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b. F'C6QR#I)
• hH)q'4'`~

l‚xP@W7•
ƒ/
dEG~

)4NEH4G7CH
5!.)97%I*)4NO&'/
d;'U`PPƒZ~
V„
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PP<Zf1~
V„
• #7;(=CH)q'4`

P/a)H@W`∀ a, b ∈ Z
n
•:∈ Z
n
V/[W;76`∀ a,b ∈ Z

•:f:•
1/[W;%N6`∀ a, b, c ∈ Z

•:•f•:•
m/lMF+=W∀ a ∈ ~

•lfl•f
Z/[MFu)*=W=MF:(%R∈ Z
n
) là n-a, nghĩa
là a+(n-a) = (n-a)+a= 0 @∀ a ∈ Z

/
„/a)H@WG6`∀ a,b ∈ Z

:∈ Z

/
ˆ/[WG;7`∀ a,b ∈ Z
n ,
:f:
w/[WG;%N`∀ a, b, c ∈ Z
n ,
:f:

y/PMF+=WG6∀∈ Z

ƒPfPƒf
Pl/[WG;(GH)H@W/
4
6`∀a,b, c∈ Z
n
, (a+b)c = •::•f:•
• #7;(W'`
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x:'f'x:''
b) mod n = ((a mod n) (b mod n)) mod n
(b + c)) mod n = (((ab) mod n) + ((ac) mod n)) mod n
2.1.2  !S#/U612I(6'6' !J#
- ,*CF%>:*L[7>)E!.:*B7g
CHMF=g`sgsf
- \>:*#•[
- a9`)7CH6B7l//xP
- \>%\f~
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%
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- ,*`'
%
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d;'U`

g Š # ‚  3 ‚ Q ~
l P V ‚ PP PV P1 ‚ Vm VZ
34`%f~
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KG"g3, ]h$Cp)4N"^S‹Œd$/
 CH:Y;)O=E*`
Không gian khóa là n nhỏ (bảng chữ tiếng anh n=26) nên có thể thám mã
bằng phương pháp vét cạn các khóa.
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<•%'f

<'•%''f'
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‰<•%fI'<∈ Z
m
, k ∈ Z
m
)
x%‰<fI
x%'f<'
<fx%'
∀ y ∈ Z
n
, 48 trình có nghiệm duy nhất. Do đó, e
k
là song
ánh và ánh xạ ngược là d
k
(y)=x= (y-k)mod n.
2.1.3  !S#/U612/'0,(
- ,*CF%>:*L[7>)E!.:*B7g
CHMF=g`sgsf
- \>:*#•[
- a9`)7CH6B7l//xP
- \77u=V„%;ElP///VZ
- d@bW7u•∈K , ta đu`
&

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xP
7u4N=•/
d;'U`W7u•`
 V   W X   Y Z :  
K 3 Q g  [ Œ , ~ S Ž Š 
  [ P \     ] ^  T
h • o # d  j ] \ ‹ ^ i
34`&

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‹fS‚
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 V   W X   Y Z :  
^ o i d Œ  ] ~ K Ž [ 
  [ P \     ] ^  T
Š , • ‹ S 3  j h \ g # i
34`'

gf^'

Sf‹‚
 CH:`
hH77uV„•@8mƒPl
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R%7W!%>9E)4N;:n7;/

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F&MC(%J/
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HOT
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k
(x)=7x+3

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k
(H)= (7 × 7 +3) mod 26 =0
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 e
k
(T)=(7 × 19 +3) mod 26 =6
12
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