МЕТОД КОЛИЧЕСТВЕННОЙ ОЦЕНКИ ПОКАЗАТЕЛЕЙ ЭФФЕКТИВНОСТИ СИСТЕМ ЗАЩИТЫ ИНФОРМАЦИИ ОТ НЕСАНКЦИОНИРОВАННОГО ДОСТУПА

  • Published on
    05-Apr-2017

  • View
    220

  • Download
    6

Embed Size (px)

Transcript

  • .. , ,

    .. , , - ()

    METHOD OF QUANTITATIVE ESTIMATION OF EFFICIENCY INDICATORS OF INFORMATION PROTECTION SYSTEMS

    AGAINST UNAUTHORIZED ACCESS -

    . - -, .

    Method of quantitative estimation of efficiency indicators of information security sys-

    tems is developed. The method is based on the representation of the dynamics of the operation of systems to protect information from unauthorized access to end the semi-Markov process, characterized by a semi-Markov matrix.

    - , [1]. - , . - (, ) (). - : ; - ; .

    , - , - , , . , 1, - , 0 .

    () - . - E-. , - , [2,3], :

    ( )max PE = , (1)

    ; max .

    , [0, 1].

  • (1) , E- [2,3]. - , - , . - [4].

    , - ,

    )(H)(H ij = , n,1i = , n,1j = . (2) )(H ij , -

    , i, j, , , :

    )(Gp)(H iijij = , n,1i = , n,1j = , (3)

    ijp i j

    , i; )(G i - i.

    ijp , n,1i = , n,1j =

    , )(G i , n,1i = E-, -

    . )(G i .

    ijp . . - - .

    , - , - . , - , , , , - [4]:

    )(Q)(Gp)(Gp)(Q ji1n

    1jijiini +=

    =, 1n,1i = , (4)

    Q i() , i n, , .

    (- ) ( - ).

  • (4) - . - :

    )(Q)(gp)(gp)(q ji1n

    1jijiini +=

    = , ,n,i 11 = (5)

    q i() Qi(); g i() - Gi ().

    H ij()

    h ij () = p ij g i(). (6) g i(), -

    i, . i -

    [ai ;bi] ,

    [ ]

    .b

    )bexp()aexp()(g

    i

    iii

    =

    1 (7)

    i, bi, :

    +=

    ii b1

    1)(g . (8)

    i - i - 2i ,

    ).exp()(g iii22

    2

    1 += (9)

    : hij = h ij(); qi=q i(). (6), (5) -

    :

    =+

    =+=

    .hq)h(...qhqhqh

    .....................................................................

    ;hqh...qhq)h(qh

    ;hqh...qhqhq)h(

    n,nnn,n,n,n,n

    n,nn,,,,

    n,nn,,,,

    1111331221111

    2112332222112

    1111331221111

    1

    1

    1

    (10)

    . : . -

    , hii < 1 1n,1i = (1hii) .

    (1h11),

    q1 )(,h121 q2

    )(,h131 q3

    )(n,h1

    11 qn-1 = )(

    n,h1

    1 , (11)

    11

    11

    1 ,

    j,)(j,i h

    hh

    = , j = n,2 .

  • q1 (10) - (11) q1 (hi,1) -

    (10) i- (i= 1n,2 ). :

    ( ) ( ) ( ) ( )

    ( ) ( ) ( ) ( )

    ( ) ( ) ( ) ( )

    =+

    =

    =

    .hq)h(...qhqh

    .................................................................................

    ;hqh...qhq)h(

    ;hqh...qhqhq

    n,nnn,n,n,n

    n,nn,,,

    n,nn,,,

    111

    1113

    1312

    121

    121

    1123

    1322

    122

    111

    1113

    1312

    1211

    1

    1 (12)

    ( ) ( ),hhhh j,,ij,ij,i1

    111 += .n,j,n,i 212 == (13)

    (12) q2 , (13) .. - .

    : ( ) ( ) ( ) ( )

    ( ) ( ) ( )

    ( )

    =

    =

    =

    .hq

    .............................................................

    ;hqh...qhq

    ;hqh...qhqhq

    nn,nn

    n,nn,,

    n,nn,,,

    111

    221

    2123

    2322

    111

    1113

    1312

    1211

    (14)

    )k(

    k,k

    )k(j,k)k(

    j,kh

    hh

    1

    1

    1

    = ,

    ( ) ,hhhh )k( j,k)k(

    k,i)k(

    j,ikj,i

    11 += ( ) ijij hh =0 , (15)

    ,n,k 11 = .n,kj,n,ki 111 +=+=

    .

    ( )

    ( ) ( )

    ( ) ( ) ( ) ( )

    ++++=

    +=

    =

    .qh...qhqhhq

    ..........................................

    ;qhhq

    ;hq

    ,nn,nn,n,

    nn

    n,nn

    n,nn

    nn,nn

    21212

    1211

    111

    111

    12

    122

    22

    111

    (16)

    m

    m 1= -

    max . - m max .

    (1) , , - :

    )(qE m 1= . (17) m. ,

    () gi (m) (7)(9) - , hij(m) (6), (14) (15), , -

  • (), (17), (16) = m.

    - .

    - (), - , . - -.

    - , :

    1E = ; 1E = . (18) :

    1EE = . (19) () -

    , , , - :

    min EE , (20) min , , , - , - ( - ). , :

    ( ) =

    =.,

    ,EEEE,EE min

    0

    1 (21)

    , , - min .

    1. .., .. - // : -- ( ). : - , 2005. . 1415.

    2. .. - : . . . . -. , 2008.

    3. - : / .. [ .]. : , 2012.

    4. .., .. . .: . , 1977.

Recommended

View more >