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7/22/2019 Thuat Toan RSA
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N H M 1 2 :
1 . V N G C I P
2 . N I N H T T I P
3 . N G U Y N V N T O N
THUT TON M HARSA
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Nhm 12 - lp KHMT4 - k3
AN TON V BO MT
THNG TIN
GV hng dn: Thc s Th Minh Nguyt
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- Thutton cRon Rivest,AdiShamir v Len Adleman
(R.S.A) m t ln u tin vonm1977
THUT TON M HA RSA
1. Gii thiu chung
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- Trc,vo nm1973, Clifford Cocks - mtnh ton
hcngiAnhm tmtthutton tngt.- Nhng ti thi im th thut ton ny khng khthi v cha bao gic thc nghim
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1. bo mt cao (ngha l gii m c m khng bit kho
mt th phi tn hng triu nm).
2. Thao tc nhanh(thao tc m ho v gii mtn t thi gian).
3. Dng chung c.4. C ng dng rng ri.
5. C th dng xc nh ch nhn (dng lm ch k in t).
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THUT TON M HA RSA
Thut ton m ha RSA tho mn 5 yu cu ca mt hm hin i:
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THUT TON M HA RSA
Thutton RSA c hai Kha:
- Kha cng khai (Public key):
c cng b rng ri cho mingiv cdng m ha
- Kha bmt(Private key):
Nhng thng tin c m habng kha cng khai ch c thc gii m bng kha b mttngng
2. M t hot ng
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THUT TON M HA RSA
2. M t hot ng(tip)Chn p,q nguyn t
Tnh n =p*q
Tnh (n) = (p-1)(q-1)
e
Chn kha ring dd
Chn kha cng khai e(0< e < (n)) (e< >(n))
Bn m C
Bn r m
Bn r gc m
nmc e mod
ncm d mod1
ed
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2.1 To kha
THUT TON M HA RSA
L thuytBc 1:B (ngi nhn) to hai s nguyn tlnngunhin pv q
Bc 2: tnh n=p*qv (n) = (p-1)(q-1)
Bc 3: chn mt s ngu nhin e(0< e< (n)) sao cho CLN(e,(n))=1
Bc 4: tnh bng cch dng
thut ton EuclideTm s t nhinx sao cho
Bc 5:- nv elm kho cng khai (public key),- dlm kho b mt (pivate key).
V d:Bc 1: Chn s 23v 41(hai s ny l 2 s nguyn t)Bc 2: n = 23 * 41 = 943
(n) = 22 * 40 = 880Bc 3:chn e= 7 v CLN(7, 880)=1
Bc 4: => 7d=1+880x
=>d= 503 vx = 4
Bc 5:- n = 943 v e = 7
- d = 503
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1 ed
e
nxd
1)(*
e
nxd
1)(*
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THUT TON M HA RSA
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Nhm 12 - lp KHMT4 - k3
2.2 M ho v gii m
nmce
mod
Bc1: A nhnkho cng khai caB.
Bc 2: A biu din thng tin cn gi
thnh sm (0 m = 35
943mod357c
545c
ncm d mod 943mod545
503m
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- an ton cah thngRSA da trn 2 vn : biton phn tch ra thasnguyn t cc snguyn ln
v bi ton RSA.- V vymunxy dnghRSA an ton th n=p*qphi
l mtsln,khng c khnngphn tch n vmt tnh ton. m bo an ton nn chn ccsnguyntpv qt100 chstrln.
- Diylbngthigian phn tch m RSA
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THUT TON M HA RSA
3. an ton m ha RSA
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S cc ch s trong
s c phn tch
Thi gian phn tch
50 4 gi
75 104 gi
100 74 nm
200 4000 nm
300 500.000 nm
500 4x 10^25 nm
THUT TON M HA RSA
3. an ton m ha RSA(tip)
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THUT TON M HA RSA
3. an ton m ha RSA(tip)-Cch thc phn phi kha cng khai l mt trong nhng yu tquyt nh i vi an ton ca RSA.-Vn ny ny sinh ra 1 l hng gi l Man-in-the-middle attack
(tn cng vo gia)- Khi A v B trao i thng tin th C c th gi cho A mt kha
bt k A tin rng l kha cng khai ca B gi.- Sau C s gii m v nh cp c thng tin. ng thi m
ha li thng tin theo kha cng khai ca B v gi li cho B.- V nguyn tc, c A v B u khng pht hin c s canthip ca C
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THUT TON M HA RSA
- Thng tin truynitrn mngcngcnthitphicxc nhnngigi.
- Cc vnbntruyntrn mng(didngsho) cnphic chk cangigixc nhntrch nhimcangigi.
- Chk dng yl mtdy bitv cgilchk int.
- Mi ngi cn 1 cp kha gm kha cng khai & kha bmt.
Kha b mt dng to chk s(CKS)
kha cng khai dng thm nh CKS-> xc thc
4. ng dng ca RSA vo ch k in t
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Bntm lc
Hm bm
Gn vithng ip d liu
M ha
Thng ip d liu
Kha b mt
Ch k s
Thng ip d liuc k s
THUT TON M HA RSA
4.1 To ch k s
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Bntm lc
Hm bm
Tch
Gii m Thng ip d liu
Kha cng khai
Ch k s
Thng ip d liuc k s
Gii m c ?
Khng ng ngi gi
Bntm lc
Ging nhau ?
Ni dung thng ip b thay i
Ni dung thng iptan vn
THUT TON M HA RSA
4.1 Thm nh ch k s
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Ti liu tham kho
Wikipedia Gio trnh An ton bo mt thng tin
thongtincongnghe.com
Internet
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