:




                                         
                       __________________________________

                                  " "



                                   


                          ,

                      

                               



                                   1993

                                  .
                                  -----------


        1.   ................................

        2.  ................................

        3.      ........

        4.    
               
          .....................................................


                       1.  " "
                       ---------------------------------

                    60-70  
          ,      
          .    -
                
              . -
           .
                    1977     
              "  "
        , , " ".
                       -
        ,     ()     ,  
          ()   ,     -
         .
              "" -      -
          ""      -
         ,      .
                   -    
        -       ,    -
            -    -
          .    -
               
         .

                       2.   
                       --------------------------------

                        -
            RSA,    1977    
               -
           : R.Rivest, A.Shamir, L.Adleman. -
                   
         .
               -    
        ""    M.   ("-") -
              .,
          " "  .
              ""        
         d        
            n, ..,:

                                   d
                             S =    mod n

               -       [M,S].  
              d.
                      -
          e,     


                            e  ?
                           S   =   M mod n

.
               ,     S  -
              d,    e 
        d  ,       n.  
           n   ,    
            150-170  .
               "-"        
         ,  RSA.
                       
          .
                          El
        Gamal  T.,  A public-key cryptosysems and signature schme based
        on discret logarithms,IEEE Trans.Inform  Theory,  v.31  N4,  pp.
        469-472 (1985).
                    -
                    4  
            ,    
           1000 .


                   3.    
                   -----------------------------------------


                     -
        .      
          .
                    .-
          ..,    1976 .   
           

                                x
                        f(x) = a (mod p)

               ,   -  ,   . -
         ,     ,    f(x), -
            .
                     
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        ,     a (mod p)     .
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         .

.

                                           
                                   
                X                                      X      
             |X|->a -------------------------------------> a       
                                                              
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                 ,
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          RSA.
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                     ()    
        "-" 200/.   -286,   
            DES.

.

             4.     
             ------------------------------------------------------
                       
                  -------------------------------------------


                 N+1  :   N -
        .   i = 1, 2,..., N.   
            .       
           (,    ..).  
               .   -
             .      
               .


                           - .

        I .      .
        II .       () -
                     .                                  X
                         
                  Y
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        III .           
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        IV .            
                  .
        V .    .


                                         
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        I         X->a ------------------------> a                    I
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        I         +-----+    I               I   +-----+              I
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        I        a    I               I     | -   XYI
        I                    I               I     |        a  I
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        I                    I               I    +-+   |   +-+       I
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        I                    I               I    +sign     +-+       I
        +====================+               +========================+
                     -
        .




.
                       ,   

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                 ,
          ,    .

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                                                  |:  |:|
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                                                                |||||||||
                                                     |||||||||
                                                   |||||||||
                                                                |||||||||

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             | * * * | i | * * * | s | * * * | j |  j |
             +----------------------------------------------+


               i        
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     .




                     
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                      .  
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                  ,   
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                      -
             .


         



         .
         
        " "


             

             1.   () ............. 4

                1.1.  RSA....................................... 5

                1.2.   ................................ 7

                1.3.   " "................... 9

                1.4.    ..............11

             2.   ................................13

                2.1.  DES....................................14

                2.2.    28147-89.........................15

                2.3.   "".....................16

                2.4.   .....................17

             3.   ........................19

                3.1.    - .........................20

                3.2.  .........................21

                3.3.    ""............22

                3.4.  ................................23

             ..............................................24

             ..............................................25

              .
               " "...........................26

              .
                 "H "...29

              .
                 ...........35

              .
                  ..........40

              .
                .....................47



             1.   () .


                         
        .  . [ 1 ]  1976 .       
            
                 ,
              .

                     ,  
                 
         ,       , 
                   (
        ),       -
        ,   ,    -
         ,        -,   
          .

                     
         ,     -  
           (,  ,  ...)  
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              , ..
            .

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           .

               "  "     
                 -
        .

               ,      -
                 -
        (   "   ")
               -  
                -
              .
             1.1.  RSA.


                       
        "  RSA",      1977      -
           ()    -
                 :  R.Rivest,   A.Shamir,
        L.Adleman [ 4 ].

                  ,  ,        
         n,       
         ,   n = P*Q,     
         e, d, 1

* *

    .

() ......... . , .............................. ( - ), , ; - ; , ; - , -- ; , - , , - , : I. () , () . II. , () , - - () , . III. - , () , ............... . , ............................ , - , - () , - , . ............................ . - ................. , , - . IV. , , . . () - , .......................... . V. ... , , , - . .......................... . ___________________________________________________ __________________________ (_____________) .. ___________________________________________________ __________________________ (_____________) .. . . . . . . . . . . . . . . . . . . . . . . . . .

, , , - - .......................... . 1. , , , ( ), . , , - - , . 2. - ( ), - . .58 /1/ , , , . , , - , . ____________________ /1/ 31 1991 . (- . 1991. N 26. .733). - 14 1992 . " - - " ( . 1992. N 30. .1800) 3 1992 . ( - ). , , . - , , - , , , .., , (.2 .58 ). - . - , -- , , , - . , , . - , , , - . 1974 , - - , - - ./1/ .2 - , , , , - . , , -- , - , . ____________________ /1/ 29 1979 . N -1-4 " - , - .// - . . 1989. .47-49. , -- - ( , ..). - - , .9 29 1979 . N -1-4, , - (, , - , ..), , , . , , : , , , , , . 3. , , : 3.1. .6 - , , , . 4 1991 . " - "/1/ , - , - ( ) - ( ). .1 .20 - /2/ , , , - , -, - ( - ), - , - . , - ... , . , .7 .27 , , , _______________________________ 1. . 1991, N30, .1013; . 1992, N34, . 1965. ( ). 2. 5 1992.// .1991, N16, .836. ( - ) . , - , (.157). 3.2. .7 , ..21 157 , , - 24 1992. /1/ .2 - , - . . , , ,- , , , - , , , , , - , , - , . , , (, , , , ) , , - . - (.. , - () ). , - , , - , . _________________________________ 1. - .1992, N30, .1790. ( - ). 3.3. , V .157 . - : -, .2 .157 .25 - - - , - , ; -, .5 .157 .26 - , : ) ; ). - ; ). , - , - ; ). - . , - . , .3 .26 - , - - , , , . 3.4. : 3.4.1. ... , . , ... - .... - , ... , .. - , - , . 3.4.2. , ... , .3.4.1 - .... .7 , .21 .3 . , - . , , . , ... , , . 3.4.1. ... , (.. ). - , ( ) . , .. . , : , . - , , ,2 . 4. , - ... : 1) ; 2) , . 3.4 .

() ........................ . I. . 1. (- ) - , , ....... ........................ , - . 2. () , . . 3. - : . , , ( ), , , - . , " " , , - - . : - - ( ), . 4. () ( - ) - () . , ( - ), . .................. .............. , . 5. . - , . II. 6. : - ( ); - ; - ; - - ; - , ( , ); - - - , ; - - ( ) - ; 7. : - , - - ; - , ( , , ..); - , - ; - - - ; - , - ; - - , , - - , ; - , - ; - ; - ; - - . - - . III. 8. , : - , , , - -; - , , ; - ; - ; - ; : , - : - ; - ; - ( ) () ( ); - , . 9. , - , , , - - . , , / - . IV. 10. , - , - , : , - ; ; - , , , , , , - - , , , , - - . 11. , , , , : , , , - ; - , - , , . , : - - ; , - , - , - , ; - - - .

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