1.8.1
.
1.8.1
1.
=11, Q =7, k =37. (Ek, Dk) RSA-.
:
N = P*Q = 11*7 = 77.
j (N) = (P -1)(Q -1) = 10*6 =60 = 22 3 5.
Dk
.
(1.58)
.
ϳ j (Nj) Ek
.
/ b
;
60/37=1+23/37; 37/23=1+14/23; 23/14=1+9/14; 14/9=1+5/9; 9/5=1+4/5; 5/4=1+1/4; 4/1=4+0.
, =6.
.
ϳ , 0, 1, 2, 3, 4 5.
y = Dk = (-1)6*13 = 13;
.
Ek Dk
.
(Ek =37 Dk = 13) RSA-.
2.
=11 Q =7. (Ek, Dk) RSA-, .
:
j (N)
.
ij
.
Ek =17 , , (Ek, j (N)) = 1,
.
a / b :
;
60/17=3+9/17; 17/9=1+8/9; 9/8=1+1/8; 8/1=8+0.
.
y=Dk, (1.59)
.
2:
ϳ 2. (1.10.12),
.
RSA .
:
ϳ Ek =17 Dk = 53,
.
10.
=11 Q =7. Ek =9 (Ek, Dk) RSA .
:
RSA :
Dk
,
ij
:
;
60/9=6+6/9; 9/6=1+3/6; 6/3=2+0.
, (Ek, Dk) .
1.8.2
1. (Ek, Dk) RSA , ( Q . 1.3).
1.3 Q 1
n | ||||||||||
P | ||||||||||
Q |
.
, .
2. , N = N ( Q . 1.4).
1.4 Q 2
|
|
n | ||||||||||
N |
- .
, .
1.
=11, Q =7, k =37. (Ek, Dk) RSA-.
:
N = P*Q = 11*7 = 77.
j (N) = (P -1)(Q -1) = 10*6 =60 = 22 3 5.
Dk
.
(1.58)
.
ϳ j (Nj) Ek
.
/ b
;
60/37=1+23/37; 37/23=1+14/23; 23/14=1+9/14; 14/9=1+5/9; 9/5=1+4/5; 5/4=1+1/4; 4/1=4+0.
, =6.
.
ϳ , 0, 1, 2, 3, 4 5.
y = Dk = (-1)6*13 = 13;
.
Ek Dk
.
(Ek =37 Dk = 13) RSA-.
2.
=11 Q =7. (Ek, Dk) RSA-, .
:
j (N)
.
ij
.
Ek =17 , , (Ek, j (N)) = 1,
.
a / b :
;
60/17=3+9/17; 17/9=1+8/9; 9/8=1+1/8; 8/1=8+0.
.
y=Dk, (1.59)
.
2:
ϳ 2. (1.10.12),
.
RSA .
:
ϳ Ek =17 Dk = 53,
.
10.
=11 Q =7. Ek =9 (Ek, Dk) RSA .
:
RSA :
Dk
,
ij
:
;
60/9=6+6/9; 9/6=1+3/6; 6/3=2+0.
, (Ek, Dk) .
1.8.2
1. (Ek, Dk) RSA , ( Q . 1.3).
1.3 Q 1
n | ||||||||||
P | ||||||||||
Q |
.
, .
2. , N = N ( Q . 1.4).
1.4 Q 2
n | ||||||||||
N |
- .
, .