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BY (11) 7002
(13) C1
(19)
(46) 2005.06.30
(12)
7
(51) G 06F 7/50
(54)
(21)
(22) 2002.05.28
(43) 2003.12.30
(71)
:
: a 20020460
(BY)
(72)
:
(BY)
;
(73)
:
(56) BY 2629 C1, 1999.
BY a 19981000, 2000.
BY a 20000624, 2001.
RU 2006915 C1, 1994.
SU 1827672 A1, 1993.
US 4229802 A, 1980.
JP 3108023 A, 1991.
JP 4128922 A, 1992.
(BY)
(57)
,
,
,
,
, i- (i = 1,5 )
i-
, i-
-
i-
,
,
,
BY 7002 C1 2005.06.30
,
.1
BY 7002 C1 2005.06.30
,
,
,
,
-
,
,
,
,
,
,
, i-
i-
,
-
,
,
,
,
-
,
,
,
,
(i + 4)-
-
,
ii-
i-
,
-
.
.
(
-
),
,
[1].
,
.
(
,
-
),
,
,
,
[2].
,
,
.
.
,
-
.
,
,
,
,
.
i- (i = 1,5 )
i-
, i-
i.
,
2
-
BY 7002 C1 2005.06.30
.
,
.
,
.
,
,
.
,
,
-
.
, i-
i-
.
.
.
-
.
.
,
.
.
(i + 4).
(i + 4).
i-
(i + 4)-
-
ii-
.
(
. 1)
.
1-9,
10
13,
14
-
11,
12
15,
16, 17
18,
19,
25-29,
20-24,
30,
31-34.
.
(
5
5
i =1
i =1
):
S = ∑ X i = ∑ (2 x 1i + x 2i ),
∈ {0,1} Xi = 2x1i + x2i, i = 1,5 .
,a
1i
2i
∈ {0,1} -
Xi ∈ {0,1,2,3}
,
(1)
S ∈ {0,1,...,15}.
(s1,s2,s3,s4),
(1)
:
S = 8s1 + 4s2 + 2s3 + s4 = 4(2s1 + s2) + (2s3 + s4),
s1,s2,s3,s4 ∈ {0,1} .
-
(2)
.
30
x11-x15 (
),
)
s1,s2,s3
s4
u = 0.
25-29 Xi.
,
3
20-24
31, 32, 33,
x21-x25 (
34
(2)
S.
BY 7002 C1 2005.06.30
-
,
:
1i
∈ {0,1} Xi = -2
,
5
5
i =1
i =1
S = ∑ X i =∑ (−2 x 1i + x 2i ),
(3)
∈ {0,1} -
(
(
), a
1i + x2i, i = 1,5 .
Xi ∈ {-2,-1,0,1}
2i
)
-
S ∈ {-10,-9,...,-1,0,1,...,4,5}.
(s1,s2,s3,s4),
(3)
:
S = -8s1 + 4s2-2s3 + s4 = 4(-2s1 + s2) + (-2s3 + s4),
s1, s3 ∈ {0,1} ;
s2, s4 ∈ {0,1} .
-
(4)
.
)
)
31, 32, 33,
30
x11-x15 (
x21-x25 (
34
(4)
S.
u = 1.
20-24
25-29 -
),
(
)
s1,s2,s3
Xi.
,
s4
-
. 2).
(
. 1)
s1 = M 4 (X 1 ) ∨ M 2 (X1 ) ⋅ M 2 (X *2 ) ∨ M 2 (X 1 ) ⋅ L(X 1 ) ⋅ M 4 (X *2 );
:


s 2 = u ⊕ M 4 (X *2 ) ⊕ L(X 1 ) ⋅ M 2 (X *2 ) ⋅ M 4 (X *2 ) ⊕ M 2 (X 1 ) ⋅ M 4 (X 1 );

s 3 = M 2 (X *2 ) ⋅ M 4 (X *2 ) ⊕ L(X1 );


s 4 = L(X 2 ),

X1 = (x11,x12,…,x15), X2 = (x21,x22,...,x25), X *2 = (x *21 ,x *22 ,...,x *25 ),
L(X1) = x11⊕ 12⊕...⊕ 15; L(X2) = x21⊕ 22⊕...⊕ 25.
(5) Mh(Z), Z = (z1,z2,...,zn), zj ∈ {0,1}, j = 1, n , h,
(h ≤ n):
1,
z 1 + z 2 + ... + z n ≥ h;
M h ( Z) =
0,
z 1 + z 2 + ... + z n < h.
,
u=0
*
2
= X2,
(5)
*
2i
= u⊕x2i, i = 1,5 ;
,
:
s1 = M 4 (X 1 ) ∨ M 2 (X1 ) ⋅ M 2 (X 2 ) ∨ M 2 (X 1 ) ⋅ L(X 1 ) ⋅ M 4 (X 2 ); 

s 2 = M 4 (X 2 ) ⊕ L(X 1 ) ⋅ M 2 (X 2 ) ⋅ M 4 (X 2 ) ⊕ M 2 (X 1 ) ⋅ M 4 (X1 );

s 3 = M 2 (X 2 ) ⋅ M 4 (X 2 ) ⊕ L(X1 );


s 4 = L(X 2 ).

*
u=1
X 2 = X 2 , X 2 = ( x 21 , x 22 ,..., x 25 ), (5)
4
(5)
(6)
:
BY 7002 C1 2005.06.30
s1 = M 4 (X 1 ) ∨ M 2 (X1 ) ⋅ M 2 ( X 2 ) ∨ M 2 (X 1 ) ⋅ L(X 1 ) ⋅ M 4 ( X 2 ); 

s 2 = M 4 ( X 2 ) ⊕ L(X 1 ) ⋅ M 2 ( X 2 ) ⋅ M 4 ( X 2 ) ⊕ M 2 (X 1 ) ⋅ M 4 (X1 );

s 3 = M 2 ( X 2 ) ⋅ M 4 ( X 2 ) ⊕ L(X1 );


s 4 = L(X 2 ).

M2( X 2 ) = M 2 (X2), M4( X 2 ) = M 2 (X2), (7)
s1 = M 4 (X 1 ) ∨ M 2 (X1 ) ⋅ M 2 (X 2 ) ∨ M 2 (X 1 ) ⋅ L(X 1 ) ⋅ M 4 (X 2 ); 

s 2 = M 4 (X 2 ) ⊕ L(X 1 ) ⋅ M 2 (X 2 ) ⋅ M 4 (X 2 ) ⊕ M 2 (X 1 ) ⋅ M 4 (X1 );

s 3 = M 2 (X 2 ) ⋅ M 4 (X 2 ) ⊕ L(X1 );


s 4 = L(X 2 ).

,
(6),
(8).
(7)
:
(8)
-
,
.
:
1.
2.
.
1827672,
2629,
G 06 F 7/50, 1993.
G 06F 7/50, 1999 (
).
.2
.
220034, .
,
.
, 20.
5
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