26 ( ). , 26 0, 27 1, 28 2 . .
d ³ 2. . d . ³ d = 2.
d ´ d . 0 25. , , 1. ,
= 1 = .
, 26. , ,
2 17 + 5 9 = 79 = 1 + 3 26 = 1,
, , .
= ,
d - -. : d , . , d .
, HELP :
P 1 = = P 2 = = .
P 1 = = C 1 P 2 = = C 2
HTE.
. , , d = 2. , , 1. HELP , HTE. ,
= = .
= = = .
1 . ϳ 1.
. , HELP, , , .
, " ". : , CKVOZ , SAHARA. , , .
,
= , = = .
, -, ' .
,
′ =
, SAHARA CKVOZ. ,
′ = ,
( ′)1 = .
. ³ NAFG
= = .
- NAZ.
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|
= = ,
NAVY.
, .
ճ.
= .
1 D :
D = 11 22 12 21 = 3 5 2 3 = 15 6 = 9.
2 *, , ij j - - .
* = .
ϳ ij ij ij, (1) i + j :
ij = (1) i+j ij,
11 = (1)1+1 11 = (1)2 22 = 1 5 = 5;
12 = (1)2+1 12 = (1)3 12 = 1 2 = 2;
21 = (1)1+2 21 = (1)3 21 = 1 3 = 3;
22 = (1)2+2 22 = (1)4 11 = 1 3 = 3.
, :
* = .
3 1.
, * D.
1 = = .
, 1 = , .
, , - j - , - j - 1.
1 = = = =
= = .
, , .
4 26.
1 mod 26 = mod 26 = mod 26 = .
: 135 , 5 26. 9 . 153, 180, 81.
5 .
= , ; , . 3.1; , . 3.1.
HELP.
' n - . . 3.1.
HELP :
1 = = 2 = = ;
1 = 1 = = mod 26 = mod 26 = ;
2 = 2 = = mod 26 = mod 26 = .
, 7, 8, 0, 19.
. 3.1 HAT.
.
1 = 1 1 = = mod 26 = mod 26 = ;
2 = 1 2 = = mod 26 = mod 26 = .
7, 4, 11, 15 . 3.1 : HELP.
3.3
. ′ , : .
, .
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, ′ .
, , , .
, , . - . .
, , . , 㳺.
,- .
3.4 DS
DES (Data Encryption Standard) 1977 . . , DES , . , , 1980 (Ͳ). DES .
, .
.
' 64 . 64- , 56 ( 8 - ).
DES 2.
, DES . DES (.3.1)
3.1- DES
64- . , , , .
= m1, m2, , m64 M= m58, m50, ,m7, m 0 1. 3.2.
3.2
58 50 42 34 26 18 10 2
60 52 44 36 28 20 12 4
62 54 46 38 30 22 14 6
64 56 48 40 32 24 16 8
57 49 41 33 25 17 9 1
59 51 43 35 27 19 11 3
61 53 45 37 29 21 13 5
63 55 47 39 31 23 15 7
IP, 8 8 .
, . 2,4,6,8,1,3,5,7. , , .
- IP -1.
, . 5,1,6,2,7,3,8,4. , 3.3, .
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3.3 ʳ
40 8 48 16 56 24 64 32
39 7 47 15 55 23 63 31
38 6 46 14 54 22 62 30
37 5 45 13 53 21 61 29
36 4 44 12 52 20 60 28
35 3 43 11 51 19 59 27
34 2 42 10 50 18 58 26
33 1 41 9 49 17 57 25
(.2.10).
.
64- M 32- L0 R0 .
, 16- .
Mi - i - :
Mi = Li Ri
L i = m 1, m 2, , m 32; R i = m 33, m 34,, m 64... :
Li = Ri-1, i =1,2,,16;
Ri = Li-1 Å f (Ri-1, Ki ), i =1,2,,16;
f . Ri-1, 48- K, 64- K.
, DES, 3.2
K 1
K 2
K 16
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3.2 DES
L0 R0 M, , . , L1 , L1 = R0. R1, f (R1, K1 ). (. 3.3).
R i-132
i, 48
f (Ri-1, Ki), 32
3.3 - f (Ri-1, Ki ).
32- 48- . , 16 , , 3.4.
3.4
32 1 2 3 4 5
4 5 6 7 8 9
8 9 10 11 12 13
12 13 14 15 16 17
16 17 18 19 20 21
20 21 22 23 24 25
24 25 26 27 28 29
28 29 30 31 32 1
, 48- 2 48- K1.
48- 8 6 6- , 3.5 4- . ϳ , 4- 32- , ( 3.6).
3.5 Sj
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
S1 | ||||||||||||||||
0 1 2 3 | 14 | 4 | 13 | 1 | 2 | 15 | 11 | 8 | 3 | 10 | 6 | 12 | 5 | 9 | 0 | 7 |
0 | 15 | 7 | 4 | 14 | 2 | 13 | 1 | 10 | 6 | 12 | 11 | 9 | 5 | 3 | 8 | |
4 | 1 | 14 | 8 | 13 | 6 | 2 | 11 | 15 | 12 | 9 | 7 | 3 | 10 | 5 | 0 | |
15 | 12 | 8 | 2 | 4 | 9 | 1 | 7 | 5 | 11 | 3 | 14 | 10 | 0 | 6 | 13 | |
S2 | ||||||||||||||||
0 1 2 3 | 15 | 1 | 8 | 14 | 6 | 11 | 3 | 4 | 9 | 7 | 2 | 13 | 12 | 0 | 5 | 10 |
3 | 13 | 4 | 7 | 15 | 2 | 8 | 14 | 12 | 0 | 1 | 10 | 6 | 9 | 4 | 5 | |
0 | 14 | 7 | 11 | 10 | 4 | 13 | 1 | 5 | 8 | 12 | 6 | 9 | 3 | 2 | 15 | |
13 | 8 | 10 | 1 | 3 | 15 | 4 | 2 | 11 | 6 | 7 | 12 | 0 | 5 | 14 | 9 | |
S3 | ||||||||||||||||
0 1 2 3 | 10 | 0 | 9 | 14 | 6 | 3 | 15 | 5 | 1 | 13 | 12 | 7 | 11 | 4 | 2 | 8 |
13 | 7 | 0 | 9 | 3 | 4 | 6 | 10 | 2 | 8 | 5 | 14 | 12 | 11 | 15 | 1 | |
13 | 6 | 4 | 9 | 8 | 15 | 3 | 0 | 11 | 1 | 2 | 12 | 15 | 10 | 14 | 7 | |
1 | 10 | 13 | 0 | 6 | 9 | 8 | 7 | 4 | 15 | 14 | 3 | 11 | 5 | 2 | 12 | |
S4 | ||||||||||||||||
0 1 2 3 | 7 | 13 | 14 | 3 | 0 | 6 | 9 | 10 | 1 | 2 | 8 | 5 | 11 | 12 | 4 | 15 |
13 | 8 | 11 | 5 | 6 | 15 | 0 | 3 | 4 | 7 | 2 | 12 | 1 | 10 | 14 | 9 | |
10 | 6 | 9 | 0 | 12 | 11 | 7 | 13 | 15 | 1 | 3 | 14 | 5 | 2 | 8 | 4 | |
3 | 15 | 0 | 6 | 10 | 1 | 13 | 8 | 9 | 4 | 5 | 11 | 12 | 7 | 2 | 14 |
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