mã khoá công khai và rsa

8/13/2019 M kho cng khai v RSA

1/24

M HA KHA KHNGNG B(KHA BTI XNG)


2/24

CHNG 3: M HA

KHA BT I XNG

M bt i xng

Chk in t

Chng thc in t


3/24

M ha kha cng khaiI. M HA KHA CNG KHAI

M ha khai xng c mt nhcim cn bn l: cn phi traoikha b mt trc.

M ha kha cng khai (hay kha bti xng)ca ra nh lmt gii php thay th.

Thut ton m ha kha cng khai c c s hon chnhu tin c

Ron Rivest, Adi Shamir v Leonard Adleman khi xng vo nm 1977ti Hc vin K thut Massachusett (MIT Massachusett Institute ofTechnology). Cng trnh nyc cng b vo nm 1978 v thut tonct tn l thut ton RSA


4/24

M ha kha cng khai1.1. Khi nim chung

M ha kha cng khai l mt dng m ha cho php ngi s dng traoi ccthng tin mt m khng cn phi traoi cc kha b mt trc.

Cc h thng m ha kha cng khai s dng mt cp kha c quan h ton hcvi nhau Kha cng khai Public key

Kha ring Private key (hay kha b mt secret key)

Hthng mt m ha kha cng khai c thsdng vi cc mc ch: M ha: gib mt thng tin v chc ngi c kha b mt mi gii m c.

To chk s: cho php kim tra mt vn bn xem n c phi c to vi mtkha b mt no hay khng.

Tha thun kha: cho php thit lp kha trao i thng tin mt gia hai bn.


5/24

M ha kha cng khai1.2. M hnh hot ng

Sinh Kha A chn thut ton sinh cp kha - kha cng khai E (public key) v kha b

mt D (private key).

A gi E (public key) cho B, giD (private key) cho mnh.

M ha B nhn c kha cng khai E.

B c thng ip gc P, dng E m ha E(P) = C

C l thng ip m ha gi cho A

Gii m A nhn c C Dng D gii m D(C) = Pc li thng ip gc.

Dng kho cng khai m ha, nhng dng kho b mt gii m


6/24

M ha kha cng khai1.3. Thut ton RSA

Sinh Kha Chn 2 snguyn tkh ln (>1024bit) P v Q, PQ

Ly tch s: N = PQ, N c gi l modulo m ha.

Chn sE sao cho: 1< E < PQ, E v (P-1)(Q-1) nguyn tcng nhau (vyE phi chn l mt sl). E c gi l smm ha

Tnh sD sao cho tch sDE 1[mod(P-1)(Q-1)] c ngha l tch sDEchia cho tch s(P-1)(Q-1) c sdl 1, hay l DE -1 chia ht cho (P-1)(Q-1) Ta dng phng php thdn cc snguyn X sao cho c c cho: D =[X(P-1)(Q-1) +1]/E l snguyn. D c gi l smgii m.

Kha cng khai An gi cho Bnh (qua ng thng tin bt k) l cp s[N,E]

Kha b mt An gicho ring mnh l cp s[N,D]


7/24


M Ha M ha: B nhn c kha cng khai ca A gi. B c thng ip gc

plaintext P

thng ip c sha P thc ra l mt con sdng nhphn c ithnh sthp phn no cn gi cho A.

B m ha bng php ton:

C= PE mod N (P = plaintext, C = ciphertext)

Bnh gi thng ip m ha C cho A.


8/24


Gii M A nhn c C

A gii m bng php ton

P = CD

mod N

Nhvy l y ta cn phi chng minh c rng:

(PE mod N)D mod N = P

iu ny c chng minh bng cch ng dng

nh l sdTrung hoa The Chinese Remainders Theorem .


9/24


V d: minh ha phng php nn ta chn p, q kh b cho d tnh ton. Chn 2 snguyn t: p = 17 ; q = 11

n = pq = 187

( n)=(p-1)(q-1)=160

e = 7 : smm ha (cng bcng khai) Kha cng khai A gi i cho B: (7,187)

d=e-1 mod ( n); d=7-1mod 160=23: smgii m ( A giring )

C thng ip gc (sha thnh sdng nhphn ri i ra sthp phn):

M=88

B dng kha cng khai (n,e) m ha : Me mod(187) ; 887 mod 187 = 11

Thng ip m ha c gi i: 187

A dng kha ring (n,d) gii m : Cd mod n; 1123 mod 187 = 88

i 123 vm nhphn v chuyn thnh vn bn gc theo bng m


10/24

M ha kha cng khai1.4. Trao i kha cng khai

RSA operation gm mt dy php tnh ly tha modulo kh ln.phc tp tnh ton:

- Kha cng khai = O(k2) bc tnh ton,

- Kha ring = O(k3),

Tng qut m RSA c phc tp tnh ton l O(k4) k l sbit ca modulo.V vy m RSA c nhc im u tin l tc lp m v gii m rt chm

Nhc im ln khc ca m RSA l nguy csau y. Khi B dng kha cngkhai nhn tA gi tin, chc chn chA c c: tin cy pha ngi gi tin.

Khi A nhn tin, cha chc do B gi (v kha cng khai c thlv ngi thba

bit kha cng khai, c thdng m ha nhng thng ip gigi cho A):khng tin cy pha ngi nhn tin.

khc phc iu , phi c phng php phn phi kha cng khai mtcch tin cy hn


11/24

M ha kha cng khai1.4. Trao i kha cng khai

Strao i kha cng khai:- A to mt cp kha, kha cng khai l E1 v kha ring D1- B to mt cp kha, kha cng khai l E2 v kha ring D2- Dng E1 nhn c ca A m ha E2: E1(E2) = E2, B gi E2 cho A v giD2 cho ring mnh

- A nhn c E2, gii m bng D1 (Chmnh A c D1): Chc A c c E2.Khi chc 2 i tc A v B cng shu kha cng khai E2.

- A c thng ip gc P, dng E2 (ca B m ha thng ip: E2(P) = C, gi thngip m ha (bng kha cng khai ca B) cho B chc chn chc B c c

- B: nhn chc chn do A gi, c: D2(C) = P

Bi tp: Sdng thut ton trao i kha v m ha RSA trao i thng tin


12/24

M ha kha cng khai1.5. Phong b s

M bti xngm boc an ton trong vic chuyn giao kha mnhng li c nhcim l tc lp m, gii m r t chm

Phong b s (Digital envelope) l mt bin php k t hp ca hai loimi xng v bti xng chuyn giao thngip an ton v tincy


13/24

M ha kha cng khai1.5. Phong b s

S chuyn giao kha b mt bng phong b s dngn ginBc 1 : To phong b s

A to kha cng khai E1 gi cho B, gikha ring D1

B to kha cng khai E2, to kha cng khai E2,

dng E1 (nhn tA) m ha: E1(E2) = E2 gi E2 cho A. Chc A shu kha ring D1 nn gii m c: E1(E2) = E2.

T Chc A v B cng shu kha cng khai E2 (do B to)

Bc 2: Chuyn giao kha di xng

A to kha i xng K dng E2 m ha: E2(K) = K gi cho B B dng D2 gii m: D2(K) = K

Chc A v B cng bit kha K, t giao dch bng kha i xng K


14/24

M ha kha cng khai1.6. Cc thut ton m ha thng dng

H mt m Elgamal da trn bi ton logarit ri rc cng l mt thuttonc dng kh phbin trong nhiu th tc mt m

Mt m xp ba l Merkle-Hellman l mt trong nhng h mt m

kha cng khai rai sm nht, do Ralph Merkle v Martin Hellmanpht minh vo nm 1978

Mt mng cong elliptic Elliptic curve cryptography ECClmt dng m ha kha cng khai da trn cu trc i s ca cc

ng cong -lip trn nhng tr ng hu hn. Vic s dng ccngcong e-lip trong mt m hc do Neal Koblitz v Victor S, Millerxut vo nm 1985


15/24

M ha kha cng khaiII. CHKiN T

Trong mt giao dch thng tin gia 2 tc nhn, vic traoi thng tintrc ht phim bo bn yu cu sauy trong cc nguyn l bo mtthng tin

Tnh bo mt: thng tin d lt vo tay ngi khc th ngi cng khng hiuc ni dung th.

Tnh ton vn thng tin:Nu thng tin blm bin i ni dung trong qu trnhtruyn tin th phi nhn bit l thng tin bcan thip (chpht hindetect -nhng c thkhng bit ni dung bcan thip nhthno nh chnh li chong correct)

Tnh xc thc (nhn bit): Khi nhn c thng tin, ngi nhn xc nh cng l thng tin do ngi gi gi khng phi l do mt kthba gimo.

Tnh khng chi b(trch nhim): Sau ny ngi gi khng thchi brngthng tin khng phi ca mnh.


16/24

M ha kha cng khaiV d: Trong giao dch thng thng, An k tn vo l thxc nhnrng th do mnh pht hnh, sau ny khng thchi bc. Khi Bnhthy chk ca An cui thth tin tng l thca An

Vy c cch no gii quyt c cc tnh cht an ton thng tin trong giaodch in t? Ni cch khc, c thto ra mt cng cng vai tr nhchk ca ngi pht hnh thng ip trong dng giao dch thng thngkhng?

Chk in t(Electronic signature) chnh l cng cp ng cnhng yu cu ra trn y cho vic trao i thng ip in t


17/24

M ha kha cng khai2.1. Chk in t

V d: Trong giao dch thng thng, An k tn vo l thxc nhnrng th do mnh pht hnh, sau ny khng thchi bc. Khi Bnhthy chk ca An cui thth tin tng l thca An

Vy c cch no gii quyt c cc tnh cht an ton thng tin trong giaodch in t? Ni cch khc, c thto ra mt cng cng vai tr nhchk ca ngi pht hnh thng ip trong dng giao dch thng thngkhng?

Chk in t(Electronic signature) chnh l cng cp ng cnhng yu cu ra trn y cho vic trao i thng ip in t


18/24

M ha kha cng khai2.1. Chk in t

Qu trnh m ha ngc sdng kha b mt v gii m bng kha cngkhai c gi l qu trnh k v xc nhn (private key authentication)

Sk nhn v xc nhn chk

abcd Encrypt/SignEncrypt/Sign$#&*$#&*

Decrypt/VerifyDecrypt/Verify abcd

Private Key Public Key

Plain textPlain text Plain textPlain text


19/24

M ha kha cng khai2.2. Cc thut ton chk in t

Qu trnh m ha ngc sdng kha b mt v gii m bng kha cngkhai c gi l qu trnh k v xc nhn (private key authentication)

Chk in tvi RSA

Chk in tvi DSA

abcdPrivate KeyPrivate Key

$#

&*

$#

&* Public KeyPublic Key abcd

Plain textPlain text Plain textPlain text

HashHash

abcd SignSign$#&*$#&*

VerifyVerify

Yes

Plain textPlain textNo

$#

HashHash

$#


20/24

M ha kha cng khai2.3. Hm bm

L mt chui i din (message digest) ca dliu c to ra tphng phpton hc (hash function) sdng kim tra tnh chnh xc ca dliu khi trao i

Tnh cht ca hm bm:

Mt chiu h: x x; khng tn ti h-1

Khng c va chm yu x x h(x) h(x)

Khng c va chm mnh Vx x h(x) h(x)

Cng dng ca hm bm:

Kim tra thng d(tnh ng n ca dliu)

So snh hoc kim tra dliu kch thc ln

Sdng trong chk in tHm bm thng dng: MDx (128 bits), SHA-x (160-512 bits), RIPMD(160)

Ch : MAC l mt loi message digest sdng kha ng b


21/24

M ha kha cng khaiIII. CHNG THCIN T

Chng thc in tl mt trong nhng ng dng quan trng ca chkin t. Nhchng ta bit tnh cht quan trng ca chk in tlphi m bo tnh ton vn ca dliu tnh xc thc, v tnh trch nhim

ca ngi gi thng tin. Vy cu hi t ra l:

C phi ng ngi chshu gi thng tin?

Tnh ng n v trch nhim ca ngi chshu nhthno?


22/24

M ha kha cng khai3.1. M hnh chng thc in t

Chng thc in tbao gm 2 phn: Plaintext:Xc nhn chshu v kha cng khai Message digest:bao gm kha cng khai, c xl bi hm bm v

c k bi thnh phn c thm quyn

Mt snh cung cp chng thc: VeriSign, Red Hat, Nexus, FPT, Bkav

Digital Certificate

Issuer: BCng An

Owner: CMND

Public Key: A1BC34

Time: 12/12/2022

A#$1BC^&EFF*&86 Sign


23/24

M ha kha cng khai3.1. Htng cskha cng khai

Public key Infrastructure (PKI) Trong mt m hc, h tng c skha cng khai l mt cch cho mt bn th 3 (thng l nh cungcp chng thc s) cp pht v xc thcnh danh cc bn tham gia voqu trnh traoi thng tin.

Hin nay c 2 m hnh vhtng kha cng khai c sdng:

Tiu chun X.509

Giao thc PGP v Web of Trust


24/24

M ha kha cng khai

KT THC

mã khoá công khai và rsa

Documents