lam quen ly thuyet mat ma

Nguyn Khanh Vn Bi m u v ATBM Thng tin HUT-2000

CHNG 0. BI M U

Vi s pht trin bng n hin nay ca cc kin trc h thng tin hc, c bit l cc h thng mng truyn tin v cc h thng thng mi in t, cc vn v an ton v bo mt tr nn c tm quan trng thi s. Trc mc ch ch o ca thit k h thng l lm sao cho h thng c m bo cc chc nng lm vic, chy tt, t li v d pht trin, d kt ni vi cc h thng khc. Ring cc vn ny cng lm au u cc nh thit k, v th bo mt l mi quan tm th yu (mc d vn c nu cao trong giy t). Tuy nhin vi xu hng xch li gn nhau ca c th gii, cng vic ca mi c s mi doanh nghip khng cn l vic bp nc ca tng nh na. Cc mng truyn thng din rng cho ta m ca giao tip vi bn b khp ni nhng cng v th m to c hi cho cc hng xm th ch" thng xuyn tm cch "dm ng" v "quy ph". Cu hi lt ngc by gi l liu mt h thng c gi tr hay khng nu n khng c bo v chng li mi loi tn cng v xm nhp ca k c k ch bn ngoi ln gin ip bn trong. V nhiu h thng quan trng, thc s bi ton bo mt c t ln hng u vi chi ph ln ti 60% chi ph tng th. Qua chng ta thy mt nhim v khng xa ca kin thc nht nh khng lc hu trong tng lai.

Chuyn ny nhm a ra mt tip cn tng th vi cc khi nim c bn v vn bo v cc h thng tin hc (HTTH). ng thi cc kin thc c th v cc lnh vc ring trong an ton v bo mt my tnh (computer securrity) cng c gii thiu mc cn chuyn su; qua ngi c c c mt hnh dung c th tuy cn cha y ton din v cc m hnh nghin cu. Mt s khi nim c bn m chng ta s cp ti l m ho i xng, m ho phi i xng (khai cng khai), hm bm, ch k in t... Cc m hnh pht trin hn s c gii thiu l giao thc mt m (cryptographic protocol), vn trao chuyn kho, chng thc (authentication), iu khin quyn truy nhp (access control), bc tng la (firewall), bo mt c s d liu, thng mi in t (electronic commerce) v bi ton thanh ton in t (electronic payments)... Tuy nhin khi lng ny s cn c iu chnh tu theo thi gian cho php. Ring vn v virus ng nh phi c trong danh sch trn nhng v n tr thnh kin thc ph thng, t nht l i vi cc sinh vin nm cui nn phi nhng ch cho cc phn khc.

V y l mt chuyn mi ang trong qu trnh hnh thnh, son ging th, nn khng th trnh khi nhng khim khuyt nht nh, c bit, do tnh gp rt ca thi gian, nn c nhiu phn trnh by c ng hn cc phn khc, thiu cc din gii chi tit, nhiu vn ch nu m cha minh ho. Nhng ch ny s c b p trong cc bi ging trn lp, ng thi s c b sung khi c iu kin v nhng dp son li sau ny. Ngi vit s tp trung vo din gii r rng nhng kin thc c bn v then cht trong khi cho mc u tin vi xu hng thp hn i vi cc k thut chuyn su hn v cc phn m rng. Mt s s ch c nu ra nh l cc cu hi bi tp.


Mong thu nhn c tht nhiu kin ng gp c th ca cc bn c gi.

Xut pht

Trc ht, nh bt u ca mi chuyn ngnh, mt ci nhn tng th vi cc khi nim mc khi qut ho cao nht s c gii thiu nhm to ra cho chng ta mt tip cn y v cn i nht.

Chng ta hy tm hiu khi nim "bo v h thng"1. y ta c th t ra mt s cu hi nh:+ H thng l g? + Ci g trong h thng cn phi bo v?+ Bo v khi ci g? v + Bo v bng cch no?Li tr li cho cu hi th nht th qu cao xa v khng nm trong khun kh cu chuyn ny, nhng tr li cho ba cu hi sau chnh l ba yu t lm thnh xut pht im ca chng ta:+ cc ti sn cn bo v (asssets).+ nhng mi e do (threats).+ nhng bin php ngn chn (control).hiu qu ca cc BPNC c nh gi qua chi ph (cost) v kt qu thu c.Ti snH thng my tnh l mt tp hp gm cc thnh phn ca hardwware, software & d liu. Mi thnh t l mt ti sn cn bo v. Nh vy ti sn y c th l thit b, chng trnh ci t v cc d liu lm vic v tch t qua thi gian.Nhng mi e do:C 3 hnh thc chnh:

+ Ph hoi : trong mt ti sn no b lm mt gi tr. V d nh: ph hng mt thit b phn cng hay xo mt chng trnh ci t.+Can thip (interrception): ti sn b truy nhp tri php bi nhng ngi khng c thm quyn.V d: nghe trm trn mng (wiretapping network), sao chp tri php. Thng thng rt kh pht hin.+ Sa i: cc ti sn b sa i, nh tro tri php. V d: sa i d liu trong cc CSDL hoc ang trn ng truyn qua mng.

Thit hi cho ti sn c th v hay c . Chng hn thit b c th hng do cc nguyn nhn chng may nh: bi lu ngy, s c ngun. Thit hi cng c th do c nh: n cp, nc ni trm. Tuy nhin y chng ta s ch nghin cu nhng thit hi do c .


Thit hi i vi phn mm v d liu c th d dng pht hin thng qua vic chng trnh treo khi chy hoc d liu hng. Tuy nhin cng c th rt kh pht hin khi i phng c tnh khng li du vt (trng hp cc virus "mn hn gi". Nhng loi nyc th pht hin c do nhng cc hiu ng hy bng cc chng trnh kim tra thng xuyn.Cc loi thit hi cho phn mm/ d liu bao gm:1. Xo: xo hoc copy .2. Sa i:- Sa i chng trnh c th gy ra chng trnh b treo ngay lp tc hoc mt thi im no sau ny (logic bomb -"mn hn gi"). Hoc l n c th khin cho chng trnh hot ng v to ra nhng hiu ng khng trong thit k, chng hn nh sa i tri php quyn truy nhp.- Sa i d liu c th gy ra bng nhiu hnh thc: salami attacks, ch bin cc thng bo gi.3. Can thip: n trm chng trnh, d liu. Ph hoi tnh b mt ca cc d liu thng qua c phng php nghe trm (wiretaping, monitoring, electromagnetic radiation...)

Rt kh pht hin nhng xm phm vo tnh nguyn vn ca ti sn v chng trnh/d liu khng h b thay i m ch b l b mt.+Truyn d liu gia cc im phn tn d lm bc l d liu, to nn nhiu im tn cng cho nhng k xm nhp sa i d liu.+Chia s ti nguyn v iu khin truy nhp tr nn mt vn hc ba.

Cc bin php iu khin kim sot an ton v bo mt ca HTTH1. iu khin thng qua phn mm:+ Cc tiu chun v m ho, kim tra v bo tr.+ Cc h iu hnh.+ Cc c ch iu khin ring ca cc chng trnh. V d DBMS access control.2. iu khin thng qua phn cng: + Cc thit b cho vic nh danh ngi s dng h thng+ Phn cng cho cc thut ton m ho.3. iu khin qua cc chnh sch (plicies): cc ni qui trong lao ng c nui dng qui ch v vic bt buc ngi s dng trong h thng lin tc nh k thay i mt khu.

y ta ch n mt chuyn ngnh hp l khoa m ho (cryptography) c coi l cng c nn tng sng to ra nhng m hnh thut ton v xy dng cc kin trc bo mt.

Trong gio trnh ny chng ta s ch yu quan tm n an ton v bo mt cho phn mm v d liu.Mc tiu v nguyn tc chung cu ATBM (an ton & bo mt - security)Ba mc tiu ca ATBM:


1. m bo tnh b mt (Cofidentiality): ti sn khng th b truy nhp tri php bi nhng ngi c thm quyn.2. m bo tnh nguyn vn (Intergrity): ti sn khng th b sa i, b lm gi bi nhng ngi khng c thm quyn.3. Tnh sn dng (Availability): ti sn l sn sng p ng s dng cho ngi c thm quyn2Ba mc ch ny thng c ghp vit tt cho d nh l CIA. Ch rng thng thng phi c s tho hip cng t c ba mc ch trn mt cch cn bng.

Hai nguyn tc quan trng trong vic thit k v nh gi cc h thng bo mt:+ Phi tnh n tt c cc kh nng m k ch c th thm nhp. K ch thng th mi cch c th c hng thm nhp ph hoi cho nn khng c php gi s rng k s tn cng ch mt s im ny m khng nhng ch khc, ni cch khc phi phng c nhng kh nng kh tin nht. Nguyn tc ny lm cho vic thm nh v bo mt tr nn rt kh, do tt c cc kh nng b ph hoi phi c tnh n.+ Ti sn phi c bo v cho n khi ht gi tr s dng hoc ht ngha mt.Trn c s cc mc ch v nguyn tc ni trn ngi ta s thit k/ pht trin v nh gi c cc m hnh v kin trc bo v.Qua phn trnh by c tnh dn dt va ri, chng ta c th hnh dung rng bi ton ATBM l ht sc phc tp, y tt c cc yu t u phi c tnh n bo v. Trong khi bn thn cc h thng tin hc cn bo v li ht sc a dng v phong ph lm cho cc vn cn nghin cu cng tri rng ra, tng nh khng th c th bao qut ht trong mt ngnh. Qu tht chng ta c th chia cc vn v ATBM thnh cc lnh vc c th khc nhau vi: ATBM cho cc c s d liu, ATBM cho mng truyn tin, ATBM cho cc h iu hnh hay ATBM trong cc m hnh thng mi in t... Tuy nhin tt c cc to nh ny vn c xy dng trn nhng m hnh bo mt c bn nh mt m ho, trao chuyn kho, giao thc mt, chng thc, iu kin truy nhp... V tt c cc m hnh ny li c xy dng trn ci nn ca mt khoa hc l thuyt pht trin lu nm hn, l ngnh Mt m (Cryptology). do vy trong cc phn sau ca gio trnh chng ta s bt y t vic lm quen vi cc khi nim v k thut c bn ca mt m nh mt m c in, mt m i xng, mt m phi i xng, hm bm, ch k in t.. ri sau mi chuyn sang mc kin trc cao hn l cc m hnh bo mt. Cui cng mi l cc bi ton ng dng c th cp trn.


Mt M (Cryptology)Trong tin Hy lp, kryptos ngha l che du, logos ngha l t.Mt M (Cryptology) l ngnh khoa hc ca cc phng php truyn tin bo mt.Ngnh ny li c th c chia lm hai:1. To m (cryptography): nghin cu cc phng php bo m b mt v/hoc tnh xc tht.2. Gii (ph) m: ph mt m v/hoc to ra cc on m gi m c th nh la lm pha bn kia chp nhn.Tuy nhin v sau ny chng ta ch yu cp n cryptography v do thi quen, n cng c dch l ngnh Mt m.

M hnh c bn.

y l m hnh c bn ca truyn tin bo mt. Khc vi truyn tin thng thng, c cc yu t mi thm vo nh l khi nim k ch n giu v cc pha m ho v gii m chng li.Sau y l c ch hot ng c th: Ngi pht S (sender) mun gi mt thng tin (message) X ti ngi nhn R (receiver) qua mt knh truyn tin (communication channel). K th E (enenmy) c th trm ly c thng tin X.S s dng mt php bin i, tc m ho (encryption), ln thng tin X dng c c (plaintext), ch bin ra mt on m ho Y (cryptogram), khng th c c.Cryptogram (cn gi l ciphertext) che giu ni dung ca thng tin plaintext.Kho (key) l thng s iu khin ca php bin i ny. Kho Z ch c bit n bi cc bn tham gia truyn tin S v R.Gii m (decryption) l qu trnh ngc li cho php ngi nhn thu c thng tin ban u X t on m ho Y.

Ch : Mt qu trnh bin i khng kho (khng ph thuc vo mt kho no c gi l mt code. V d: Morse code, ASCII code.

Lut Kirchoff (1835-1903), mt gi thit c bn trong mn m ho: Ton b c ch m/gii m tr kho l khng b mt vi k th.Cc kiu tn cng khc nhau:1. E bit c Y (ciphertext only attack).2. E bit mt s cp plaintext-ciphertext X-Y (known plaintext attack).

Sender S Receiver R

Enemy EKey Z

YY=EZ(X)

Key Z

X=DZ(Y)


3. E bit c cryptogram cho mt s tin X do bn thn son ra (chosen plaintext attack).

Ngy nay kin thc ngnh m ho l cn thit cho c cc chnh ph, cc khi doanh nghip v c cho c nhn:

+ Trong chnh ph: bo v truyn tin trong qun s v ngoi giao, bo v cc lnh vc tm c li ch quc gia.+ Trong cc hot ng kinh t: bo v cc thng tin nhy cm (health and legal records, fenancial transactions, credit ratings)

+ Cho c nhn: bo v cc thng tin nhy cm v thuc ring t trong lin lc vi th gii bngcc phng php ngy cng t ng, my tnh ho v ni mng.

Nhng k nguyn trong Khoa M ho:+ Thi k tin khoa hc: t thng c cho n 1949. Trong thi k ny, khoa m ho c coi l mt ngnh mang nhiu tnh ngh thut hn l tnh khoa hc.V d: 1. Mt php m ho (cipher) trong thi k ny l ca Xe-da (Caesar's cipher), cch y 2000 nm: cc ch ci c thay th bng cc ch ci cch chng 3 v tr v bn phi trong bn alphabet:

DASEAR FDHVDU

2. Vernam cipher (1926): ngi ta em thc hin php XOR vn bn gc (plaintext) vi mt chui nh phn ngu nhin c di bng di ca vn bn gc (chui ny l chnh l kho ca php m ho).

Trong cipher loi ny, kho ch c dng ng mt ln duy nht. Vernam tin rng cipher ca ng l khng th ph c nhng khng th chng minh c.

+ K nguyn ca ngnh khoa hc m ho c nh du bi bi bo ca Shannon.(Commication Theory of secretcy systems, 1949). Cng trnh ny da trn mt bi bo trc ca ng trong ng sng lp ra ngnh khoa hc l thuyt v thng tin (inforrmation theory).S bng n thc s trong l thuyt v m ho (Cryptolagy) bt u t bi bo ca Diffie & Hellman "New directions in cryptography". Cc ng ny chng t rng trong truyn tin b mt, khng nht thit l c hai bn u phi bit kho b mt (tc bn gi phi lm cch no chuyn c kho cho bn nhn). Hn na h ln u tin gii thiu khi nim v ch k in t (digital signature).


CHNG 1. MT S CIPHER C IN

Vic nghin cu cc cipher c in l cn thit v cc nguyn tc hc c s c th p dng c trong thit k v phn tch cc cipher hin i.

Monoalphabetic ciphers

y thut ton da trn php hon v trong mt bng alphabet.V d1.1 y l mt cipher da trn mt bng hon v ca ting Anh:a b c d e ... x y z

F G N T A ... K P L

Plaintext: a Bad day

Ciphertext: F GFT TFP

Nh vy kho trong mt cipher loi ny l mt bng hon v (A F, bG, ..., zL) nh trn, hoc ngn gn hn, ch vit dng th hai ca php bin i ny, l FGNT..PL.Dng th nht ca bng bin i ny l bng ch ci gc, v n c nh nn khng c tnh ti trong kho. Dng th hai, c gi l bng thay th (substitution alphabet).

Ch rng khng nht thit phi dng mt bng ch ci m bt c mt th bng k hiu no .V d 1.2 Plainext alphabet l mt tp hp ca cc xu nh phn vi di l 3.Bng bin i:p.text 000 001 010 011 100 101 110 111

c.text 101 111 000 110 010 100 001 011

Do xu plaintext 100101111 s c m ho thnh 010100011

gii m mt xu ciphertext to ra bi thut ton nh trn, ngi nhn c ciphertext cn bit kha, do yu cu mt giao thc v trao kho. n gin nht vic ny c th lm l ngi ghi kho ra a v chuyn a cho ngi nhn. R rng cch lm ny n gin nhng khng thc t. Trong thc t ngi ta s dng nhiu giao thc phc tp v tinh vi hn.Nu nh k th khng bit c kho th liu chng c th on c khng ? Hin nhin l iu ph thuc vo s lng kho c th c ( ln ca khng gian kho c th c). Nu kch thc ca bng alphabet l N th s kho c th l N! =N(N-1)...1 v c tnh xp x theo cng thc:

N! (2n)1/2(n/e)n

Cho N=26, ta c N!=26!926.Ch rng, s lng bit c chuyn mt ny c gi l chiu di ca kho.


V d 1.3 Chiu di kho ca mt cipher loi ang xt l 26*5 bits = s lng bits yu cu chuyn i dng th hai trong bng chuyn v trn. (Dng th nht c ngm nh l ABC..XYZ, nn khng cn chuyn).Ch : Khng phi tt c cc cipher nh trn l che giu c ni dung ca thng tin.V d 1.4: Sau y l mt cipher hu nh khng lm thay i plaintext.a b c d e ... x y z

A B C D E ... X Z Y

Additive cipher - Mt m Xeda (Ceasar)V d 1.5 a b c d e ... x y z

D E F G H ... A B C

Additive cipher c th c biu din thng qua php cng ng d.Gi s ta gn cc gi tr t A-Z vi cc s 1-25,0Th th mt ch plaintext X c th m thnh ciphertext Y theo cng thc:Y = X Z. vi Z l gi tr ca kho, l php cng ng d 26.Ly v d ta dng m Xe-da ni trn th:D=a 3, E=b 3,... A=x 3, B=y 3, C=z 3

R rng s lng kho c th dng c l 25 v s lng bt cn thit cho vic chuyn kho l 5 (24 < 25


R rng kho 2 khng tho mn, v khng to ra nh x 1-1 t bng ch gc sang bng thay th. S kin ng thi c bc, v oc s lm cho ta khng th gii m c m (ciphertext) c.

tng s lng kho c th, ngi ta c th kt hp c hai php additive & multiplicative cipher to ra afine cipher:Y = X ZX, Y, Z { 0,1,2,3,...25} { 1,3,5,7,9,11,15,17,19,21,23,25}Nh vy s lng kho s l 12 * 26 = 312 tuy nhin vn qu nh.

Phn tch gii m theo phng php thng k ( Statistical cryptanalysis)

D dng quan st mt c tnh ca ngn ng t nhin l s xut hin (tn xut) khng u ca cc ch ci c dng khi din t mt ngn ng.

V d 1.7: theo di mt on vn bn sau y trong ting Anh.

THIS IS A PROPER SAMPLE FOR ENGLISH TEXT. THE FREQUENCIES OF LETTERS IN

THIS SAMPLE IS NOT UNIFORM AND VARY FOR DIFFERENT CHARACTERS. IN

GENERAL THE MOST FREQUENT LETTER IS FOLLOWED BY A SECOND GROUP. IF

WE TAKE A CLOSER LOOK WE WILL NOTICE THAT FOR BIGRAMS AND TRIGRAMS

THE NONUNIFORM IS EVEN MORE.

y ta d dng m thy l fx=1 v fA=15.Nh vy trong ting Anh, cn c vo tn xut xut hin ca cc ch ci trong vn vit, ta c th chia 26 ch ci thnh 5 nhm theo th t t hay dng n t dng nh sau:I e

II t,a,o,i,n,s,h,r

III d,l

VI c,u,m,w,f,g,y,p,b

V v,k,j,x,q,z

Mt s cc cp 2 ch, hoc b 3 ch lin tip hay xut hin l;Th, he, in, an, re, ed, on, es, st, en at, to

The, ing, and, hex, ent, tha, nth, was eth, for, dth.

Ch l quan st trn ch ng vi ting Anh v nh vy ting Vit ca chng ta s c qui lut khc.


Sau khi c cc quan st nh trn, ngi ta c th dng phng php on ch v gii m da trn vic thng k tn xut xut hin cc ch ci trn m v so snh vi bng thng k quan stca plaintext.

V d 1.8 sau y s minh ho phng php ny.Example 0.11 What is the key?

Algorithm: key phrase substitution

YKHLBA JCZ SVIJ JZB TZVHI JCZ VHJ DR IZXKHLBA VSS RDHEI DR YVJV

LBXSKYLBA YLALJVS IFZZXC CVI LEFHDNZY EVBLRDSY JCZ FHLEVHT HZVIDB RDH

JCLI CVI WZZB JCZ VYNZBJ DR ELXHDZSZXJHDBLXI JCZ XDEFSZQLJT DR JCZ

RKBXJLDBI JCVJ XVB BDP WZ FZHRDHEZY WT JCZ EVXCLBZ CVI HLIZB

YHVEVJLXVSST VI V HXXIKSJ DR JCLI HZXZBJ YZNZXDFEZBJ LB JZXCBDSDAT EVBT DR

JCZ XLFCZH ITIJZEIJCVJ PZHZ DBXZ XDBILYXHZYIZKHZ VHZBDP WHZVMVWSZ.

on m trn bao gm 338 ch, thng k tn xut nh sau:

Letter: A B C D E F G

Frequency: 5 24 19 23 12 7 0

Letter: H I J K L M N

Frequency: 24 21 29 6 21 1 3

Letter: O P Q R S T U

Frequency: 0 3 1 11 14 8 0

Letter: V W X Y Z

Frequency: 27 5 17 12 45

e Zfj = 29, fv = 27

fjcz = 8 t J h Ca V (ng ring, mo t a)J,V,B,H,D,I,L,C {t,a,o,i,n,s,h,r}

t,a hteoTen

JZB = te ? ter n BTheTes


VI = a ? Asan s I

VHZ = a ?e Ateare r H

JCLI = th?s i L, o D

a b c d e f g h i jV Z C Lk l m n o p q r s t

B D H I J

u v w x y z

Ch ci u l fb W, c X, d Y

on n BDR = o ? of f

or r Hox f,x R

Nhng khng r rngWT = b ? y T

BDP = no ? w PBy gi t u tin s l

d-rin-

u K g A

Tm li:Mt h thng mt m tt khng cc c tnh thng k ca tin gc (bn r) duy tr sang bn m.Mt bn m c sinh bi mt h mt m cho l tt phi l khng phn bit c bng thng k hc so vi mt vn bn sinh ngu nhin (random text).


Cipher c in (tip theo)

Phng php bng phng ho th tn sut

M vi bng th ng m (homophonic substitution ciphers)Trong cc cipher loi ny, nh x ch ci TIN- M khng cn l 1-1 na m l mt-nhiu. Tc l mi ch ca bng ch ci tin s c m ho thnh 1 ch trong 1 tp hp cc ch m c th. Mi ch m ny c gi l ng m (homophone)VD1.7

Ch tin ng m

A 17 11 25 64 2 19 4 31I 22 95 14 21 79 54L 12 93 71NOPTE 64 7 8 47 ... (15 ng m)... ...

Nh vy c th thy y l mt bng bin i t ch tin sang ng m m.

Tin P l A i N p i l o t

M 27 12 11 53 64 36 79 71 15 41

Thng thng ngi ta b tr s lng ng m ng vi mi ch tin t l vi tn xut xut hin ca ch . V vy th tn xut tr nn bng phng. Mc d cc cipher loi ny kh ph nhng chng li b tng thm d tha so vi tin gc.BT. Hy gii thch ti sao TTX ca cc cipher loi ny l bng phng v ti sao m li c d tha.

S dng nhiu bng th

VD 1.8


Xt mt h m n gin vi bng ch plaintext alphabet:{a,b,c,d}Gi s tn xut xut hin ca mi ch nh sau:Pa = 0.5, Pb =0.05, Pc = 0.2, Pd = 0.25Ta dng hai bng th v mt chui kha quyt nh th t ha trn hai bng th ny.

Bng th 1a b C d P.text alphabetB D A C C. text alphabet

Bng th 2P.text alph A b c D

C.text alph D B C D

To m bng phng php trn 2 bng th theo kha 12X : aba cada da ca baaZ : 121 2121 21 21 212Y : BBB CBAB AB CB BBD

v d trn ngi ta ho trn hai bng th lin tc k tip nhau. Nh Phn b tn xut xut hin ca cc ch m s b thay i so vi tin v bng phng hn.M a bng th (polyalphabetic cipher)Trong th loi ny, ngi ta dng nhiu bng th theo phng php va g/t trn.Sau y l mt v d v mt cipher c in ni ting. Vigenere cipherVigenere cipher

Trong Vigenere Cipher, ngi ta dng tt c 26 bng th l s thu c t bng gc ch ci ting Anh m dch i t 0-25 v tr. S ho trn ny c quy lut hon ton xc nh bi kho. Mi ch ca kho s xc nh mi bng th c dng.

A b c d e F g H I j k l m n o p q r s T u v0 A B C D E F G H I J K L M N O P Q R S T U V1 B C D E F G H I J K L M N O P Q R S T U V W2 C D E F G H I J K L M N O P Q R S T U V W X3 D E F G H I J K L M N O P Q R S T U V W X Y4 E F G H I J K L M N O P Q R S T U V W X Y Z5 F G H I J K L M N O P Q R S T U V W X Y Z A6 G H I J K L M N O P P R S T U V W X Y Z A B... ...24 Y Z A B C D E F G H I J K L M N O P Q R S T25 Z A B C D E F G H I J K L M N O P Q R S T U

keyword : r a d I o r a d i o r aplaintext : c o d E b r e a k i n gciphertext : T O G M P I E D S W E G


Nh v d trn, tt c cc ch ng d tr chia 5 d 1 trong TIN s c m ho bi bng th vi ch ng u l R. Tt c cc ch tin ng v tr chia 5 d 2 trong TIN s c m ho bi bng th vi ch ng u l A,...

Phng php gii m Vigenere.Bao gm 3 bc1. i tm chu k p ( di kho)2. Chia tch M thnh p on phn m, mi on bao gm cc ch v tr kp+i (k=1,2,3 ... ; i=0,p-1), tc l c m ho theo bng th vi ch kho [i].3. Dng phng php mt bng th bit gii tng on phn m

Ngi ta s dng khi nim IC (Index of Coincidence) tnh chu k p.Theo nh ngha, IC xc nh qua cng thc:

25i=0 fi (fi-1) IC = -----------------

n(n-1)

Trong l xc xut ca php th - nht ra 2 con ch ngu nhin bt k t trong mt on vn bn - thu c cng mt ch cho trc.

S bng th (p) 1 2 3 4 5 ... 10IC 0.068 0.052 0.047 0.044 0.043 ... 0.041

IC ca vn bn ting Anh (p=1) t gia tr 0.068. Khi qua m ho, IC s gim dn i khi tng dn s lng bng th (hay tng chiu di kho). Qua ta thy IC th hin khng ng u ca cc tn xut xut hin cc ch ci. Trong vn bn gc, khng ng u (li lm) l ln nht nn IC l ln nht. Cn khi m ho vi nhiu bng th, th tn xut c lm "bng phng ho" nn tt nhin IC gim i.Phng php thc hnh.1. t k=12. Kim tra xem p c phi nhn gi tr k hay khng.2.a. Chia M thnh k phn m v tnh IC ca cc phn m.2.b. Nu nh chng u xp x nhau v u xp x 0.068 th p=kNu chng khc nhau nhiu v nh hn nhiu so vi 0.068 th p>k4. Tng k ln mt n v v lp li bc 2.

One-time-pad (Vernam cipher)

X: x n t f u h b z t

Z: A s u n n y d a y

Y: Y G O I I G F A S


xut bi G. Vernam (1917), sau c chng mnh l c perfect secretcy (1949) One-time pad: kha vit trn 1 bng (tape) di, s dng ng 1 ln Chui kha l chui ngu nhin

Sinh m Y = X + Z (mod 26)

Gii m X = Y - Z (mod 26) One-time-pad c th coi l m Vigenere vi kha l mt chui ngu nhin c di ng

bng vn bn


L thuyt v s b mt tuyt i (Shannon)

Ta hy ng vo vai ngi mun ph m. Gi s ta ch c kh nng ca Eve, tc l ch c trong tay m )ciphertext only, tuy nhin cng gi s rng ta c phng tin cc k hng hu (coi nh v hn) c th tin hnh c bt c php tm kim vt cn no.1. C th lun lun tm c mt TIN (plaintext) duy nht, tc l kha duy nht, khng nu nh ch bit m ng vi n (Cu tr li c s c ngha l mi thut ton m ho u khng phi l an ton tuyt i v c th ph c trn l thuyt).2. Nu cu tr li l c th c phng php no nh gi v so snh mc an ton ca cc thut ton m ho.V d 1.12.

Gi s chng ta c mt on M (cryptogram) Y c to ra t php m ha mt bng th. tm TIN tng ng, ta c th s dng tm kim vt cn. Vi Y ngn ta c th tm c nhiu on TIN X sinh ra cng M Y (tt nhin vi cc php th khc nhau). V d ta c on M sau:

AZNPTFZHLKZ

Ta c th to ra t nht l 2 on TIN tng ng bng 2 bng th nh sau:Bng th mt

a b c d e f g h i j k l m n o p q r s t u v w x y z

K B C D T E G I J M O L A Q R H S F N P U V W X Z Y

Bng th haia b c d e f g h i j k l m n o p q r s t u v w x y z

L P H N Z K T A F E

M: A Z N P T F Z H L K Z

TIN 1: m y s t e r y p l a y

TIN 2: r e d b l u e c a k e


V d 1.13. Vi M HLKZ c th d dng tm ra 4 TIN tng ng:C.text: H L K Z

P.text1: p l a y

P.text2: c a k e

P.text3: m i s t

P.text4: W a s h

bng cc bng th nh sau:A B c d e f g h I J k l m n o P q r s t u v w x y z

K L H Z

L H Z K

L H K Z

Qua cc v d 12 v 13 c th thy c rng i vi monalphabetic, khi M cn tng i ngn th lun lun tn ti cng lc nhiu on TIN c ngha m c th m ho thnh m ang xt c (tt nhin l kho d on tng ng). Tuy nhin vi M c di trn 50 tr ln th s ch c duy nht mt plaintext tho mn, tc chnh n l TIN cn tm. Nh vy, nu nh E nh phn tch gii ph m (cryptanalyst) tm c mt on M c di ln, th ni chung lun lun c th ph c m loi 1-bng th ny.Trong v d 14 ta quan st mt qu trnh c th gii ph m cng tnh. C 26 kho l 26 kh nng th. Eve s nghe trm v ln lt bt c tng k t m c pht trn ng truyn. Mi khi nghe c thm mt t m th E tin hnh th lun c 26 kh nng tm TIN c ngha lun. Khi mi nghe trm c t m u tin th kh nng ca c 26 kho u ngang nga nhau (xc xut on ng u nh, c nh hn 0.1), khi nghe trm c t kho 2,3.. th cc xc xut s thay i, hu ht l tip tc gim i, tr trng hp vi kho 15. Khi nghe c t m 5 th xc sut ng vi kho 15 s l 1 trong khi cc xc sut khc u l khoong t l kho 15 l kho ng (ch consi ng vi n l on u ca mt s t c ngha trong ting Anh nh consider, consideration...).

V d 1.14. Hy xt mt h m cng vi 26 kha khc bit (y 0 25 v tr). Gi s ta bt c M = sdchx. Ta s th c 26 kha ph m ny. Bng i y minh ha php th vt cn ny, vi n l di on M b tm tnh n thi im tng ng.

Shift Decruption N = 1 n = 2 n = 3 n = 4 n = 5

0 rdchx 0.060 0.070

25 sediy 0.063 0.257 0.427 0.182

24 tfejz 0.091 0.003


23 ugfka 0.28 0.052

22 vhglb 0.010

21 wihmc 0.024 0.128

20 xjind 0.002

19 ykjoe 0,020

18 zlkpf 0.001 0.001

17 amlqg 0.082 0.072 0.004

16 bnmrh 0.015

15 consi 0.028 0.202 0.515 0.818 1

14 dpotj 0.043

13 eqpuk 0.127 0.044

12 frqvl 0.022 0.058

11 gsrwm 0.020 0.015

10 htsxn 0.061 0.052 0.046

9 iutyo 0.070 0.001

8 jvuzp 0.002

7 kwvaq 0.008

6 lxwbr 0.040

5 myxcs 0.024 0.028

4 nzydt 0.067 0.028

3 oazeu 0.075 0.014

2 pbafv 0.019

1 qcbgw 0.001


L thuyt v b mt tuyt i.Trong h thng m bo b mt tuyt i, m d b tit l cho k th cng khng h em li mt ngha no. N khng lm thay i phn phi xc xut ban u ca plaintext.Hay l, mt h thng l c b mt tuyt i nu:P(X) = P(X/Y) TIN X V M Ynh l Shannon:Trong h thng c BMT, s lng kho c th ( ln khng gian kho) phi ln hn hoc bng s lng thng bo c th ( ln khng gian TIN). iu ny cho thy t c BMT th kho phi rt di, do vic trao chuyn khoa gia hai bn truyn tin s lm cho h thng tr nn phi thc t.Nh vy, nhn chung chng ta khng th t c an ton v bo mt v iu kin m ch c th c c cc h thng vi mc an ton thc t (Practical security) c ci t tu theo gi tr ca thng tin cn bo v v thi gian sng ca n.nh gi mc bo mt ca mt cipher.Shannon a ra mt khi nim, unicity distance, o mc security ca mt h thng: Unicity distance, k hiu N0, l s t nht cc ch m cn tm c c th xc nh c kha ng duy nht. Unicity distance c th c tnh theo cng thc:

d

EN 20

log

Trong d l d tha ca ngn ng s dng ca TIN.

V d 1.15. Cu tc k sau y thc t c th khi phc c v dng y mt cch duy nht:Mst ids cn b xprsd n fwr ltrs, bt th xprsn s mst nplsnt Most ideas can be expressed in fewer letters, but the expression is most unpleasant.

iu ny chng t nhng ch b mt trong cu ban u l d tha v mt thng tin.

Khi nim d tha c th c nh ngha thng qua cng thc:d = R - r bits

Trong R: absolute rate v r: true rate ca ngn ng.R c nh ngha nh l s lng bit c s dng biu th mt ch ci trong bng ch vi gi s cc ch c tn xut xut hin nh nhau:

R = log2A bits

vi A l kch thc ca bng chV d 1.16. i vi ting Anh ta c R = log226 4.7 bits.True rate r c nh ngha nh l s lng bit trung bnh biu th mt ch ci khi vn bn c x l theo kiu tc k, gt b cc ch khng cn thit (hoc p dng k thut nn trn c s cc thuc tnh thng k ca vn bn) m vn khng lm mt thng tin chuyn ti.V d 1.17. i vi vn bn ting Anh, tnh trung bnh, r nm trong khong 1 - 1,5 bit


d tha c th coi l mt thc o ca tnh cu trc v tnh d on (predictability) ca ngn ng. d tha cao hn chng t tnh cu trc v tnh d on cao hn. Mt ngun pht tin thc s ngu nhin s khng c d tha.

Trong ting Anh, d tha nm trong khong t 3.2 n 3.7 bits (gy nn bi biu tn xut li lm, cc mu t 2-ch, 3-ch - bigrams v trigrams - ph bin)

S dng Unicity distance ta c th so snh an ton ca cc thut ton m ha khc nhau.

V d 1.18. Vi m 1-bng th, ta quan st thyE= |Z| = 26!P(Z) =1/26!

log2E = log2(26!) 88.4 bitsN0 88.4 / 3.7 23.9 k t

Nh vy cc M cha 24 k t tr ln s c th b gii m mt cch duy nht.

V d 1.19. Vi m one-time-pad:X = khng gian kha = {tp hp cc on vn bn ting Anh c di k}Z = khng gian kha = {tp cc chui ch di k trng bng ch ci ting Anh}Gi thit cc kha c chn mt cch ngu nhin vi xc xut ng nht

N0 = log2E/dE= 26k log2(26k) = k log2264.7kN0 = (4.7k)/3.7 = 1.37k

Do , thm ch nu E nghe trm ton b tt c cc ch ci ca on M, c ta vn khng th gii ph m (tm c TIN tng ng duy nht).

Ta c th tng tnh mt ca mt h m cho trc hay khng?1. Tng ln khng gian kha2. Gim tnh d tha ca ngn ng vn bn TIN: tin x l qua 1 bc thut ton nnCh : mt thut ton nn l tng c th em li d tha 0, do N0 03. C th chn thm mt on vn bn ngu nhin phng ha th tn xut ca vn

bn TIN. Ta s xt c th bin php ny di y

Cng thc sau cho bit d tha ca vn bn mi (sau khi chn thm chui k t ngu nhin)d

ML

Md ~

Vn bn TIN gc Chui ngu nhin chn

M L

lam quen ly thuyet mat ma

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