai Kp, p, . -

K:

- Chn ngu nhin r sao cho UCLN(r,p-1)= 1 Tnh r-1: r*r-1 1 mod (p-1) - Yu t xc thc ha: y= eKp(x,r) = (, ). Trong , c tnh: = r mod p = (x - Ks*)*r-1 mod (p - 1) Xc thc:Page 16


BI TP LNBn B tnh:

CH K RSA

Z= (Kp) * mod p, nu Z = x mod p l ng, Z x mod p l sai. Nu ch k c thit lp ng th xc minh s thnh cng v: (Kp) * (Ks) * (r) mod p x mod p Bn B tnh ch k bng cch dng c gii tr mt Kp ln s ngu nhin mt r(gia tri ky bc in). Vic xc minh c th thc hin duy nht bng thng tin cng khai.

III. V d K chui 3CNTK8. i chui k t trn ra h thp phn theo bng m ASCII ta c: 51 67 78 84 75 56 Sinh kha: - Chn p = 11 - Chn = 2-

Chn Ks = 8 ==> Kp = Ks mod p = 28 mod 11 = 3

K: - Chn r = 9-

Tnh r-1 mod(p-1) = 9-1 mod 10 = 9Page 17


BI TP LN- Tnh = r mod p = 29 mod 11 = 6 1 = (x1 - Ks*)*r-1 mod (p - 1) = (51- 8*6)*9 mod 10 = 7 2 = (67 8*6)*9 mod 10 = 1 3 = (78 8*6)*9 mod 10 = 0 4 = (84 8*6)*9 mod 10 = 4 5 = (75 8*6)*9 mod 10 = 3 6 = (56 8*6)*9 mod 10 = 2

CH K RSA

Xc nhn: Z= (Kp) * mod p, nu Z= x mod p l ng, Z x mod p l sai. -

Z1 = (Kp) * 1 mod p = 36 * 67 mod 11 = 2 x mod p = 251 mod 11 = 2 ==> Z1 = x (ng).1 1

-

Z2 = 36 * 61 mod 11 = 7 x mod p = 267 mod 11 = 7 ==> Z2 = x (ng).2 2

-


-


-



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BI TP LN-

CH K RSA

Z6 = (Kp) * 6 mod p = 36 * 62 mod 11 = 9 x mod p = 256 mod 11 = 9 ==> Z6 = x (ng).6 6

IV.

Chun ch k s(bn ci tin ca ch k Elgamal)

Chun ch k s ( DSS) l phin bn ci tin ca s ch k Elgamal. N c cng b trong H s lin bang M vo ngy 19/5/1994 v c chp nhn lm chun vo 1/12/1994 tuy c xut t 8/1991. Trc ht ta s nu ra nhng thay i ca n so vi s Elgamal v sau s m t cch thc hin n. Trong nhiu tnh hung, thng bo c th c m v gii m ch mt ln nn n ph hp cho vic dng vi h mt bt k (an ton ti thi im c m). Song trn thc t, nhiu khi mt bc in c dng lm ti liu i chng, chng hn nh bn hp ng hay mt chc th v v th c th cn xc minh ch k sau nhiu nm k t lc bc in c k. Bi vy, iu quan trng l c phng n d phng lin quan n s an ton ca s ch k khi i mt vi h thng m. V s Elgamal khng an ton hn bi ton logarithm ri rc nn cn dng modulo p ln. Chc chn l p cn t nht 512 bt v nhiu ngi nht tr l p nn ly = 1024 bt c an ton tt. Tuy nhin, khi ch ly modulo p = 512 th ch k s c 1024 bt. i vi nhiu ng dng dng th thng minh th li cn c ch k ngn hn. DSS ci tin s Elgamal theo hng sao cho mt bc in 160 bt c k bng ch k 320 bt song li dng = 512 bt. Khi h thng lm vic trong nhm con Zp* kch thc 2160. mt ca h thng da trn s an ton ca vic tm cc logarithm ri rc trong nhm con Zp*. S thay i u tin l thay du - bng du + trong nh ngha . V th : = (x+ )k-1 mod (p-1) thay i ny ko theo s thay i iu kin xc minh nh sau: x

(mod p)-1

(1) mod (p-1) tn ti v ta c th thay i iu

Nu UCLN(x+ ,p -1) =1 th kin (6.1) nh sau:


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BI TP LNx -1

CH K RSA -1

(mod p)

(2)

y l thay i ch yu trong DSS. Gi s q l s nguyn t 160 bt sao cho q (q-1) v l cn bc q ca 1 modulo p. ( D dng xy dng c mt nh vy: Cho 0 l phn t nguyn thu ca Zp v nh ngha = 0(p-1)/q mod p). Khi v cng s l cn bc q ca mt. V th cc s m bt k ca , v c th rt gn theo modulo q m khng nh hng n iu kin xc minh (2). im rc ri y l xut hin di dng s m v tri ca (2) song khng nh vy v phi. V th, nu rt gn theo modulo q th cng phi rt gn ton b v tri ca (2) theo modulo q thc hin php kim tra. Nhn xt rng, s (1) s khng lm vic nu thc hin rt gn theo modulo q trn (1). DSS c m t y nh sau :


Page 20

BI TP LN

CH K RSA

Chun ch k s Gi s p l s nguyn t 512 bt sao cho bi ton logarithm ri rc trong Zp khng gii c, cho p l s nguyn t 160 bt l c ca (p -1). Gi thit Zp l cn bc q ca 1 modulo p ; Cho P = Zp*, A = Zq x Zp v nh ngha: K = { ( p, q, , a, ): a(mod p) } cc s p, q, v l cng khai, cn a mt. Vi K = ( p, q, , a, ) v vi mt s ngu nhin (mt ) k, 1 k q1, ta nh ngha: sigk(x,k) = ( , ) trong v

= ( k mod p) mod q = (x + a ) k -1 mod q

Vi x Zp* v , Zq, qu trnh xc minh s hon thnh sau cc tnh ton: e1 = x -1

mod q-1

e2 =

mod qe1

verk (x, , ) = true (

e2

mod p ) mod q =

Ch cn c 0 (mod q) v gi tr -1 mod q cn thit xc minh ch k (iu ny tng t vi yu cu USCLN( , p-1 ) = 1 khi bin i (1) thnh (2). Nu Bob tnh 0 (mod q) theo thut ton ch k, anh ta s loi i v xy dng ch k mi vi s ngu nhin k mi. Cn ch ra rng, iu ny c th khng gy vn trn thc t: xc sut 0 (mod q) chc s xy ra vo c 2-160 nn n s hu nh khng bao gi xy ra. Nhm 10: ng nh T Nguyn Trng TiPage 21

BI TP LNDi y l mt v d minh ho nh. V d:

CH K RSA

Gi s q = 101, p = 78q+1 = 7879. 3 l phn t nguyn thu trong Z 7879 nn ta c th ly: = 378 mod 7879 = 170 Gi s a= 75, khi : = a mod 7879 = 4576 By gi gi s Bn A mun k bc in x = 1234 v anh ta chn s ngu nhin k = 50, v th: k -1 mod 101 = 99 khi : = (17050mod 7879) mod 101 = 2518 mod 101= 94 v = ( 1234 +75 b 94 ) 99 mod 101 = 97 Ch k ( 94,97 ) trn bc in 1234 c xc minh bng cc tnh ton sau : -1

= 97-1 mod 101 = 25

e1 = 1234 25 mod 101 = 45 e2 = 94 25 mod 101 = 27 ( 17045456727 mod 7879 ) mod 101 = 2518 mod 101 = 94 V th ch k hp l. Khi DSS c xut nm 1991 , c mt vi ch trch a ra. Mt kin cho rng , vic x l la chn ca NIST l khng cng khai. Tiu chun c Cc an ninh Quc Gia (NSA) pht trin m khng c s tham gia ca khi Cng nghip


Page 22

BI TP LN

CH K RSA

M. Bt chp nhng u th ca s , nhiu ngi vn ng cht ca khng chp nhn. Cn nhng ch trch v mt k thut th ch yu l v kch thc modulo p b c nh = 512 bt. Nhiu ngi mun kch thc ny c th thay i c nu cn, c th dng kch thc c ln hn . p ng nhng i hi ny, NIST chn tiu chun cho php c nhiu c modulo , ngha l c modulo bt k chia ht cho 64 trong phm vi t 512 n 1024 bt. Mt phn nn khc v DSS l ch k c to ra nhanh hn vic xc minh n. Trong khi , nu dng RSA lm s ch k vi s m xc minh cng khai nh hn ( chng hn 3 ) th c th xc minh nhanh hn nhiu so vi vic to lp ch k. iu ny dn n hai vn lin quan n nhng ng dng ca s ch k: 1.Bc in ch c k mt ln, song nhiu khi li cn xc minh ch k nhiu ln trong nhiu nm. iu ny li gi nhu cu c thut ton xc minh nhanh hn. 2.Nhng kiu my tnh no c th dng k v xc minh? Nhiu ng dng, chng hn cc th thng minh c kh nng s l hn ch li lin lc vi my tinh mnh hn. V th c nhu cu th thit k mt s c th thc hin trn th mt vi tnh ton. Tuy nhin, c nhng tnh hung cn th thng minh to ch k, trong nhng tnh hung khc li cn th thng minh xc minh ch k. V th kh c th a ra gii php xc nh y. S p ng ca NIST i vi yu cu v s ln to/xc minh ch k thc ra khng c vn g ngoi yu cu v tc , min l c hai c th thc hin nhanh.


Page 23

BI TP LN

CH K RSA

Kt LunDa trn mc ch v nhim v ca ti , bi bo co gii thiu v S ch k Elgamal , cc yu cu v mc ch s dng s , mt s bn ci tin ca s Elgamal. Mt ln na , em xin chn thnh cm n c gio b mn an ton v bo mt thng tin tn tnh hng dn v gip nhm em trong sut qu trnh lm bi bo co, nhm em cng xin cm n cc thy c gio trong khoa Cng ngh thng tin to mi iu kin gip nhm em hon thnh bo bo co ny , cm n tt c cc bn c kin ng gp cho bi bo co ny.


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