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MÔN: AN TON BO MT TRONG CÔNG NGH THÔNG TIN
ĐỀ TI: H MT MÃ KHOÁ CÔNG KHAI
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1.2 Các thành phần của mật mã khoá công khai.
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1.3. Nguyên tắc hoạt động
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1.4. Một số kỹ thuật phân phối khoá công khai
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1.4.1. Thông báo công khai khoá công khai
G„,$XR,YZ$!T7"82H9N"+#!)$N"7,!p9"n$P,"+•!S"#9N"+#!)$N"7,
!T77"97!"+2~,$XR,YZ$N"#!9521$
1!"3!k^q!T7Nƒ9"%H9=&g=^i9N.7,!*$!p9"n$,q21+9")$^#+!)$N"7,

!T7$XR,!p9"…2L%&E
k!"3"+19Q>$"XO7%F
h$P,2>99")$^#+!p9e29"R,$,79_,$XR,9"…2L%&EN"+#!)$N"7,QnQ},"‚,
N"+#!)$N"7,!T7
h$XR,9"…2L%&E$P,g1,2>99")$^#+QXv!2IYZ$N"+#,5$7%9"!T79"…2
L%&EN"+#!)$N"7,"XMH&!p9"n$,q,2IYZ$N"+#!)$N"7,!T7$XR,9"…2
L%&E")$^#+^7+$r2F
• "+#!)$N"7,^!T72=!p9"nYZ$Qn2I9")$^#+!"+
• },"‚,$%&5^q!T7Qnj#!Q6"QXv!Q},"‚,9Xk$ $9X_!QpM=
Qnj#!"Ho$Q},"‚,^7Q%N")$9"7&QK,9X_!N",QXv!$XR,9"…2
L%&E!"iS"H
• e29"R,$,7$%&5^q?"XMH&!p9"nj#!Q6"o$Q/&N")$S"q,g=
2>99")$^#+!*9w$XR,9"…2L%&E!" 72>9N"+#N"#!N"+#!)$N"7,
",891,!T7
hgX%$,tN"+#!)$N"7,!T7M=YZ$pQn2I2>99")$^#+9_,!" 7Q6"Y7"
{!T7M=2>9$,#96+!e;C<?QXv!YZ$QnQ6"Y7"Y%&"i9$,7+Y6!"=&
V
E9=,F8GH9GI"+#)$"7,
h9"%QXv!N"+#!)$N"7,!T79w$XR,9"…2L%&E9"e+!Z$!#!"9" !"Xgi&
QXv!N"+#!)$N"7,!T7
h$P,2>99")$^#+9_,QXv!2I^o$7M=!" 7$,#96C!T7M=:2_,
QXv!O,"!T7]!"u!p2_,!p9"n$,q,2I9")$^#+;D<5O`!p2•9!T7C
9+$9")$^#+;@<Qq2^q+M_,o$$XR,Q#S $g=
h$P,9qg1,:QXv!2I^o$N"+#!)$N"7,!T7QnQq2^q+o$$XR,Q#S $g=

"XMH&!p[9")$^#+QXv!Q},"‚,%&",5d9")$^#+N"y,91+QXv!YZ$N")$
9"XR$j%&5M]!qM=!p9"ngX%g1,N"+#!)$N"7,!T7$XR,N"#!QnYZ$g1,
6"N.?2>9$XR,YZ$S"q,Q},"‚,2>9^qO7+2_,!T7!#!N"+#!)$N"7,!T7!#!
9"="M,59Xk$ $
$XR,9",39N3"89"W$!j/&Y`$^>S"2E2!p!" !($9"`!",8Nƒ9"%H9

L%&E
G>9N‡ji%^,39QXv!N"+#^a2H9!T7",O,"72>9!•SN"+#2_,M=j,$XR,
9"…2L%&E!iS2>9!" $!"u2_,?N‡ji%YZ$g1,!" $!"u!*!T7M=$P,!"+
3%2I9")$^#+YZ$N"+#!)$N"7,!*9"]N‡ji%!p9"nQ~!!#!9")$^#+=&
#!&5%!%QW,M_,OkQr95g=F
hG>99"="M,5^i9N.!p9"nQ~!2>9!" $!"uQnj#!Q6"95M=N"+#!)$N"7,!T7
$XR,!"T!T7!" $!"u
h"="M,5^i9N.!p9"nj#!"Ho$!" $!"ug=$%&5^q9w$XR,9"…2L%&E
!" $!"uM=N")$^6$,q
h"u$XR,9"…2L%&E!" $!"u2_,!p9"nQ~!M=!HS"H9!" $!"u
"="M,5^i9N.!p9"nj#!"H9"R,$,7gX%"="!T7!" $!"u
1.5. Một số thuật toán thường dùng
82I"+#N"+#!)$N"7,QXv!9"`!",8?j/&Y`$952>9OW!kOy9+#"+!7,
9+$OW9"%H99+#9"XR$YZ$g=FM=fg727g
El Gamal:
Xv!S"#99,n^y,7"efg727g
a!"9"X_!Ne&FVC:"+•!CB:d^,9O
‰9S"K^,3"Xg=?OPYb$$,7+9" !00
RSA:
Xv!S"#99,n^y,,MeO9?"72,M7YYge27
a!"9"X_!Ne&FVC:?CB:d"+•!:Bd\^,9O
[
E9=,F8GH9GI"+#)$"7,
0"K^,3?",E%$XR,YZ$?YZ$N"+#!)$N"7,QnL%qgx
2. Hệ mật RSA
2.1 Lịch sử hình thành
"%H99+#QXv!+,MeO9?Y,"72,M=4eYge272)9qgQ%9,5M=+
(2Cc[[91,~!M,8)$$"8G7OO7!"%Oe99O;G<5!T79"%H99+#gi&9wD!"t
!#,Q%!T795D9#!$,q/&g=9"%H99+#Q%9,5S"Z"vSM_,M,8!91+7!"tNxQ,8
9PQr$9"R,M_,M,8!2I"p7pQ#"Yi%2>9O`9,3^>MXv9^H!!T7gs"M`!2H92I

2+YCYe ϕ=⋅

@"p7!)$N"7,^7+$r2FM=e"p72H9FY!}S?LM=
<;n
ϕ
9"XR$g=jp7O7%N",
9a"9+#N"p7
Quá trình mã hóaF
,qOP+^2%W$P,Q+19")$9,2‹!"+g,!e?9"]+^9a"^q2I"XO7%
<;2+Ynmc
e
=
%W,!Z$+^$P,c!"+g,!e
Quá trình giải mãF
g,!e"Hc9w+^M=N"p7^a2H9dg,!e!p9"n9]2QXv!29wc9"e+!)$9" !O7%F
<;2+Yncm
d
=
-%#9]"$,q,2I"+19Q>$M]97!p
<;2+Y<; nmmc
edded
≡≡
{+edŒC;2+YphC<M=edŒC;2+YqhC<?9"e+6"gx•e279"‚5F
<;2+Y pmm
ed
≡
<;2+Yqmm
ed
≡
{+SM=Lg="7,OW$%&59W!Z$"7%?#SYb$Q6"gxS"YX9%$"+7?!"m$97!pF

 D :dD DD
 :C dB\dCBC :C
 C\ C\\cV@\ :D
f V DC:V CB
3%91,Q/&?Ytg,8%95QXR$!"%&nQ3$XR,"H^62>9$XR,N"#!^U9
QXv!?7"97O•N")$^,39QXv!>,Y%$2%Wp,Q,E%$]?2=!"u"HQXv!Qp!"ug=
"t$!+OW?N")$p,g5QXv!Q,E%$]3%2%WQ~!QXv!>,Y%$?7"97S"q,!p
0,M79ee&?2= $M_,0%^g,!e&YZ$Qn2I"+#Ytg,8%959"]S"q,!pS,M79ee&
9"a!""vS{+Qp?Ytg,8%O•79+=
",Ytg,8%Q397&$XR,"H?2%WN"),S"b!g1,Ytg,8%$W!^7Q%?97O•Ye!&S9g1,
M_,ŠDV?YŠ:c
Bảng giải mã chuổi SECURE
c
E9=,F8GH9GI"+#)$"7,
>,Y%$^62I"+# GŠ!
Y
2+Y {tg,8%$W!
:d Cc 
CB V f
DD D 
:C :C 
:D C\ 
CB V f
0%^g,!e&Š;?e<Š;DV?V<
0,M79ee&Š;?Y<Š;DV?:c<
2.4 Key Length (chiều dài khoá)
W!Q>2I"+#M=$,q,2IYtg,8%!T7N")$S"b9"%>!M=+Na!"9"X_!!T7
e&;<
Bảng Tốc độ mã hóa, giải mã của RSA
Độ dài n VC:^,9 [@\^,9O C?B:d^,9O

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α
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Quá trình mã hóa bản tin TF
C"~OW$†%",5
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3.3 Ví dụ
CGI"+#M=$,q,2INx9`09+$^q$!"t!#, $M_,M69aC@
:"~SŠ:V[c
D"~NŠ\VD
d"~$M=j9"+qF$‹SM=j‹S5$Š:?jŠ[@V
Va"&Š$
j
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0%^g,!e&Š;j<Š[@V
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Quá trình mã hoá
7Š$
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\VD
2+Y:V[cŠdDV
^Š2Ž&
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2+YSŠC@Žcdc
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2+Y:V[cŠ:Vc

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qpn ⋅=
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Ž
n
Z∈
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Quá trình mã hóaF
n$y,9")$9,2H9
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n
ZM ∈
!"+g,!e?+^!91+7^q$2I!"XO7%F
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:
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QXv!9"`!",8^y,g,!eO•N"),S"b!g1,^q€QXv!2I"p7^_,+^
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q
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p
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m p m p C p
+
+
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L2+Y2
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CL
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d
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( ) ( )
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C C
C C
C
2+Y 2+Y 2+Y

C C
d
2+Y 2+Y 2+Y
p q
M m q q p m p p q n
− −
= +
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4.2 Ví dụ
SŠCDD:[
LŠCV@[
Š:B\\DdBc
2

C
S
2
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2
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( )
n
sss ???
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∑
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"%H99+#=&2,5%9q"XO7%F

C
then
<???;
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xxxx =
là giải pháp cần tìm
Else
Không tồn tại giải pháp nào.
End
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M,8!9]2YI&O,5%9($9"e+N"p7!)$!>$g=^=,9+#N"pG>9!#!"^,3QK,2=Gegeh
egg275%7g=^,3QK,YI&O,5%9($9"e+2+Y%g+$%&59WS?O7+!"+F
∑
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n
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sp
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CC −≤≤ pa
7%Qpj#!Q6"9"="S"
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ii
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xxxx =
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∑
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i
ii
txy
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Quá trình giải mã.
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Ca"
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C
pyaz
−
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( )
n
sss ???
:C
M=9K$g=•
CV
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82H9G!fg,e!e"]"9"=""XO7%F
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"]"9"="N"p7"XO7%F
Quá trình hình thành khóaF
Cg,!e!"~2I9%&39a"”?N•!p9"nOP7QXv!9g„,GI=&S"q,!p9"%H99+#$,q,
2I",8%L%q
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nk ×
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kk
×
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nn ×

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nk
×
F–Š0
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Quá trình mã hóaF
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"="2I"p79"e+!#!^X_!O7%F
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:a"M“!9k!–Šj–
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d]"9"="^q2IF&Š!–‘e
Quá trình giải mãF
Ca"279HN"q$"6!"!T70g=0

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$,qOPg,!e!"~279HM=0"XO7%F
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