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519.6+681.83

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3- 1

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2000 .

蠠 , ࠠ 堠 堠 ⠠ ,   . ࠠ . ࠠ ࠠ :

-   젠 젠 堠 젠  蠠 ;

-   , 堠 堠  ࠠ .

ࠠ ⠠ ,  ⠠ , 堠 ࠠ ( ) ( ) ( ), 堠 蠠 ꠠ , ꠠ 蠠 . 蠠 蠠  ࠠ 蠠 ⠠ , ࠠ 頠 蠠 .   堠 .

1.    4

2.    ..5

3.    堠 ...6

4.    1. 堠 ....7

5.    2. 셅8

5.1.      (time lock puzzles) 9

5.2.      堠 .12

5.3.      ࠠ 젠 ⅅ14

6.    充19

7.    ꠠ ..20

, . - . . . 堠 堠 頠 젠 :

     ;

  • , , ;

     .

   .

蠠 蠠  蠠 . Ѡ 젠 , , , 젠 , 蠠 - ࠠ 蠠 ⠠ .

젠  ࠠ 蠠 頠 ⠠ 堠 ࠠ  頠 頠 .  ࠠ 񸠠 , ⠠ 蠠 - .

, , 堠

 ࠠ  頠 蠠 ࠠ 蠠  堠 . 蠠 , , 頠 頠 , 蠠 . ,  젠 蠠 蠠 , 頠 , 頠 ⠠ . , 蠠 , ,   ,  , .  蠠 ࠠ 蠠 . , 黠 젠 ࠠ - . , 堠 ( , 堠 堠 , 蠠 , . .), 堠    .

堠 蠠 蠠 蠠 젠 蠠 ࠠ .

.

頠 ࠠ 󠠠 頠 . , ,  頠 蠠 ⠠ 頠 . , Intrnet 젠 , 蠠 , 렠 . 렠 堠 . ࠠ 蠠 蠠 , 蠠 . , . . 堠 , , . 頠 , 堠 , , ࠠ 蠠 頠 堠 蠠 596 蠠 . ,  堠 ࠠ , 蠠  ⠠ 頠 頠 .

.

- .

- , .

t - , 堠 .

- .

S - .

- .

p ,q .

n , 렠 p q.

f(n) , 堠 (p-1) (q-1).

d , .

i[1]  .

θ .

Si,t- .

Di,t .

yj , j-

rj , j-

F -.

 

1. 堠 .

堠 , ࠠ ꠠ ,  蠠 堠 堠 堠 蠠 젠 :

     ꠠ 堠 ,     蠠 ;

     蠠 젠  (digital cash) 蠠 蠠 , ࠠ ⠠ 堠   ;

      頠 , 㠠   ;

     젠 頠 (key-escrow scheme) ࠠ ࠠ 䔠 젠 젠 , 堠 蠠 蠠 蠠 蠠   蠠  .

  砠 ࠠ 堠 堠 젠 ⠠ 1 , ࠠ 堠 񠠠 컠 젠 蠠 頠 ࠠ ꠠ , ꠠ , 2-3 , ࠠ 堠 . 堠 , ࠠ , 2-3 , ,  . 頠 砠 ⠠ .

  , ࠠ 젠 , ࠠ ࠠ ࠠ ( 젠 蠠 젠 )  蠠  ࠠ . ࠠ ࠠ , 蠠  堠 . 頠 ᠠ , 頠  蠠  , 頠 젠 젠 ( timed - release crypto ).

2. .

ࠠ 젠 , .., . ..젠 ࠠ 젠 젠 (time lock puzzles ). 䠠 堠 蠠  , 蠠 蠠 堠  ⠠ .  ࠠ ⠠ ,  ⠠ , 堠 ࠠ ( ) ( ) ( ) , 堠 蠠 ꠠ , ꠠ 蠠 .

  ࠠ ࠠ 젠 :

-   젠 젠 堠 젠  蠠 ;

-   , 堠 堠  ࠠ .

,  蠠 ⠠ , ࠠ 頠 蠠 . 堠 ࠠ 蠠 ࠠ  , 堠 頠 ⠠ 蠠 . .

(time lock puzzles)

,  堠 頠 堠 . , 󻠠 (頠 ), ꠠ , , ࠠ , 젠 堠 .  , ( ) ࠠ . 젠 , ࠠ 蠠 頠 ꠠ ࠠ , , 頠 ⠠ 堠 蠠 ( )   堠 蠠 堠 . 젠 堠 ⠠ .

 ꠠ 仠 , ꠠ 򠠠 ꠠ . , 頠 ࠠ 蠠 , 젠 ,   頠 .

, 頠 仠 蠠 堠 , 򠠠 頠 ࠠ 堠  . , , 堠 10 , 頠 ⠠ 堠   . ,  堠 堠 򠠠 10 , 頠 렠 5 ( ࠠ , 頠 ) 堠 , ꠠ . 젠  , 頠 򠠠  ࠠ ( ) ( ).

蠠 젠 . ̠ , 堠 , ࠠ S ( ) . ̠ ,   蠠 Ҡ , ( RC5 ).Ƞ 젠 堠 堠

K = lg ( 2ST )

. . 堠 軠 ( ࠠ ⠠ 젠 ) Ҡ .

  蠠 젠 堠 :

-   ໠ 堠 , ⠠  N ⠠ ⠠ N

-   T 젠 젠 ;  蠠 , 蠠 , ⠠ 堠 .

 ,  , ࠠ ࠠ 젠 , 堠 . 頠 蠠 , ꠠ ࠠ ,  젠 , 젠 , . 頠 , .

젠 䠠 , .., ., ..젠 蠠 頠 ࠠ 젠 蠠 蠠 .

, ࠠ 堠 , ,    砠 .

 :

     頠 n = pq 堠 렠 p q 򠠠 f(n) = (p-1) (q-1);

     򠠠 t = T S , 堠 S (  n ) ,  ;

     頠 , RC5 . ;

     RC5 . C(M) = RC5( K, M ) ;

     젠 젠 n (1<a<n), 頠 ʠ : C() = K + b ,  ࠠ 򠠠 e = 2t(mod f(n)) (1), b = ae (mod n) (2);

     ⠠ 堠 ࠠ ⠠ (n, a, t, C(K), C(M) ) 蠠 ( , : p, q, e, b, n ), 堠 堠 .

젠 , 堠 蠠 頠 . 頠 頠 ᠠ  堠

b = ae (mod n).

蠠 젠 f(n)   e,  堠 (1) 蠠 젠 b  堠 (2). ,  堠 f(n) n 堠 ,  堠 n ࠠ . 젠 , 頠 頠 ⠠ 堠 ᠠ b ( p, q, ) ꠠ ⠠ (t ), ( 젠 ).

n ࠠ ,  蠠 p q 頠 䠠 堠 , 젠 堠 堠 .

 頠 ⠠ t , 䔠 蠠 .

堠 堠 , 젠 b(2) . 蠠 , 젠 b(2) ⠠ 堠 . 頠 蠠 , 젠 , 頠 蠠 , , .

, ࠠ ࠠ ࠠ 堠  ⠠ ,   f(n), ⠠ 頠 蠠 e (1) b (2), 頠 蠠  .

 ⠠ , ࠠ Ҡ 堠 򠠠 5 , 蠠 . 頠   젠 젠 ⠠ 堠 . .  ࠠ 򠠠 , ,  砠 堠 5 ⠠ 10 . , , , ,  砠 򠠠 ( 堠 , 蠠 ) 10 堠 , 堠  1 . 젠 񸠠 蠠  6 ,   .

,  ,  ࠠ S ( ) , ,  , 蠠 蠠 頠 , , ( ,  ࠠ 㠠 頠 頠 򠠠 ) ࠠ ࠠ 蠠 . , ࠠ ࠠ , 򠠠  . ʠ . , , ⠠ 堠 , 젠 .

 

,  젠 젠 堠 堠 .

     젠 .   堠 젠 젠 , [public] 蠠 [private, secret], 堠 젠 ,  堠 堠 ꠠ 󠠠 ⠠ 砠 . ࠠ 򠠠 頠 , - . 堠 ࠠ 砠 蠠 ; ⠠ , 蠠 ࠠ  ࠠ  󠠠 󠠠 .  蠠 񠠠 젠 頠 ࠠ . 蠠 蠠 蠠   頠 ,  젠 堠 頠 蠠  蠠 ⠠ 젠 堠 蠠 .

     . 頠 ꠠ , 頠 젠   . 蠠 񠠠  ࠠ  ,  堠 蠠  񠠠   . 젠 :  堠 蠠 젠 ,  󠠠 ; , 젠 ; 頠 堠 . 蠠 , ,  堠   (⠠ ,  젠 , 젠  ). 堠 蠠 ࠠ (timestamp) ࠠ : , 頠 ,  젠 蠠   ࠠ , , ,  堠 렠 ⠠ , 頠 ⠠ 堠 .

     . - 帠 , . 堠 򠠠 젠 젠 (""). ⠠ , ,  "" - .

     RC5. RC5  -蠠 頠 頠 𠠠 RSA Data Security. 젠 , .. 񠠠 젠 , 頠 ࠠ 蠠 젠 . 32, 64, 128 .  ⠠ ⠠ 0 2048 .  ࠠ 蠠 . RC5 砠 ࠠ ࠠ (key expansion), . 蠠 ࠠ 堠  , .. 堠 砠 3 : , XOR 蠠 (rotation). ࠠ RC5  젠 ⠠ , RC5 , 堠 ꠠ 蠠 RSA, ⠠ ࠠ ⠠ 젠 . RC5 ࠠ 젠 젠 蠠 젠 ⠠ . RC5 񠠠 젠 ࠠ 64 12 堠 ⠠ ⠠  .

     . ࠠ  , 頠 , 堠  . 頠 ࠠ , 򠠠 n , 堠 堠 ( ࠠ ) 蠠 , - 蠠 頠  젠 . , (n , θ ) , 򠠠 , 젠 堠 θ 蠠 堠 .

ࠠ 젠 .

頠 , ࠠ ࠠ ࠠ 軠 , ꠠ ꠠ 堠 , ࠠ .

, 䠠  ࠠ ⠠ 堠 t . , , d , ࠠ ., 蠠 젠 , ,  t . ,  ࠠ ࠠ 蠠 򠠠 , ࠠ . = ( , ) ⠠ 堠 , 堠 ( ) t .

, 蠠 䠠 :

     , 堠 堠 .. 頠 , . 頠 젠 , 䠠 , 堠 , .

     , 頠 򠠠 頠 頠 , ⠠ t . , ,  .

     ࠠ : ( , ⠠ 堠  ) - Si,t ( -) 蠠 頠 頠 ࠠ 젠 , . 䠠 젠 堠 - Si,t 頠 -.

     , ࠠ : 頠 tE( y , Si,t ) ࠠ 젠 堠 Si,t , 頠 ⠠ t. , 堠 ࠠ 젠 , ꠠ Si,t , 蠠 ⠠ 젠 堠 Si,t. , ࠠ 젠 堠 蠠 ࠠ 젠 . 堠 , , t, Si,t E( y , Si,t ).

     頠 򠠠 蠠 .

, ࠠ 젠 ⠠ : ࠠ , 蠠

=( , ).

, d i1, [2] i2, ,id :

( , i1, [3] i2, ,id. , r1, r[4] rrRRg2, ,rd ) ,

r1, r[5] rrRRg2, ,rd - d . 蔠 堠 , t ,堠 , . 򠠠 ࠠ , . θ (0 < θ d ) , 堠  蠠 θ 蠠 젠 堠 .  d 锠 堠 젠 θ.

.

堠 򠠠 ࠠ , , 軠 .

rj = E( yj , Si,t ) ,

(y1, y2 , . ,yd) d .

, 頠

n = pq ,

堠 렠 p q . 堠  򠠠

f(n) = (p-1) (q-1)

e = 2t(mod f(n)).

ࠠ 렠 (e, n) 젠 젠 .

, 頠 젠 . 頠 砠 頠 頠 , 堠 - ,  頠 , , 蠠 堠 頠 頠 , 젠 .

젠 젠 :

Þ   蠠 堠 堠 -. Sij,t ij t . , , . 젠 : 砠  Sij, Sij,t t ., 頠  : Si,(t-1) = F ( Si,t ) (3), f - - (Si,(t-1) , Si, t , 񠠠 (t-1) - , 1 , ࠠ 蠠 򠠠 , ) F , Si,t Si,t. (  堠 (3), , F , Si,t - Si,(t-1) ). 頠 ࠠ . , 頠 젠 蠠 ࠠ , 蠠 .

Þ   , 젠 , ࠠ (y, t, (e, n)) , y - 堠 頠 .

Þ   堠 y Si,t , 蠠 t . 󠠠 E(Si,t ,y).

Þ   :

m=( i, t, t˚ , E(Si,t ,y)),

i - 񠠠 , t , - (

). 堠

(e, n) 蠠 젠 - Si,:

E( E( m , (e, n) ) , Si,).

t > t˚ , 

.

     Si,t t .

蠠 蔠 ʠ 頠 -, 堠 Si,t , . 頠 - . 젠 򠠠 堠 蠠 砠 蠠 ࠠ .  ,  頠 堠 . 堠 頠 蠠 젠 ࠠ 蠠 . , 򠠠 : , .. ; 頠 堠 .

頠 ⠠ 堠  ꠠ , ,  . 頠 堠 , 頠 堠 蠠 蠠 . 堠 򠠠  堠 ,  젠 , 頠 蠠 , ࠠ 蠠 . ꠠ   , 頠 򠠠 頠 , 頠 t, ⠠ 堠 ⠠ ࠠ , ࠠ , 堠 . , ⠠ 堠 蠠 , 蠠 젠 , 㠠 堠 .

頠 頠 , , ࠠ 蠠 蠠 . ⠠ 堠 θ , 堠 堠 , 젠 堠 .

ࠠ ⠠ 젠 ,   젠 젠  堠 堠  .  蠠 , rj 񠠠 yj.

 唠 .

ࠠ 頠 ꠠ : , 蠠 堠 Di,t Si,t , Di,t = f (Si,t). 򠠠 蠠 蠠 . Di,t . 򠠠 堠 堠 젠 y , 頠 젠 Di,t. 젠 蠠 :

     Di,t .

     堠  ࠠ 젠 Si,t.

     頠 Si,t t .

젠 , ⠠ 蠠 ࠠ , .

堠 堠 . ,  頠 堠 : 蠠 . . , , ( ) , , , .

頠 ,  蠠  ࠠ  ꠠ 頠 堠 ( 頠 頠 ), ꠠ 蠠  蠠 蠠 .  , ꠠ ,  堠 . , ⠠ 堠 t ⠠ ࠠ 蠠 ( , 蠠 , 젠 ) .

蠠 , ,   , 젠 젠 蔠  , 젠 , 젠 젠 젠 . , ,  - ꠠ 蠠 .

,  頠 䠠 蠠 ࠠ , 堠 , ࠠ 堠 . , 頠 젠 蠠 ࠠ ( ࠠ ࠠ ) 蠠 200 3,5 .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.

젠 젠 ࠠ ( ). : (time lock puzzles) ࠠ 젠 . , 堠 , , , . , 젠 , 頠 . , ( θ ) . , 蔠 , , 蠠 . 蔠 , . 蠠  .   , , 锠 蠠 . , , 젠 , . , , .

堠 , , . , 堠 򠠠 頠 蠠 , . ࠠ , ࠠ  4000 .

, , . , , ࠠ (  , ) . 蠠 , , 젠 . , ,  .

.

1.    Ronald L. Rivest, Adi Shamir and David A.Wagner Time lock puzzle and time-release Crypto. (http://theory.lcs.mit.edu/~rivest - 1999. 蠠 蠠 堠 )

2.    .., ⠠ 唠 , 596

3.    . . ,

4.    Tatu Ylonen Introduction to Cryptography

5.    .., .

web- http://www.ssl.stu.neva.ru/ ࠠ 蠠 . . , .


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 [5]

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