Lecture Notes on Cryptography
357 20 4MB
English Pages 283 Year 2001
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½
¾
!" # $ %&
'¾
( ) '
* % #+, * " - *+ . " "! # $ %& ' ( ) '
½
!
"##$%&&" ' !
' () * + , - "##. # ""/ ""0 -1 * 2
-1 3 ) 2 4
2 1 2 ) % 5
6 ' 2
7 *' "##" 7 2 -1 ) 5 ) + +2 8 ) ) / 0 "& #0 / 6 !
() * -
2 !
) - %&&"
%
"" "% "5 "/ "0 "
3
9 8 3
9 - ) ) 1 ! - : ) ; P , .
1
' 2 , . , . P 2 ,
T @ L . 1 =
2 1 2 ¼
¼
¼
¼
¼
¼
-2 2 =
2 '
2
2
= 1
2 -
1
1 6= 2 2 =
; = , R S . 2 2 4 = V 2 2 2 2 2 /
71 / , . P *3 , . 0 / , . =
2 2 = *3 : + L J"5/℄ 0 ! " = : P 2 ,. P 2 , "., ".
2 Æ =
) % = 2
&
'(
2 R S R S @ 2
:
1 = -1 ) $ %
) 4 P 9 " , . P " 4 > 2 4 X 4 "
3 # M # P " P , .
" 2 !& ' !
3 ' 7 0 0,. P 9 " , . P "
0 / 0 7 1 " 0, . P ½ , ".
%/
- /,, 0
7 ,. P " 0,. P 0,.0,. ( 2 0 /0
0,. P 0, .
P P
0,
. , ".
$
- 2 2 2 2 P P &, ,Æ .. P &,Æ . -
3 Æ
: ' P , . 9 4 3E6 P 3E6 9 4 4 3E6 ,. P
3E6
1
%
' 1 ,
5 3$
(
1
" 0,. 2 + + - ,. 0,.
Æ
5 3& ( + - + -
=
¾ , ! " / # # 0 . . 1 . ! . . ) !# #
*)+ ,& - ¼ ¼ * 2, . ℄
!""# ## & . & & ,
´½µ
%#
' 1 ,
7 ) %% + - 4£ 6 ) 2 ) 1 6 7 C @ > 7 %5/ 2 + -
!& 1 !"# ## ) +)
+ J"/℄
@ @ + - 1 +
2 @ 2 @
2 + - ( 2 3$ : ' P P 9 7 @ $8)+ 9 4 4 $8)+ ,. ¾ P ' P , .
! 2 1 : %5# = - @ : %/% = A+ 2 + ' X
@ 2 ? A+
- 8 3' : @ 1 1 , . P
: @ 4£ X
" / 5 /
6
5 /X P / M 5
@ 2 " P 9 , . ¾ ½ P P
"
@
" /X P / M "
- ) "
1 " - @ " P 9 , . ¾ ½ P " 82 ) " 1 2 2 ! " P !" " ) " % P % $ P " . $ " ¼) " 82 1 .¼ & .¼ . $ " 2
) @ 4£ ½ ½ ¼ ¼ " P 9 , . ¾ $ $ P $ ¾ " ¼ ¼
$ " , $ $ . " 1 4£ @ 1 %
@ 2 % 1 : %5# +[ , J"#℄. @
@
,
@ &,, ½¾ . . 3 " &. 82 1 1 ! 3 &
* 1 @ C
3
1 @ ) +
2 2 -1 )/ ) + : P @ 1 $)9 1 $)9 , . P
8 3
A+
- : %5# @ @ ) + @ @
6
A+
: , . P , . P /0 ( ) + , . 4 P - A+
/ 0
55
' 1 ,
; @ = 2 ,1
2. : @ @
9 :
& @ $) ,. P " =@ $) 9 : & " ' P G# P P P ,9 ,# .. P M" # =@ $) P $) 2 1 # " ? " : 1 / 0 , . ? >1
=@ # O M" 2 , # " ". ,> ( 1 Æ 8 ( 1 Æ 2 .
,
,
,
5 5% " % 5 / 0 / 0 >;
U
" 5% 2 , . @ . 1 *
@ > * @ ¼
"B% "B% ¼
2
, B. 2 1 , < . G / ? 2 - =
= B
=
+
1 ==2 7
2 9 - ( , . - 0 , . =, . =, . ¼ + P ¼ " & > C ; - #00 3@ ,#". X =, . =, . 2 @ 6D) = ' 2 = ( 2
! 2 + - @ '
2 4 = @ 1 @ , 0 J4 ℄. * 31 7 31 ,( * .
6 ,0 J4 ℄. ' * ℄ : (
6 & # @ ) ) " M # 2 ,) ) ". # = , , # ) ) @. *%/ *%+ , . M %% P M ) ) &, . ) ) P % # P %
1 '
#"5 > '
1 * * ' @ * 1 7 '
'
@ * 2 & =
@ * 2 ( =
- #"5 2 2 2 , . 2 P 2
2
> Æ + -
2 +
2 = + - 6 & #"/
&8 2 2
?
B
B
5 '3 " > ℄ : (
) )
6
" M # 2
# @
+ = , ¼ M % ½ . *% , # ) ) @. *%/ , . M J5,) ) ". ℄ ,%
P M
) )
&, .
J%/℄ 1 #"/ 2 2 C 6
.& :
+
% E
ÈË˹Ê
$ 2 2 R S 2 9
M , . 2 2
2
7 2
, . , ) . 7
*3
0 > ½ *8 P , P 7 1 0 2
1 2 1 0 8
1 2
1 7 P , . ,= 7 . = P 2 ,= 7 . (
*8 P = P 2 >
1 7
2
2 P ,7 .
2 1 2 2 2 @ *8
%&%
- /,, 0
6
-
& *2
- 2 0 P 2
0 *3 82 2 ' 2 2 ; 2 1 *8 2 %/# >
2 P 2 2 0 1 2 *8 3 ? = >6=
Y = Y
2 ,
. 2 2
2 2 ? , . = = ? = 2 2 2 >6 ? =
' 1 ,
9
%"#
,"" $# <
I 2 2 ? J"&& #℄ 2 ( ? =
2
2 2 2 ? = ?
2 2 7 J#℄ 2 2 2 2 ? = J"&&℄ @ Æ
.
= 2 2 2 , Æ
. 2
2 RS 2 2
2 2
&
2 ! J55 ""℄ =
2 2 V 2 ! > 4 :'
- 2 P 2 > 32 9
2
2 ,; U ! 2 . M " X '
*
( (
*
(
B !
1 , . 2 U 2 R S 2 R S 2 2 * 2 V J5℄ X * 2 32 D J%℄ V J%&%℄ 32 J℄
2
7
7
¼
+1
+1
+
,
,
7
+1
+1
,
+)
,
' 1 ,
%%"
X J"℄ 1 2 R S = 1
: " 0 & : 0 2
2 2 '
7 2 P , . 1
J" ℄ P , .
- 2 , . . . P , , 7
+
;
C
+
+
+
;
7
7
7
?
+
+
7
+
¼
+
4
4
¼
4
?
4
¼
7
- 2
2
2 ' ,". ,%. ,5. 2 2 2
2 2
,/. 2 2 1
,0. ,. 9
2
1 -
2 2 , . > 2
2 , 2
. ,. @
2 R S 2 "
2 82 2 2 1
,. 2
2 2
2 2
1 7
7
7
;
?
C
C
?
;
, '
0
,/.
2 , . * @ 2 2
, ,.
2. = 9 1 R S
2
2 , ,. 2.
, @ ,.. V ) "# -) J0℄ : - ) 6 + + ; "
0 ""9"5$%& "#5 J℄ 0 J""℄ !
+ [ 6 + E;+ -)9 > * ) * !B*7 CD "0$% "##0 : > ) > #5 J"%℄ !
O D 6 + V2 * * C= 2 5# % '
5/"$50 =F "##/ 7
2 " ! # $ 2 2
%5"
%5%
- /,, 0
J"5℄ !
O D 6 +
@
",5.95%$5## * %&&& J"/℄ !
8 2 @ " 0 5#,".9%"/$ %55 O "##% J"0℄ !
6 + + 9 - Æ " 0
%$5 7 1 "##5 -) J"℄ !
6 + 3 * + * !B*7 C ) > %&# J5&℄ * ! 8 9 @ "%,5.9"0$"#% "###
' 1 ,
%55
J5"℄ + ! - 8 ? 6 O D + 2 V = O 7 * !B*7 C: //$" "##% : > ) > 0 J5%℄ O ! 8 2 8 D ? D 2? 6
+ (-)9 * !B*7GCC : > ) = F "### J55℄ + !
* "1* :CHC '
5"5$5" -7 6 "## J5/℄ * ! - 1 + -
G" * CF 2 "/% % '
= F "## J50℄ : ! ! - = 1"0 @ "0,%.95/$55 "# J5℄ ! ) H * 1 70* 70 "55$"5 333 "#% J5℄ ! 8 1 ,
.
"9"0$"#5 "#5 ,6 2 -) ;) '5 //&$//. J5℄ ! H
9 - 2
* %0 1
/%0$/55 "#/ 333 J5#℄ ! - Æ =
+ ! * ) ) * !B*7 F= %#$5&% "#0 : > ) > "# J/&℄ ! 8
@ = 1"0 @ "5,/.90&$5 >2 "#/ J/"℄ ! - * 6 > 2 ? = 1"0 @ %&,.9"&/$""" * "##" J/%℄ * ! + F 8
*Æ=8
* !B*7GCE : > ) = =F "## J/5℄
! ) ) [ I =
- ; ? * !B*7 FE %%5$%55 =F "# : > ) > %5 J//℄ 3 7 !
2 * ) * !B*7 F V "#/ 6 6 J/0℄ !
- + > - " 0
,".9"$5 7 "##& J/℄ + ) ) * > + ; 2 *
* !B*7 CH : > ) =F "## J/℄ + ) +
* 5 1
"## J/℄ 3+ ) 6 3 f ) 6 ; ; T7 > ' @ ' "9"$% "#5
%5/
- /,, 0
J/#℄ ) 8 3Æ =
1 1
3$ -,/.905%$0/0 "##5 J0&℄ * ) (
" 0 %/9/$ 7 "#" J0"℄ * ) ) ) [ *^
) 6 = * !B*7 FH /%$/% =F "# : > ) > %#5 J0%℄ * ) - 7 > ( * !B*7 FF 5"#$5% =F "# : > ) > /&5 J05℄ * : ) F -
"
# " ! !B*7 F: "5$"5# () ! * 3 ) 3 "#% + %=&/ J0/℄ ! ) ; (
= 1 1"0 @ ",%.9%5&$%" - "# J00℄ ! ) ! - F
2 = * % 1
55$5#0 6 "#0 333 J0℄ ! ) + : +2 - =
1
1 5/,0.9#&"$#&# "# J0℄ * ) 32 2* ,% . * " " 0 %&"$%& ) F "&& J0#℄ 8 ) ) 3 : + : +2 1 " 6 B =8
"##& J&℄ + ) 7 ! V =
=
8!7 !B*GCE 2 "&& % '
%$5 =F "## J"℄ + ) F + - ) = : + ##=&" "### J%℄ O * F +4 - 9 +4 %&&& J5℄ *^ - ! * !B*7 FC /"$/% =F "##& : > ) > /50 J/℄ * *
" 0 %/,.9055$05 "#" J0℄ V * V 7 O 7 * !B*7 C: /0$/# "##% : > ) > 0 J℄ V2 *
0,/.9//#$ /0 O "##/
' 1 ,
%50
J℄ O "# -7 6 J℄
1
1 = %%9//$0/ >2 "# J#℄ V "#5 6 6 J5℄ * * 2 - ) V ; * %% 1
50&$50 >2
"#" 333 J/℄ ) * > - Æ 1
V2 * * !B*7 C= %5/$%/ "##/ : > ) > 5# J0℄ 6 3 Æ @ "
0 /5,5.90$ & "#% J℄ 32 ; ; = = * %/ 1
5/$5# "#5 333 J℄ 32 ; - : - ?
" 0 %95$/ "#0 J℄ 6 7 - = 2 2
* % 1
/%$/5 : - "# 333 J#℄ - 7 - 8 2 9 - ; ? * !B*7 FE "$"#/ "# : > ) > %5 J&℄ + 7 )
+ - + 8!7 !B*GCH 2 "%%5 % '
%$%# =F "## J"℄ > - ,* . + 7 6 6(! EE > - "##" *+-7 J%℄ V 7 6
V ) =F "### J℄ + O 8 D ? + + Æ !B*7GCE 2 ""&# % '
=F "## J#℄ + O 8 D ? + + 8 !7 !B*GCE 2 "&& % '
50/$5" =F "## J#&℄ ; = =+2
+ B:) B =5"0 : ) "# J#"℄ ; - 1
? = @ ,".9%"$05 "##5 J#%℄ ; 8 @ " 0 55,/.9#%$& ; "#/ J#5℄ ; ;
+ ! * ) ) * !B*7 F= %$% "#0 : > ) > "# J#/℄ ; : :2 - =
= ;: " 0 "## J#0℄ ; - ) > /5 J"%0℄ : : ) = + ) :=# + ; "##
%5
- /,, 0
J"%℄ - D : 8 "# " . "% 5$"0 3 2 6 "##& J"%℄ - D : 8 %#5 J"50℄ ( @ 2 *Æ=8
V2 * * !B*7 C= %"$%" "##/ : > ) > 5# J"5℄ + O 3 " * 4 9 " ""/$"" O 6 : "# * > 6 + // J"5℄ + 8
8 1
1 =%/90%0$05& "# J"5℄ + ) - ! * !B*7 FC %"$%5 =F "##& : > ) > /50 J"5#℄ + )
(2 O "## J"/&℄
* 6* 7 "#5 J"/"℄ ) + L + 8
1"0 @ ",%.9/"%$/% - "# J"/%℄ :
+' @ "5,5.95&&$5" "# J"/5℄ > ; + ?
=
* 5 1
333 "##0 J"//℄ > ; + > = Æ = * 5 1
333 "## J"/0℄ > V (2 =
* %" " 0 55$/5 "## -) J"/℄ > V 6 =
2 1 * "
" 0 /%$/5 ! "##& -)
' 1 ,
%5#
J"/℄ > ,> . 1* * =E# "
O "# ;
> ! J"/℄ + > * (
=
" 0 %","%.9##5$### * "# J"/#℄ + > * - 2 7 ! %",".9 O "# J"0&℄ >2 8 I " 1 ' ) * 8!7 !B* F= %%/$5"/ 6 "#0 : > ) > %&# J"05℄ ) 6 D D > 1 1
3#$-,".9$#5 "## J"0/℄ 6 * 2 GC: "##" J"00℄ 6 6 >= 2 = 2
O 7= * !B*7 C: "%#$"/& "##% : > ) > 0 J"0℄ 3 6 ) + L ) =
"## J"0℄ O 6
@ * %5 1
"05$"0# ) "#% 333 J"0℄ ) 6 3 8
- 2 2 2* , .
1
1 =%/9"&$""& O "# J"0#℄ * 6 2 O * 8!7 !B*GCE 2 "&& % '
5$5# =F "## J"&℄ O 6
? * * 90%"$0% "#/ J""℄ F 6 32
1"0 @ /9%"/$%%& "#0 J"%℄ ! 6 6) 2 ; ; -) * 8!7 !B*GCE 2 "&& % '
"#$5% =F "## J"5℄ ! 6 6 ) 2 ; *1=-) -) * ) * !B*7 C= "$"/ "##0 : > ) > #5 J"/℄ + * ? ? + B:) B +=%"% : ) O "## J"0℄ + 6 @ ' "%9"%$"5 "#& J"℄ + 8 1
2 + +=" 8 2 - ) : "#" J"℄ + !=; F
4 ;: " 0 5$0 "##
%/&
- /,, 0
J"℄ + : +2 - 8 1 2
" 0 %95#5$5#0 - "#/ J"#℄ + : +2 *0 = +@ ) - "##% +7) "5%" J"&℄ + : +2 - : - - =
" 0 %",%.9"%&$"% "# J""℄ O + ;= Æ * %% " 0 5$5#/ ! "##& -) J"%℄ O + : - 1 1 @ 0 9/$#/ "#% J"5℄ + - * *4 J:# ! "
O "##" F "/ J"/℄ + - * *4 JH# 0
O "##" F "/ J"0℄ D O D + = 1= 2 2= 8!7 !B*GCD 2 #%" % '
5#5$/&5 =F "##0 J"℄ ( F F? @ = @ =
* %0 1
/5/$//& "#/ 333 J"℄ -
* V2 * V 7 V 8 * % " 0 0%%$055 ) "##/ -) J"℄ ) 6
3Æ @ /9""$"/ "##" J"#℄ + O 3
2 2 @ 0 //9/5$/#/ "#0 J"&℄ + - - 9 ¾ P &,% . B L >6= * %& 1
5%$55 O 6 + "## 333 J""℄ - 8
" 0 %%9"%$"5 >2 "## J"%℄ - ;
1 * "" " 0 ""$"%# - "## -) J"5℄ - ;
= @ * 1 "%* 0//$00& "#" J"/℄ - - = =8
* %5 1
"/0$"0% ) "#% 333 J"0℄ - + : +2 : - * D 0 ( 5$/5 ) =F %&&" J"#℄ F - + ( * !B*7 CE =F "## : > ) > "&&
' 1 ,
%/"
J"#&℄ +* 2 @ 2 0
/95%#$55# "# J"#"℄ + 2 F - =) 1"0 @ 9/$0 "# J"#%℄ @ 2 , . >6 1 =
2
=
- " 5 -00
- !66 1 ,
.
.
" 6 J , .
℄ % 6 J , .
℄ 5 , . , .
- 1
M 1 !66 @ 6 , . RS '
4
RS
6 6 !66 6
. 00
7
!66 2 , . - H
2 6 > >6 6 ( 2 !66 P >6 Æ C 6 1 >6 2 2 , .
2 @ , ?. 6 2 Æ ? 2 2 , . 2 2 ? 2 2
2 1 , . = 2 = 2 1 = 7 1 = ) % &
-5 % . 00
3 J 2' @ ℄ I 2 =2 2 2 " & 6 J ℄ 3'> ℄
3" J ℄ : # # &=" 2 ,!
2 . @ 6 J @ 3℄ " " Æ 2 " Æ
$
2
= 2 -
2 = 4
1 =
7 1 - ' J℄ ) 55 ) : +2 J0#℄
- 2 , , , -
9 / 0 2 , /0 29 , , . , P , , , . /0 ' ' , P , ' P
2 / 0 32 2 2 ½ , ½ P ½ , P ' 1 9 9 ' P &X ½ P + 9 ' P "X ½ P "% U U : 6 3 > 1 R S
" P % 7 3
P "
P % M "
L P "
2 > 2 P % M " C 7 3
2 %
P P , . 4 P " P "
P M 4 2 P $ P $ ! % % $ P " 6
C -
2 % P " % >
/,%. P " C 6 P " P " 2 @ @ ? 2 ) ,
. ! ? @ @ 2 - @ 2 @
1 @ 2 @ P !
7 3"
" ) P , ., M . & : P P M 2 2 2 2 " , . P , . P P . > , /, .. P " # + - 9
6 J""℄ 2 2 2 &, . 2 6
@ &, .
%0
- /,, 0
C
0)) 0 !
C
% 0 !
/ "
2 ½ ½ , . 82
1 2 ¾
"
"
%"
' 1 ,
" "
2 2 > @ P
P " 2 , ". "
2
2 4
2
1 : '
2 C>
3 #. ; 0 !
=D
2 )# 1
2 + ,4 . 4 ! 2
2 1 =D
P % 5 . " +
4
4 ,/ M % . P "
% ) + ,4 . , J"#℄. 5 ( = , 2=
=+ . + ,4 . " &, . + ,4 . " / P , . + ,4 . 4 @
M M 1 M M @ 0 )
,. P & , . " % J0℄. 2 2 ,
" . ; - 6 + , J0℄. ,. P & /
1 ! 0
, .?
CC
!& 3 #. ; , &
> )#5 5 1
=D
)5%
) )5" 5 3 : " " , . P " : + ,4 .
2 P & + ,4 . " , 4 M ". P &
%%
- /,, 0
6
2
: 3 , .
2 + P & P & 3 , .
82 3 , .
+ ,4 . M " M %
4 M " M %
4
, 8' @ .
2 3 , . P " P & P &
! @ @ =D 2 &, .
5 3
6 :
P @ @
, . , . ,/ M % . P " P & + ,4 ½ . " 4 M " M % 4 P & "
2 &, . 2 ! )5%
" 7 5 % ½ ½ ?
&, . 2 &, . 7
2 &, .
?
C6
'5"
# + ! 3 #. ;
+ ,4 . &, . + ,4 . P " &, . @ &, . 2=
=+ 1
, 2 2 @ &, . .
>1 P , . @ 1 3 % 2 M M @ > @ , . &, . 1 + ,4 . P + ,4 . 4 ½ 4 ¾ P + ,4 . " /
2 1 1
P &, . 7 @ &, . &, . / 0 @ &, . 1 6
6
- 2 &, .
2 + ,4 . + ,4 . P P &, . ! : + ,4 . , M " M " M . , J"%℄. &, . . , M " M " M .
M " M .
> ?, . ?, . , M "
2 1
2 &, . 82 2
4
2
%5
' 1 ,
I 3 2
1
M % ]
( =D 2 &,, . C
%
. 1
'5"
# + ! , 0
- )#"& 2 )4 )5/ 8=!
2 . =D 1
. " &,% . 8=!
5 3" G J ℄ " : G J ℄ 1 2 1 : , . P & , M .
( D 2 J#℄ 1 &,. . " &,% . . J/℄ - 8 =D . =D 1 1
2 7 2
2
1
: F
2
:
% 7 7
2 : '
2
2 2 4 A "
-
! 2 " 896 * ,
.
;
6 6 2 5 (
' 1 B * J"#%℄
'
3 *'
: b : *3 ,.
*3
P *3 ,.
b P *3 . ,b . 1 7 3)!
2
1
%
1
- /,, 0
# &
)
: 2 P
B P 6 , . ,B ". L " B + ,B ". P " 2 B P , , ".
P > 2 0 P = " 2
% C '>
& &
;
: , ? . B P
¾
:
P , ½ .¾
, B.
2
½ P % M % ¾ P % , % . ,½ ¾ . 2 P ½¾ M B¾¾ " 6 2 2 @ 2 % C 9 'C
. #
&
)
- (
2 M "
: 9 : ; 2 2 L 2 2 2 2 ,:' . - ;
,
. & # 8 >; L )
%"
' 1 ,
'C
& .& &
* 2
_ P (
2 2 2
'C
G E; . #
" # &
: 2 P -
2 ! 2 8 C , 2 ? = .
'C
) % !
- 2 - ! - 2 - ! - 2
- "=% 2 - ! - 2 ! - ! - 2 2 1 "=% 2
'C
'
&
+ = 9
9 2
9 2 2 8 2 =
R$ S 2
-
2 = 2
9 2 9 ' ( & ) ' ( , - . - 1 , a". & ,. ' ( K
" & % ' ( a" & '
5 & 2 ,. , ,.. * *
" & 2 , ,.. )
%%
- /,, 0
% ) 2 ' (
& 5 & / ) 2
$ $ = & L
, ' .
2 ' ( ' ( )
" ) ,. ' ( % ' (2 a" ) '
5 ' (
$ &
2 L ,( .
( 82 ( 2 2