k = (k 0, k 1,..., k n),
, , . ,
k = (k 0, k 1,..., k n), k j = k (jmod r , 0 £ j < ¥.
, r = ¥ 15 8 2 10 11 4 18 :
15 8 2 10 11 4 18 15 8 2 10 11 4 18 15 8 2 10 11 4 18...
. VI Gk
VI Gk: (x0, x 1,..., x n-1) (y0, y 1,..., y n-1) = (x0+ k, x 1+ k,..., x n-1+ k).
:
1) x r
x i = (xi, x i+ r ,..., x i+ r (n-1)), 0 £ i < r;
2) i- x i C k:
(xi, x i+ r ,..., x i+ r (n-1)) (yi, y i+ r ,..., y i+ r (n-1)),
m =2 (1917 ).
k =(k 0, k 1,..., k -1) . , , . ( 2). AT&T , .
, k =(k 0, k 1,..., k -1) . . .
. (r=4)
(1):
____
:
4 :
_ _ _ _
( ):
H+=, += ..
(1) :
_
. .
x - SYM(Zm).
. r- r - p = (p0, p1,..., p r -1) x.
(x0, x 1,..., x n-1) (y0,y1,...,yn-1) p = (p0, p1,..., p r -1)
VI Gk: (x0,x1,...,xn-1) (y0,y1,...,yn-1) = (p0(0), p1(1),..., pn-1(xn-1)),
pi = pimod r .
, . .
.
|
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. , , .
(, 2).
.
, . . , , ( ). .
, . . . , .ʭҭΔ, . .
, .
, , . .
. , .
. T(i),
T(i+1) = (A*T(i)+C)mod m,
- , (0) - , . , .
, . m 2n, n - . , . , , , . . , , - , mod 4 = 1.
|
|
. , x (j) b, j=1, 2,..., n. G H(j).
- [5]
- , .
- , k - . k 2. .
:
r1:=r0 r2:=r1 ... rk-1:=rk-2
r0:=a0 r1 Å a1 r2 Å... Å ak-2 rk-1
i:= rk-
r0 r1 ... rk-1 - k , a0 a1 ... ak-1 - k-1. i - i- .
- 2 k -1.
- , .. - k. :
k | |
, .
, -. -. k =10 1023 (-) 388000.
( ), .
, .
. , , , . , .
28147-89 [6]
. DES, . . .
.
, , . , , DES, . .
|
|
, . :
AÅB - 2;
A[+]B - 232;
A{+}B - 232-1;.
. W 256 , 32- x (i).
W=X(7)X(6)X(5)X(4)X(3)X(2)X(1)X(0)
, .
- .
64 , T(j).
T(j) B(0) A(0) 32 ( ). , :i:
i=1, 2,..., 24, j=(i-1)mod 8;
A(i) = f (A(i-1) [+] x (j)) Å B(i-1)
B(i) = A(i-1)
i=25, 26,..., 31, j=32-i;
A(i) = f (A(i-1) [+] x (j)) Å B(i-1)
B(i) = A(i-1)
i=32
A(32) = A(31)
B(32) = f (A(31) [+] x (0)) Å B(31).
i . f .
32- .
K. 8 (1)...(8) 64 . 32- 8 4- , 4- , 16 0...15. , . 4- 32- .
- 32- , . 64-
=(32)(32).
.
, .
.
, 64- T(i) (i=1,2,...,m) (m ), 2 , 64 , ..
=((1),(2),....,(m)).
:
(i)=A(Y(i-1) Å C2, Z(i-1)) {+} C(1) Å T(i)=(i) Å T(i)
(i) 64- , - ( 32- ). 1 2 - , 28147-89. y (i) Z(i) :
(Y(0),Z(0))=A(S), S - 64-
(Y(i),Z(i))=(Y(i-1) [+] C2, Z(i-1) {+} C(1)), i=1, 2,..., m.
|
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64- , , , , .
. , 64- T(i), 2 , 64 :
=((1), (2),..., (m)).
:
(1)=A(S)ÅT(1)=(1)ÅT(1),
(i)=A((i-1)ÅT(i)=(i)ÅT(i), i=2, 3,..., m.
28147-89 , . - ( ), . . .
64 . (1) , 16 . , . 64- (2) 16 . m . 64- .
. ? ?. .