ივანე ჯავახიშვილის ... · PDF fileabcdefghijklmnoqrstuvwxyz...

Click here to load reader

  • date post

    23-Apr-2018
  • Category

    Documents

  • view

    248
  • download

    18

Embed Size (px)

Transcript of ივანე ჯავახიშვილის ... · PDF fileabcdefghijklmnoqrstuvwxyz...

  • :

    :

    :

    . , ,

    2013

  • 2

    .

    ,

    ,

    .

    .

    , ,

    , . ,

    ,

    .

    -

    , ,

    , .

    .

  • 3

    Abstract

    In the work The original digital signature algorithm and its implementation, an alternative

    algorithm for digital. The paper discussed issues related to the acquisition of the digital signature of

    the surveys, a digital signature algorithm further study, research and the results obtained from

    protocol and program implementation. signature is analyzed and obtained. Analogous to other well-

    known schemes, given algorithm is ElGamal. algorithm representing a certain modification of the

    prototype. The main idea is that by means of some functional properties of certain parameters, its

    possible to obtain needed structural alternative. Just as in other well-known and popular cases where

    a new structure is obtained by changing only one element in the prototype, we get more simplified

    and rapid structure with the aid of functional properties of the parameter. The main advantage of the

    obtained alternative algorithm is its simplicity and rapidness; however, it is less steady.

  • 4

    ..................................................................................................................................................... 5

    I ......................................................................................................................................................... 12

    ................... 12

    1.1 .............................................................................. 12

    1.2. ..................................................................... 20

    1.2.1 DES ............................................................................................ 23

    1.2.2 - ............................................................................ 25

    1.2.3 - - (RSA) ......................................................... 28

    1.2.4. ................................................................................................... 30

    II ........................................................................................................................................................ 31

    () .......................................................... 31

    2.1. ................................................................................. 31

    2.2. RSA ......................................................... 33

    2.3 ................................................................. 35

    2.4. DSA ............................................................................. 35

    2.5 P 34.10-94............................................................ 38

    III ....................................................................................................................................................... 41

    ............................................................................................. 41

    ................................................................................................ 41

    3.1. , -

    ; DSA .................................................................. 41

    3.2. ...................................................... 43

    3.3 ................................................................................. 48

    ...................................................................................................................................................... 49

    ............................................................................................................... 50

  • 5

    - ,

    ,

    ,

    .

    .

    , ,

    .

    ,

    , .

    S = (x+kRM) mod(p-1)

    .

    ,

    .

    .

    ? ,

    ,

    . ,

    , .

  • 6

    : ,

    , , , ..

    ,

    :

    ,

    .

    ,

    , ,

    .

    ,

    , :

    , , .

    , X Y ,

    . Z (, )

    .

    ,

    .

  • 7

    - ,

    ().

    4 : -,

    -, ,

    () .

    () (

    ) , -

    .

    : ()

    - ,

    . .

    () ( - ).

    - .

    ().

    .

    - ,

    , .

    , .

    ,

    .

    () ,

    , (, DES DEA-

    ), ,

    .

  • 8

    ,

    .

    ,

    ?

    ; :

    () ,

    . ,

    , (,

    ).

    ,

    , ,

    ?

    : ( ),

    X Y ,

    ; ( ).

    , ,

    .

    ,

    .

    ,

    , ,

    (

    ).

    : ,

  • 9

    (,

    , ),

    , .

    ,

    ( ).

    ,

    (, ..)

    ,

    ,

    (

    ) :

    .

    ()

    . ,

    -

    .

    . Z

    ,

    ..

    ,

    , .

    () ,

    .

    .

    ,

    , .

  • 10

    - :

    , ( ).

    ,

    .

    , ,

    :

    1) ,

    ?

    2) ,

    ?

    . ,

    .

    . ,

    ;

    () (, , ),

    .

    , ,

    ( ) ,

    . ,

    .

    , ,

    (), ,

    . , ,

    ,

    .

  • 11

    ,

    .

    ,

    .

    , .

    : , , ,

    ..

    .

    .

    .

  • 12

    I

    1.1

    _ ,

    ,

    . .

    _ .

    ,

    : .

    :

    ;

    ;

    ;

    .

    (XVI )

    .

    .

    ,

    (

  • 13

    . , .

    _

    ,

    ). :

    - .

    , , -

    , ,

    . ,

    - .

    , . A

    , , D -, B E -

    .. Z (. 1.1.) ,

    - ,

    -,

    :

    ABCDEFGHIJKLMNOQRSTUVWXYZ

    DEFGHIJKLMOPQRSTUVWXYZABC

    1.1.

    . ,

    - , ,

    , _ k , k{1,2,,26} (. k =3).

    , ,

    () .

    ,

    .

  • 14

    ( 5X5

    .

    ).

    (XV XX )

    ()

    . ,

    .

    ,

    .

    ( _ XVI ).

    (1586 ) .

    .

    -

    , (k

    s -). ,

    , . ,

    - k1 , -2- k2 ..

    l k= k1,, k1 , l

    l .

    ,

    . ,

    .

    , -

    . , -

    ( 1- 33-).

  • 15

    , .

    , .

    .

    ,

    (, ,

    )

    .

    .

    (1917). ,

    ,

    . , ,

    , .

    , .

    , ,

    k,

    (l >l), , ,

    , ,

    .

    . , -,

    , aiA

    , N. - mi

    ; mi{0,..., N-1}. , M a1, a2, a3,

    , C c1, c2, c3 ()

    BB , b1, b2, b3 . M avi

    mvi , C cui -mvi

    , B bwi -mwi , vi, ui, wi,

    {0,...,N-1}.

  • 16

    mvi + mui mwi (mod N),

    mwi + mui mvi (mod N)

    .

    , C

    , ,

    .

    . ,

    .

    C

    . C

    (

    ).

    XIX

    : .

    , ,

    . , ,

    :

    , ,

    .

    , (

    ) ,

    , .

    -

    .

  • 17

    (),

    . .

    - ( )

    - -,

    .

    , :

    ;

    :

    .

    :

    .

    ,

    , -11 -16 -

    .. - ,

    .

    , , - -

    . , , ,

    ..; ,

  • 18

    .. , -

    - .

    ,

    1917

    ( Sigama,

    Typex, Red, Orange Purple).

    ,

    .

    60-

    , ,

    .

    (XX 70- )

    ()

    ,

    ,

    .

    ,

    (), . 70-

    DES.

    70-

    ,

    .

    (1976.).

    .

  • 19

    , ,

    (

    n-

    , GF(2) n

    ).

    (), - .

    , ,

    .

    , ,

    , , .

    () -

    ,

    .

    ,

    , , ,

    . ,

    , , ,