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BY (11) 13273
(13) C1
(46) 2010.06.30
(19)
(12)
(51)
(2009)
G 06F 7/00
(54)
(21)
(22) 2008.06.13
(43) 2008.12.30
(71)
:
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BY 13273 C1 2010.06.30
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BY 13273 C1 2010.06.30
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BY 13273 C1 2010.06.30
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1-13,
14
15,
36-39,
40-43
Ek = Ek(X) = Ek(X1, X2), k = 1, 12 ,
2 = ( 5, 6, 7, 8)
1 = ( 1,
2, x3,
4)
-
16-35,
44-55.
(
.)
=
(x
,
x
,
x
,
x
)
1
1
2
3
4
.
. f = f(X) = f(X1,
2),
2 = (x5, x6, x7, x8),
-
:
f = γ0 ⊕ E1(X) ⋅ γ1 ⊕ E2(X) ⋅ γ2 ⊕ E3(X) ⋅ γ3 ⊕ E4(X) ⋅ γ4 ⊕ E5(X) ⋅ γ5 ⊕ 6 ) ⋅ γ6 ⊕
⊕ 7 ) ⋅ γ7 ⊕ 8 ) ⋅ γ8 ⊕ 9 ) ⋅ γ9 ⊕ 10 ) ⋅ γ10 ⊕ 11 ) ⋅ γ11 ⊕ 12 ) ⋅ γ12,
Ek = Ek(X) = Ek(X1, X2) ., k = 1, 12 ;
γl ∈ {0, 1}, l = 0, 12 .
,
. f = f(X) = f(X1, 2)
.
(1).
,
,
21,
1
,
20,
. f = f(X) = f(X1, 2)
X
,
.
. Ek = Ek(X) = Ek(X1, X2), k = 1, 12 ,
(
.),
:
1
2
E k = E k (X) = E k (X1, X 2 ) = ∑ ⊕ E i4 (X1 ) ⋅ E 4j (X 2 ) ,
0≤i ≤ 4
0 ≤ j≤ 4
2i + j = k
E i4 (X1 ) , E 4j (X 2 ) , i = 0, 4 , j = 0, 4 (2)
k = 1, 12 ,
:
.
E1(X ) = E1 (X1, X 2 ) = E14 (X 2 ) ;
4
(1)
2
-
(2)
E 04 (X1) ≡ 1 , E 04 (X 2 ) ≡ 1 .
. Ek = Ek(X) = Ek(X1, X2),
BY 13273 C1 2010.06.30
E 2 (X) = E 2 (X1, X 2 ) = E14 (X1) ⊕ E 24 (X 2 ) ;
E3 (X) = E 3 (X1, X 2 ) = E14 (X1 ) ⋅ E14 (X 2 ) ⊕ E34 (X 2 ) ;
E 4 (X) = E 4 (X1, X 2 ) = E14 (X1 ) ⋅ E 24 (X 2 ) ⊕ E 24 (X1 ) ⊕ E 44 (X 2 ) ;
E5 (X ) = E5 (X1, X 2 ) = E14 (X1 ) ⋅ E34 (X 2 ) ⊕ E 24 (X1 ) ⊕ E14 (X 2 ) ;
E 6 (X ) = E 6 (X1, X 2 ) = E14 (X1 ) ⋅ E 44 (X 2 ) ⊕ E 24 (X1 ) ⊕ E34 (X1 ) ;
E 7 (X) = E 7 (X1, X 2 ) = E 24 (X1 ) ⋅ E34 (X 2 ) ⊕ E 34 (X1 ) ⊕ E14 (X 2 ) ;
E8 (X) = E 7 (X1, X 2 ) = E 24 (X1 ) ⋅ E 44 (X 2 ) ⊕ E34 (X1 ) ⊕ E 24 (X 2 ) ⊕ E 44 (X1 ) ;
E9 (X) = E 7 (X1, X 2 ) = E 34 (X1 ) ⋅ E34 (X 2 ) ⊕ E 44 (X1 ) ⋅ E14 (X 2 ) ;
E10 (X ) = E 7 (X1, X 2 ) = E 34 (X1 ) ⋅ E 44 (X 2 ) ⊕ E 44 (X1 ) ⋅ E 24 (X 2 ) ;
E11 (X) = E8 (X1, X 2 ) = E 44 (X1 ) ⋅ E 34 (X 2 ) ;
E12 (X ) = E8 (X1, X 2 ) = E 44 (X1 ) ⋅ E 44 (X 2 ) ,
E14 (X1 ) = x1 ⊕ x 2 ⊕ x 3 ⊕ x 4 ;
E 24 (X1 ) = x1x 2 ⊕ x1x 3 ⊕ x1x 4 ⊕ x 2 x 3 ⊕ x 2 x 4 ⊕ x 3 x 4 ;
E34 (X1 ) = x1x 2 x 3 ⊕ x1x 2 x 4 ⊕ x1x 3 x 4 ⊕ x 2 x 3x 4 ;
E 44 (X1) = x1x 2 x 3 x 4 ;
E14 (X 2 ) = x 5 ⊕ x 6 ⊕ x 7 ⊕ x 8 ;
E 24 (X 2 ) = x 5 x 6 ⊕ x 5 x 7 ⊕ x 5 x 8 ⊕ x 6 x 7 ⊕ x 6 x 8 ⊕ x 7 x 8 ;
E34 (X 2 ) = x 5 x 6 x 7 ⊕ x 5 x 6 x 8 ⊕ x 5 x 7 x 8 ⊕ x 6 x 7 x 8 ;
E 44 (X 2 ) = x 5 x 6 x 7 x 8 .
. Ei4 (X1 )
,
):
E14 (X1 )
-
. Ek = Ek(X) = Ek(X1, X2)
E 4j (X 2 ) , k = 1, 12 , i = 1, 4 , j = 1, 4 .
.
2; E 24 (X1 ) 4; E 34 (X1 ) -
17;
E14 (X 2 )
19; E 44 (X1 ) -
-
1;
3
4
3; E (X 2 ) 16.
.
5
-
-
E 24 (X 2 )
18;
4
4
2)
-
4
R = ∑ ( 2x i + x i + 4 )
36-43
6
0
1
2
3
4
5
6
7
8
9
10
11
12
E1(X)
E2(X)
E3(X)
E4(X)
E5(X)
E6(X)
E7(X)
E8(X)
E9(X)
E10(X)
E11(X)
E12(X)
44
0
1
0
1
0
1
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1
0
1
0
45
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1
1
0
0
1
1
0
0
1
1
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46
0
0
0
1
0
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0
1
0
0
0
1
0
47
0
0
0
0
1
1
1
1
0
0
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0
1
48
0
0
0
0
0
1
0
1
0
0
0
0
0
49
0
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0
0
0
0
1
1
0
0
0
0
0
50
0
0
0
0
0
0
0
1
0
0
0
0
0
51
0
0
0
0
0
0
0
0
1
1
1
1
1
52
0
0
0
0
0
0
0
0
0
1
0
1
0
53
0
0
0
0
0
0
0
0
0
0
1
1
0
54
0
0
0
0
0
0
0
0
0
0
0
1
0
55
0
0
0
0
0
0
0
0
0
0
0
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1
BY 13273 C1 2010.06.30
i =1
BY 13273 C1 2010.06.30
36-39
(
1,
)
40-43
-
5
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8
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2
44, 45, ..., 55
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9051,
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G 06F 7/00, 2007.
G 06F 7/00, 2007.
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