GS _ Gm_ Signatur lgorithm ( ). GS , , ,- . , RS, .
-. ( - ), G, G < . (~10308 ~21024) G (~10154 ~2512), .
X, 1 < £ (-1),
Y =GX mod .Y , . Y .
.
, - h() m:
m = h(), 1 < m < (-1),, 1 < < (-1), , (-1) . :
= GK mod, , b
m = * + * b (mod (-1)).(,b) S:
S=(,b),.
(,,b) , (,) .
(,,b) , S=(,b) .
m = h(),.. .
= Ya ab (mod )
,
= Gm (mod ).,
Ya ab (mod ) = Gm (mod )., , , S=(,b) X, Y. , , X, , .
, , . - , , .
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. : = 11, G = 2 = 8. :
Y = GX mod = 28 mod 11 = 3., - m = 5.
, - m = 5, = 9. , (-1) . , (9,10) = 1. b :
= GK mod = 29 mod 11 = 6,b , :
m = * + * b (mod(-1)).m = 5, = 6, = 8, = 9, = 11
5 = 8 * 6 + 9 * b (mod 10) 9 * b = -43 (mod 10).: b = 3. : = 6, b = 3. . Y = 3, - : m = 5, :
Yaab (mod ) = 36 * 63 (mod 11) = 10 (mod 11); Gm (mod ) = 25 (mod 11) = 10 (mod 11)., .
, , (,b). .
RS:
1. , , 25% , .
2. , (-1) (.. ).
3. ( RS).
RS. , 1,5 , , , .