. . , , , , . , [21]. , , , , , . , , , . ҳ , 70- , , .
. , . ij, RSA г, , , , , , .
: . , , , .
, . , , . .
, , : . , . . : . . , , . . , . , .
. . , : , ( ) ( , ). .
|
|
. .
. . ?
, n? . ij
.
, .
, , . ( ) , . .
, 9 . 6 . ? : 15 , 3 . , ? 12 . :
9 + 6 = 15,
15 12 = 3.
3 :
15| 12
- 1
12
, 15 12 3.
15 = 3(mod 12),
, 15 3 12.
( ).
, 39
39 = 3(mod 12),
51 = 3(mod 12)
.
, ( ) , .
, - - .
:
, , .
:
, , .
ij,
6(mod 12) + 3(mod 12) = 9(mod 12),
6(mod 12) + 3(mod 12) + 3(mod 12) = 12(mod 12) = 0(mod 12).
24(mod 12) = 0(mod 12), 36(mod 12) = 0(mod 12), ..
, , , ..
, , RSA [21].
, . , , , . ? RSA - p q (, , , ). :
p > q
.
p = 17, q = 11.
() .
:
N = p q = 1711 = 187.
N e, :
|
|
q;
k (p 1) (q 1) = k (mod e) , k ≠ 0.
, , , .
= 7. : 1610 = 160, 7 .
N = 187
e = 7.
. , . . ASCII.
= Me (mod N),
, ,
.
, . ASCII 1011000, 88 .
= 887 (mod 187) = 881 (mod 187) x 882 (mod 187) x 884 (mod 187) =
= 88 (mod 187) 7744 (mod 187) 59969536 (mod 187) = 88 x 77 x 132 (mod 187) = 894432 (mod 187) = 11 (mod 187).
= 11. , .
. d. ³
e d = 1 [mod (p 1) (q 1)]
(! 1).
7 d = 1 (mod 160)
d = 161: 7 = 23.
= d (mod N).
= 1123 (mod 187) = [ 111 (mod 187) x 112 (mod 187) x 114 (mod 187) x 1116 (mod 187) ] = 11 x 121 55 x 154 (mod 187) = 88 (mod 187).
88 .