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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Model to Formation Data Base of Internal Parameters for Assessing the Status of the State Secret Protection</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Yurii Dreis</string-name>
          <email>dreisyuri@gmail.com</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Оleksandr Korchenko</string-name>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Zoreslava Brzhevska</string-name>
          <email>z.brzhevska@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Larysa Kriuchkova</string-name>
          <email>l.kriuchkova@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olena Nesterova</string-name>
          <email>o.nesterova@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Borys Grinchenko Kyiv Metropolitan University</institution>
          ,
          <addr-line>18/2 Bulvarno-Kudriavska str., Kyiv, 04053</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Dragomanov Ukrainian State University</institution>
          ,
          <addr-line>9 Pyrohova str., Kyiv, 01601</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Mariupol State University</institution>
          ,
          <addr-line>6 Preobrazhenska str., Kyiv, 10008</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>National Aviation University</institution>
          ,
          <addr-line>1 Liubomyra Huzara ave., Kyiv, 03058</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>University of the National Education Commission</institution>
          ,
          <addr-line>2 Podchorążych ul., Krakow, 30084</addr-line>
          ,
          <country country="PL">Poland</country>
        </aff>
      </contrib-group>
      <fpage>277</fpage>
      <lpage>289</lpage>
      <abstract>
        <p>Protection of information with limited access, especially state secrets, is an important task in the sphere of national and information security of the state. To minimize the possible damage to the national security of Ukraine from violations in the sphere of protection of state secrets) and to reduce the negative international rating and other serious consequences at the state level, the task of creating specialized databases, and developing and improving existing methods and models that implement relevant assessments is urgent. That is why, the theoretical-multiple presentation of the parameters of the generalized report and the report on the state of state secret protection in tuple models allow solving the actual scientific and practical task of formalizing the process of assessing the negative consequences of leaking a state secret, its disclosure or loss of material carriers of secret information, violation of the secrecy regime, etc. Previously, a tuple model of primary parameters was developed, and currently, as its continuation, a model of internal parameters and its hierarchical structure has already been proposed, due to the integrated theoretical-multiple representation of sets characterizing the information about the availability of the employees of the reporting subject of admission and access to of state secrets and the number of material carriers of secret information, allows, under the requirements of current legislation, to determine a set of input and output parameters for the formation of special databases and the formalization of the process of assessing the damage caused to national security from the leakage of state secrets. In the future, to implement the above-mentioned process, it is necessary to develop an appropriate model of formalization and processing of the database of secondary parameters of the subject of regime-secret activity.</p>
      </abstract>
      <kwd-group>
        <kwd>1 Information protection</kwd>
        <kwd>limited access</kwd>
        <kwd>state secret protection</kwd>
        <kwd>parameter model</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        According to requirements [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], the information
constituting a State Secret (SS) in the field of
defense [2], economy, science and technology,
foreign relations, state security [3, 4], and law
enforcement is subject to state protection [5],
if their disclosure could harm the national
security of Ukraine. According to the
procedure for assigning information to the SS
[
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], the State Expert on Secrets issues (SES)
decides to assign a category of information or
individual information to the SS with the
establishment of their Degree of Secrecy (DS)
by substantiating and determining the amount
of possible damage to the national security of
Ukraine in the event of disclosure of these
information, with their subsequent inclusion in
the “Compendium of information constituting
a state secret” [6] (hereinafter—CISS). It
remains the only theoretical mechanism for
determining the parameters of possible harm is
the “Methodological recommendations to state
experts on secrets on determining the grounds
for classifying information as a state secret and
the degree of their secrecy” [
        <xref ref-type="bibr" rid="ref6">7</xref>
        ] (hereinafter—
Methodological recommendations), its detailed
analysis, description of problematic issues and
individual studies are given in [
        <xref ref-type="bibr" rid="ref7 ref8">8, 9</xref>
        ]. Taking
into account the absence of any other methods
of its calculation, the “Method of analysis and
assessment of the amount of possible damage
to the national security of the state in the field
of protection of state secrets” (hereinafter—
the Method) [
        <xref ref-type="bibr" rid="ref9">10</xref>
        ] was developed, which, due to
the basic model of the integrated
representation of damage parameters and
logical linguistic approach in the processing of
dynamically changing sets of identifying and
evaluation parameters calculates indicators of
economic damage and other serious
consequences, which made it possible to
determine the amount of possible damage to
national security in case of disclosure of DT or
loss of Material Carriers of Classified
Information (MCCI). The method is based on
the main provisions of Methodological
recommendations [
        <xref ref-type="bibr" rid="ref6">7</xref>
        ], CISS [6], criteria for
determining possible damage to the national
security of Ukraine in case of disclosure of
information protected by the state, and
methods of evaluating the effectiveness of the
SS Protection System (PSS) [
        <xref ref-type="bibr" rid="ref10 ref11 ref12 ref7 ref8 ref9">8–13</xref>
        ], as well as
statistical data of the “Report on the state of
ensuring the protection of SS” (hereinafter—
the Report) [
        <xref ref-type="bibr" rid="ref13">14</xref>
        ].
      </p>
      <p>
        The number of violations related to treason
and/or sabotage, in terms of loss, disclosure, or
transfer to a foreign country of information
constituting SS, is significantly increasing both
in the world [
        <xref ref-type="bibr" rid="ref14">15</xref>
        ] and in Ukraine [
        <xref ref-type="bibr" rid="ref15">16</xref>
        ]. This
process has been intensified since 2014, after
the occupation of certain territories of Ukraine
(Donetsk and Luhansk regions, Autonomous
Republic of Crimea). At that time, to strengthen
the national security of Ukraine in the field of
PSS, the decisions of the NSDC “On additional
measures to strengthen the national security of
Ukraine” and “On the state of overcoming the
negative consequences caused by the loss of
material carriers of classified information in
the temporarily occupied territory of Ukraine,
in the area conducting an anti-terrorist
operation in the Donetsk and Luhansk
regions”, which introduced criteria for the
classification, assessment, and identification of
levels of terrorist threats, determination of a
complex of measures for the prevention,
response, and termination of terrorist acts,
taking into account these levels, the
establishment of regimes of control,
protection, and protection of objects of
possible terrorist encroachments depending
on the object category. Also since 2015, and
already in 2020, changes were made to the
Report, which was supplemented with
dynamically changing sets of identifying and
evaluation parameters for ensuring the state of
PSS, which in one way or another makes
corrections and additions to the model [
        <xref ref-type="bibr" rid="ref12">13</xref>
        ]
with the need for further improvement Method
[
        <xref ref-type="bibr" rid="ref9">10</xref>
        ], including and using a theoretical-multiple
approach to assessing damage to the national
security of Ukraine in the event of a leak of
information constituting SS [17], as a
continuation of the development of a model for
the formation of a database of parameters for
assessing the state of state secret protection in
Ukraine [18].
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Formulation of the Problem</title>
      <p>
        To minimize the possible damage to national
security from violations in the field of PSS and
reduce the negative rating at the state level, it
is necessary to create databases, methods, and
models that implement appropriate
assessments. That is why, the
theoreticalmultiple presentation of the parameters of the
“Generalized report on the state of security of
SS” [
        <xref ref-type="bibr" rid="ref13">14</xref>
        ] (hereinafter—the Generalized report)
at the state level and the Report at the level of
a separate Subject of Regime-Secret Activity
(SRSA) and Regime-Secret Department (RSD),
generalized by tuple model is an actual
scientific task, which allows solving the
scientific and practical task of forming a
database of parameters of the state of PSS for
further creation of the necessary statistical
data and formalization of the process of
assessing the negative consequences of the
leakage of SS, caused by their loss or
disclosure.
In this regard, the purpose of this article is to
develop a model for the formation of a
database of internal parameters for assessing
the state of the provision of PSS from the use of
identification, static, and other data regarding
the negative consequences (damage) in the
event of a leak of SS in violation of the
requirements of PSS established by law.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Continuation of Model</title>
    </sec>
    <sec id="sec-4">
      <title>Development</title>
      <p>One will use the set of all possible identifiers of IS
(Information about the Subject) tuples, which can
be used to display information about SRSA and
be used in the process of detecting and assessing
the consequences in case of loss of SS [19, 20]:</p>
      <p>z
IS = { IS } = {IS1,IS2,...,ISz} ,
 =1
(1)
where IS  IS ( = 1, z) is the identifier of the
tuple of parameters characterizing the φth SRSA.</p>
      <p>For example, at z=4 (1) will have the form [19]:</p>
      <p>4
 = {⋃   } = { 1,  2,  3,  4}=
 =1</p>
      <p>= { NAU,  ZhVI,  NA SBU,  SI "SSI" }
where  1 =  NAU,  2 =   ℎ ,  3 =
 NA SBU,  4 =  SI "SSI" respectively, the
identifiers of the convoys of the SRSA “National
Aviation University” (NAU), “Zhytomyr
Military Institute named after S. P. Korolev”
(ZhVI), “National Academy of the Security
Service of Ukraine” (NA SBU), State
institution “Sumy investigative detention
center” (SI “SSI”).</p>
      <p>For the φ-th SRSA, the tuple of parameters
characterizing it has the following form:</p>
      <p>IS = IS 1, IS 2 ,..., IS i ,..., IS k
(2)
where: IS i  IS (i = 1, k ) is a component of
the tuple, which is a subtuple and displays the
ith parameter identifier of the φ-th SRSA, and k
is the maximum number of such parameters.</p>
      <p>Note that all members are characterized by the
property of order.</p>
      <p>
        For example, according to the Generalized
Report and the Report [
        <xref ref-type="bibr" rid="ref13">14</xref>
        ], we define tuple (2)
as:
IS = IS1,IS 2,IS 3, IS 4,IS 5, IS 6, IS 7, IS 8,IS 9
where, for example, subtuple IS1 = Section 1
(“Information about SRSA, it’s subordination
and departmental affiliation”), and other
components are indicated in Table 1. Let’s
divide the components IS of this table. 1 by
types of parameters on primary, internal, and
secondary.
      </p>
      <p>The first group of (primary) parameters is
discussed in detail in the scientific work [18], and
therefore we will describe the following second
group of (internal) parameters IS 3 and IS 4 .</p>
      <p>IS 4
IS 5
IS 6
IS 7
IS 8
IS 9</p>
      <p>Information about the subject of reporting, his subordination, and departmental affiliation
Information about RSD, financing of activities with PSS
Information on whether employees of the reporting entity have permission and access to state
secrets
Section 4 Information on the number of material carriers of classified information
Section 5 Information on the performance (scientific and/or scientific and technical support) of secret
research, development, design, and other scientific works, the manufacture of secret products
Section 5(А) Information regarding the order (scientific and/or scientific and technical support) of secret
scientific research, research and development, design and other scientific works, production
of secret products
Section 6 Information about regime premises, objects of information activity
Section 7 Information on the facts of MCCI losses or the disclosure of information constituting a state
secret, as well as information with limited access to foreign countries or international
organizations</p>
      <p>Section 8 Information on international cooperation</p>
      <sec id="sec-4-1">
        <title>The third component of the subtuple</title>
        <p>IS 3 = Section 3 (“Information on whether the
employees of the reporting entity have
permission and access to state secrets”) is
filled in by the SRSA as of the end of the reporting
period by filling in the corresponding columns
(parameters):
where IS 3.i  IS 3 (i = 1, q) —component of
the subtuple, which displays the i-th parameter
identifier of the φth SRSA of the organization, and
q is their number.</p>
        <p>
          For example, according to [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ], at q = 11 (i = 1,11)
formula (3) can be represented as follows:
        </p>
        <p>N , nE , nP , FA , nPN , nA , nSA , nRA ,nWR , nGA , nWA .
where IS 3.1 = IS 1.1 = N (Name) is the set
“Actual and conditional (if available) name of the
reporting entity”; IS 3.2 = nE (number of
Employees) is the set “Total number of
employees according to the staff list”;
IS 3.3 = nP (number of Positions) is the set
“Total number of positions included in the
nomenclature of positions”; IS 3.4 = FA
(Forms of Aссess) is the set “Forms of access”;
IS 3.5 = nPN (number of Positions included in
the Nomenclature) is the set “Number of
positions included in the nomenclature of
positions”; IS 3.6 = nA (number of Employees
with Aссess) is the set “The number of employees
who have access to SS”; IS 3.7 = nSA (number
of Employees with Suspended Aссess) is the set
“The number of employees whose access to SS
has been terminated”; IS 3.8 = nRA (number</p>
        <p>h1
IS 3.1 = IS 11 = N = { N i } = {N 1, N 2 ,..., N h1 },
i=1
of еmployees with Revoked Aссess)—the set “The
number of employees whose access to SS has
been cancelled”; IS 3.9 = nWR  (number of
persons with Access Without Registration)—the
set “The number of persons who were granted
access to the DT in the procedure defined by the
law without obtaining admission to the DT”;
IS 3.10 = nGA (number of employees who Got
Acquainted with classified information)—the set
“The number of employees who got acquainted
with secret information in other enterprises,
institutions, organizations”; IS 3.11 = nWA
(number of secret carriers who Went Abroad on
private business)—the set “The number of secret
carriers who went abroad on private business”.</p>
        <p>
          For example, to assign specific values to the
following eleven parameters of the third
component IS 3  IS one will use SRSA  1 =
 NAU [
          <xref ref-type="bibr" rid="ref13 ref14 ref15">14–19</xref>
          ]:
(4)
where, N i  N (i = 1, h1) is ith valid full name
and conventional name of the φ-th SRSA, and
h1 is the number of these names (for example,
with,  = 1 , q1 = h1 , h1 = 1, (4) takes the form:
 1 = {⋃i1=1 NNAUi}= {⋃i1=1 N1NAU}={“National
        </p>
        <p>Aviation University (NAU)”}) [18].</p>
        <p>q2
IS 3.2 = nE = { nE i } = {nE 1,nE 2 ,...,nE q2 },</p>
        <p>i=1
where nE i  nE (i = 1, q2 ) is ith identifier of
the total number of employees according to the
staff list, and q2 is their number (for example,
for  1 =  NAU, taking into account [20], with
 = 1 , q2 = 1 (i = 1) , then (5) is defined as:</p>
        <p>q3
IS 3.3 = nP = { nP i} = {nP1,nP 2,...,nP q3 },
i=1</p>
        <p>1 1
 1 = {⋃ nENAUi}= {⋃ nENAU1}=
i−1 i−1</p>
        <p>= {“4517,8”},
that is, the total number of NAU employees,
according to the 2021 staff list, is 4517.8).</p>
        <p>(5)
(6)
where nP i  nP (i = 1, q3) is ith identifier of the
total number of positions included in the
nomenclature of positions, and q3 is their
number (let the number of positions included in
the nomenclature of cases be 10% of the total
number of positions according to the staff list of
NAU in 2021 [20], i.e. at  = 1 , q3 = 1 (i = 1) , then
(6) will be as:</p>
        <p>1 1
 1 = {⋃ nPNAUi}= {⋃ nPNAU1}= {"452"}</p>
        <p>i=1 i=1
that is, the total number of positions included
in the nomenclature of positions is 452.</p>
        <p>q4
IS 3.4 = FA = { FA i} = {FA1, FA 2 ,..., FA q4 } ,</p>
        <p>
          i=1
where FA i  FA (i = 1, q4 ) is ith set of
tolerance forms, and q4 is their number (for
example, respectively [
          <xref ref-type="bibr" rid="ref1 ref13">1, 14</xref>
          ] the tolerance forms
are defined as first (or 1), second (or 2) and third
(or 3), so when q4 = 3 (i = 1,3) , then (7) define as:
        </p>
        <p>3
FA = { FA i } = {FA 1, FA 2 , FA 3} =
i=1
where FA1 = “1”, FA 2 = “2”, FA 3 = “3”.</p>
        <p>Assume that for  = 1 , q4 = 2 (i = 1,2) , then (7)
takes the following form:</p>
        <p>2</p>
        <p>FA1 = {⋃    }=
{  1,   =1 2}={“1”, “2”},
i.e. in NAU there are forms of admission as the
first (or 1) and the second (or 2).
{“1”, “2”, “3”},
q4 q5
IS 3.5 = nPN = {{ nPN i. j}} = {{nPN1.1,...},...,{...,nPN i. j ,...},...,{...,nPN q4.q5 }},
i=1 j=1
(7)
(8)
where nPN i. j  nPN (i = 1, q4, j = 1, q5) is іth
identifier of the number of positions included
in the nomenclature of positions, and q5 is
their number for q4 , hat is, for a specific form
of admission (for example, with  = 1 , for
q4 = 2 (i = 1,2) , q5 = 1 ( j = 1) , then (8) will take
the form:
2 1
 1 = {⋃ ⋃    . } =</p>
        <p>=1  =1
= {{  1.1}, {  2.1}}=
= {{“300”}, {“150”}},
that is, the number of positions in NAU
included in the nomenclature of positions
according to the first (or 1) form of admission
is 300, and according to the second (or 2) form
of admission—150).</p>
        <p>q4 q6
IS 3.6 = nA = {{ nA i. j}} = {{nA1.1},...,{nA i. j},...,{nA q4.q6 }},
i=1 j=1
(9)
where</p>
        <p>nA i. j  nA (i = 1, q4, j = 1, q6 ) is іth
identifier of the number of employees who have
admission to SS, and q6 is their number for q4 , that
is, for a specific form of admission (for example,
with  = 1 , for q4 = 2 (i = 1,2) , q6 = 1 ( j = 1) , then
(9) will take the form of:
2 1
 1 = {⋃ ⋃  
 =1  =1</p>
        <p>= {{“250”}, {“100”}},
that is, the number of NAU employees who
have admission to SS under the first (or 1) form
of admission is 250, and 100 under the second
(or 2) form of admission).</p>
        <p>. } = {{ 
1.1}, { 
where nSA i. j  nSA (i = 1, q4 , j = 1, q7 ) is іth
identifier of the number of employees whose
access to SS has been terminated, and q7 is
their number for q4 , hat is, for a specific form
of admission (for example,  = 1 for q4 = 2
(i = 1,2) , q7 = 1 ( j = 1) , then (10) will take the
form of:
2 1
 1 = {⋃ ⋃    . } =</p>
        <p>=1  =1
= {{  1.1}, {  2.1}}=</p>
        <p>= {{“25”}, {“7”}},
i.e. the number of NAU employees whose
access to SS has been terminated for the first
(or 1) form of admission is 25, and for the
second (or 2) form of admission—7).
where nRA i. j  nRA (i = 1, q4 , j = 1, q8 ) is іth
identifier of the number of employees whose
admission to SS has been canceled, and q8 is
their number according to q4 , that is, according
to a specific form of admission (for example, if
 = 1 for q4 = 2 (i = 1,2) , q8 = 1 ( j = 1) , then (11)
will be as:
where nWR i. j  nWR (i = 1, q4, j = 1, q9 ) is іth
identifier of the number of persons who were
granted access to the SS in the manner specified
by the legislation without obtaining admission to
the SS, and q9 is their number according to q4 ,
that is, according to a specific form of admission
(for example, with  = 1 , for q4 = 2 (i = 1,2) ,
q9 = 1 ( j = 1) , then (12) will be as:
2 1
 1 = {⋃ ⋃    . } =</p>
        <p>=1  =1
= {{  1.1}, {  2.1}}=</p>
        <p>= {{“25”}, {“7”}},
i.e. the number of NAU employees whose
access to SS has been canceled for the first (or
1) form of admission is 25, and for the second
(or 2) form of admission—7, or in this case
IS 3.8 = IS 3.7 ).</p>
        <p>2 1
 1 = {⋃ ⋃    . } =</p>
        <p>=1  =1
= {{  1.1}, {  2.1}}=</p>
        <p>= {{“4”}, {“2”}},
i.e. the number of persons who were granted
access to SS at NAU following the procedure
specified by law without registration of
admission to SS according to the first (or 1)
form of admission is 4, and according to the
second (or 2) form of admission—2).</p>
        <p>q4 q9
IS 3.9 = nWR = {{nWR i. j}} = {{nWR1.1,...},...,{...,nWR i. j ,...},...,{...,nWR q4.q9 }},
i=1 j=1
(12)
where nGA i. j  nGA (i = 1, q4, j = 1, q10 ) is іth
identifier of the number of employees who got
acquainted with secret information in other
enterprises, institutions, organizations, and q10
is their number for q4 , that is, for a specific
form of admission (for example, with  = 1 , for
q4 = 2 (i = 1,2), q10 = 1 ( j = 1) , then (13) will
take the form of:
2 1
 1 = {⋃ ⋃    . } =</p>
        <p>=1  =1
= {{  1.1}, {  2.1}}={{“5”}, {“3”}},
that is, the number of NAU employees who got
acquainted with classified information in other
enterprises, institutions, and organizations
according to the first (or 1) form of admission
is 5, and according to the second (or 2) form of
admission—3).</p>
        <p>q4 q11
IS 3.11 = nWA = {{ nWA i. j}} = {{nWA1.1,...},...,{...,nWA i. j ,...},...,{...,nWA q4.q11}}(1,4)
i=1 j=1
where nWA i. j  nWA (i = 1, q4, j = 1, q11) is jth
identifier of the number of secret carriers who
went abroad on private business, and q9 is their
number for q4 , that is, for a specific ith form of
admission (for example, with  = 1 , for q4 = 2
(i = 1,2) , q11 = 1 ( j = 1) , then (14) will be as:</p>
        <p>2 1
 1 = {⋃ ⋃    . } =</p>
        <p>=1  =1
= {{  1.1}, {  2.1}}=
= {{“4”}, {“2”}},
that is, the number of secret carriers in NAU who
went abroad on private business under the first
(or 1) form of admission is 4, and under the
second (or 2) form of admission—2).</p>
      </sec>
      <sec id="sec-4-2">
        <title>The fourth component of the subtuple</title>
        <p>
          IS 4 = Section 4 (“Information on the
number of material carriers of secret
information”) is formed by filling in the SRSA of
the graphs (parameters) of the corresponding
section of the Report [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ], which is displayed as:
        </p>
        <p>IS 4 = IS 4.1,IS 4.2,...,IS 4.i ,...,IS 4.k , (15)
where IS 4.i  IS 4 (i = 1, k ) is component of
the subtuple displaying the ith identifier of the
RSO parameters of the φ-th SRSA, and k is
their number.</p>
        <p>
          For example, according to the requirements of
[
          <xref ref-type="bibr" rid="ref13">14</xref>
          ], when k = 10 (i = 1,10) formula (15) can
be represented as follows:
IS 4 = IS 4.1, IS 4.2 , IS 4.3, IS 4.4 , IS 4.5, IS 4.6 , IS 4.7 , IS 4.8, IS 4.9 , IS 4.10 =
        </p>
        <p>N ,SS ,aM ,nsM ,nrM ,nMr ,nMt ,nMf ,sU ,nMu ,
where: IS 4.1 = IS1.1 = N (Name)—set
“Actual and conditional (if available) name of
the reporting entity (SRSA)”; IS 4.2 = SS
(Stamp of Secrecy)—set “Stamp of Secrecy”;
IS 4.3 = aM (all Material Carriers of Classified
Information)—set “Total MCCI (sum of
columns 5-13)”; IS 4.4 = nsM (Number of
registered and Stored MCCI at the end of the
reporting period)—set “The number of MCCIs
that are registered and maintained as of the
end of the reporting period”; IS 4.5 = nrM
(Number of Registered MCCI in the reporting
period)—set “Number of registered MCCI in
the reporting period”; IS 4.6 = nMr (number
of MCCI, the secrecy stamps of which have been
revised)—set “The number of MCCI, the
secrecy vultures of which have been revised”;
IS 4.7 = nMt (number of MССI transferred to
foreign states and international organizations
in the reporting period)—set “The number of
MCCI that were transferred to foreign states</p>
        <p>k2
IS 4.2 = SS = { SS i} = {SS1, SS 2 ,..., SS k2 },
i=1
and international organizations in the
reporting period”; IS 4.8 = nMf (number of
MССI with stamps restricting access of foreign
states and international organizations)—set
“The number of MCCI with the access
restriction vultures of foreign states and
international organizations (provided in
columns taking into account the comparison
with the vultures of secrecy of Ukraine
following international treaties)”;
IS 4.9 = sU (stamps restricting access of
USSR)—set “Access restriction vultures of the
former USSR”; IS 4.10 = nMu (number of
MCCI with stamps restricting access of USSR)—
set “Number of MCCI with access restriction
vultures of the former USSR”.</p>
        <p>
          For example, to assign specific values to
the specified seven parameters of the fourth
component IS 4  IS one will use SRSA
 1 =   [
          <xref ref-type="bibr" rid="ref13 ref14 ref15">14–18, 20</xref>
          ]:
        </p>
        <p>IS 4.1 = IS1.1 = N , k1 = h1 (see (4) [18]).</p>
        <p>(16)
where SS i  SS (i = 1, k2 ) is ith is the
identifier of the number of secrecy vultures of
the Ministry of Internal Affairs and
Communications, and a is their number.</p>
        <p>
          According to the Law of Ukraine “On State
Secrets” [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ] and taking into account [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ] the {“S”, “TS”, “SI”}.
Ministry of Internal Affairs and
Communications is classified according to the
        </p>
        <p>k2 k3
IS 4.3 = aM = {{ aM  i. j}} = {{aM 1.1,...}, ...,{..., aM  i. j ,...},...,{..., aM  k2.k3 }},
i=1 j=1
classification of secrecy into: “secret” (or S), “top
secret” (or TS) and “of special importance” (or
SI), therefore k2 = 3 formula (16) looks like:</p>
        <p>3
SS = { SS i} = {SS1, SS 2, SS 3} =
i=1
(17)
where aM  i. j  aM (i = 1, k2 , j = 1, k3 ) is jth
identifier of all MCCI (as the number of the sum
of graphs 5–13), and k3 is their number for
each k2 , i.e. according to the specific ith secret
code (let’s imagine that  = 1 for k2 = 2 (i = 1,2) ,</p>
        <p>= {{ 
k3 = 1 ( j = 1) , then (17) will be as:</p>
        <p>2 1
 1 = {⋃ ⋃  
 =1  =1</p>
        <p>1.1}, {
that is, in the NAU of all MCCIs, according to the
secrecy vultures “secret” (or S)—215, and “top
secret” (or TS)—75.</p>
        <p>
          k2 k4.i
IS 4.4 = nsM  = {{nsM  i. j }} = {{nsM 1.1,...},...,{...,nsM  i. j ,...},...,{...,nsM  k2.k4.k(21}8}),
i=1 j=1
where nsM  i. j  nsM  (i = 1, k2 , j = 1, k4.i ) is jth
identifier of the number of MCCIs, which are
registered and stored as of the end of the
reporting period, and k4.i is their number for
each k2 , that is, according to a specific ith
security seal (for example, taking into account
[
          <xref ref-type="bibr" rid="ref13">14</xref>
          ], with k4 = 7 ( j = 1,7) , k4.1 = 4 ,
k4.2  k4.7 = 1 18) we represent as:
7 k4.i
nsM  = {{ nsM i. j }} =
        </p>
        <p>
          i=1 j=1
{{nsM1.1, nsM1.2 , nsM1.3 , nsM1.4},{nsM 2.1},{nsM 3.1},{nsM 4.1},...{nsM 7.1}},
where nsM i. j is the set number of MCCIs that
are registered and kept as of the end of the
reporting period [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ]: nsM i.1 is the set
“number of MCCIs relating to cryptographic
protection of information”: ( nsM i.1.1 is subset
“number of means of cryptographic protection
of information”; nsM i.1.2 is subset “number of
books of technical (operational) and
regulatory documentation”; nsM i.1.3 is subset
“number of key documents”; nsM i.1.4 is subset
“number of MCCI of the state recognition
system”); nsM i.2 —set of “normative and
administrative acts”; nsM i.3 is set “technical
and operational documentation”; nsM i.4 is set
of “secret products”; nsM i.5 —the set “other
MCCI (volumes of cases, copies of publications,
photo documents, notebooks, etc.)”; nsM i.6 —
set “a number of machine media (FMD, HMDD,
CDs, flash drives, microfilms)”; nsM i.7 is set
“including with the mark “Letter “M”.
        </p>
        <p>
          For example, if  = 1 for k2 = 2 (i = 1,2) ,
k4 = 7 ( j = 1,7) , k4.1 = 4 , k4.2  k4.7 = 1 then (18),
taking into account the composition of the set
nsM i.1 , will be as [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ]:
2 7 k4.i
nsM  = {{{ nsM i. j.e}} =
        </p>
        <p>i=1 j=1 e=1
= {{nsM1.1.1, nsM1.1.2 , nsM1.1.3, nsM1.1.4},{nsM1.2.1},{nsM1.3.1},{nsM1.4.1},...{nsM1.7.1},
{nsM 2.1.1, nsM 2.1.2 , nsM 2.1.3 , nsM 2.1.4},{nsM 2.2.1},{nsM 2.3.1},{nsM 2.4.1},...{nsM 2.7.1}} =
= {{nsM1.1.1, nsM1.1.2 , nsM1.1.3, nsM1.1.4},{nsM1.2.1},{nsM1.3.1},{nsM1.4.1},{nsM1.5.1},{nsM1.6.1},{nsM1.7.1}},
{{nsM 2.1.1, nsM 2.1.2 , nsM 2.1.3, nsM 2.1.4},{nsM 2.2.1},{nsM 2.3.1},{nsM 2.4.1},{nsM 2.5.1},{nsM 2.6.1},{nsM 2.7.1}} =
= {{“20”, “15”, “15”, “5”}, {“30”}, {“25”}, {“40”}, {“50”}, {“10”}, {“5”}},</p>
        <p>{{“10”, “5”, “5”, “5”}, {“5”}, {“10”}, {“10”}, “10”}, {“10”}, {“5”}},
i.e., in NAU, the number of MCCI, which are
registered and stored as of the end of the
reporting period, with secrecy vultures: 1)
“secret” (or S): the number of MCCI related to
cryptographic protection of information: the
number of means of cryptographic protection
of information—20; the number of books of
technical (operational) and regulatory
documentation—15; number of key
documents—15; number of MCCI of the state
recognition system—5; regulatory and
administrative acts—30; technical and
operational documentation—25; secret
products—40; other MCCI (volumes of cases,
copies of publications, photo documents,
notebooks, etc.)—50; the number of computer
media (FMD, HMDD, CDs, flash drives,
microfilms)—10; including with the mark
“Letter “M”—5; 2) “top secret” (or TS): number
of MCCI related to cryptographic protection of
information: number of means of
cryptographic protection of information—10;
the number of books of technical (operational)
and regulatory documentation—5; number of
key documents—5; number of MCCI of the
state recognition system—5; regulatory and
administrative acts—5; technical and
operational documentation—10; secret
products—10; other MCCI (case volumes,</p>
        <p>k2 k5
IS 4.5 = nrM = {{nrM i. j }} = {{nrM1.1,...},...,{...,nrM i. j ,...},...,{...,nrM k2.k5 }},
i=1 j=1
copies of publications, photo documents,
notebooks, etc.)—10; the number of computer
media (FMD, HMDD, CDs, flash drives,
microfilms)—10; including with the mark
“Letter “M”—5.</p>
        <p>
          (19)
where nrM  i. j  nrM (i = 1, k2 , j = 1, k5 ) is jth
identifier of other MNSI (volumes of cases,
copies of publications, photo documents,
notebooks, etc.), and k5 is their number for
each k2 , that is, according to a specific ith
classification of secrecy (for example, taking
[
          <xref ref-type="bibr" rid="ref13">14</xref>
          ] into account, when  = 1 for k2 = 2 (i = 1,2) ,
k5 = 4 ( j = 1,4), then (19) will be:
        </p>
        <p>2 4
1 = {⋃ ⋃ 
 =1  =1

where nMr i. j  nMr (i = 1, k2 , j = 1, k6 ) is jth
identifier of the number of MCCI, the security
vultures of which have been reviewed, and k6
is their number for each k2 , that is, according</p>
        <p>2 3
 1 = {⋃ ⋃    . } =</p>
        <p>
          =1  =1
{{  1.1,   1.2,   1.3}, {  2.1,   2.2, 
= {{“4”, “7”, “2”}, {“3”, “2”, “0”}},
to the specific ith security vulture (for example,
taking into account [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ], when  = 1 for k2 = 2
(i = 1,2) , k6 = 3 ( j = 1,3) , then (20) will be as:
 2.3}} =
i.e., in NAU, the number of MCCI whose secrecy
vultures were revised, namely: 1) “secret” (or S):
brought into line with the current CISS (secrecy
vulture changed)—4, transferred to the category
with the access restriction vulture “For official
use”—7, declassified (removed access restriction
        </p>
        <p>k2 k7
IS 4.7 = nMt = {{ nMt i. j }} = {{nMt1.1}, ...,{nMt i. j },...,{nMt k2.k7 }},
i=1 j=1
stamp)—2; 2) “top secret” (or TS): brought into
line with the current CISS (secrecy seal
changed)—3, transferred to the category with
the access restriction seal “For official use”—2,
declassified (access restriction seal removed)—
0).</p>
        <p>(21)
where nMt i. j  nMt (i = 1, k2 , j = 1, k7 ) is jth
identifier of the number of MNSI, which was
transferred to foreign states and international
organizations in the reporting period, and k7 is
their number for each k2 , i.e. according to the
specific ith secrecy vulture (let’s imagine that if
 = 1 , for k2 = 2 (i = 1,2) , k7 = 1 ( j = 1) , then
(21) will be as:</p>
        <p>2 1
1 = {⋃ ⋃</p>
        <p>=1  =1
= {{  1.1}, {
= {{“6”}, {“1”}},
i.e., in the NAU, the number of MCCI, which
were transferred to foreign states and
international organizations in the reporting
period with the vultures of secrecy “secret” (or</p>
        <p>
          S)—6, and “top secret” (or TS)—1.
where nMf  i. j  nMf  (i = 1, k2 , j = 1, k8.i ) is jth
identifier of the number of MNI with
restrictions on the access of foreign states and
international organizations (placed in columns
taking into account the comparison with the
secrecy of Ukraine following international
treaties), and k8.i is their number for each k2 ,
hat is, according to the specific ith security of
secrecy (for example, taking into account [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ],
when k8 = 2 ( j = 1,2) , k8.1 = 2 , k8.2 = 1 , then we
present (22) as:
        </p>
        <p>2 k8.i
nMf  = {{ nMfi.j }} =</p>
        <p>
          i=1 j=1
= {{nMfi.1.1, nMfi.1.2}, nMfi.2},
where nMfi.j is set “The number of MCCI with
international organizations (put in columns
taking into account the comparison with the
secrecy of Ukraine following international
treaties)” includes [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ]: nMfi.1 is set “Total
number of MCCI as of the end of the reporting
period” ( nMfi.1.1 is subset of “Total”; nMfi.1.2 is
subset “including
        </p>
        <p>which arrived in the
reporting period”); nMfi.2 is set “The number
of MCCI, which were produced in the reporting
period on the order of foreign states or
international organizations.”</p>
        <p>
          For example, if  = 1 for k2 = 2 (i = 1,2) ,
k8 = 2 ( j = 1,2) , k8.1 = 2 , k8.2 = 1 then (22),
taking into account the composition of the set
nMfi.1 , will be as [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ]:
restrictions on the access of foreign states and
        </p>
        <p>2 2 k8.i
nMf  = {{{ nMfi.j.u}} = {{nMfi.1.1, nMfi.1.2}, nMfi.2} =</p>
        <p>i=1 j=1 u=1
= {{nMf1.1.1, nMf1.1.2 ,},{nMf1.2}},{{nMf 2.1.1, nMf 2.1.2},{nsM 2.2}} =</p>
        <p>= {{“20”, “15”}, {“30”}}, {{“10”, “5”}, {“5”}},
i.e., in NAU, the number of MCCIs with
restrictions on the access of foreign states and
international organizations (put in columns
taking into account the comparison with
Ukrainian secrecy vultures following
international treaties) is as follows: 1) “secret”
(or S): the total number of MCCIs as of the end of
the reporting period: total—20, incl. which
arrived in the reporting period—15; the number</p>
        <p>k9
IS 4.9 = sU = { sU  i } = {sU  1, sU  2 , ..., sU  k9 },
i=1
of MCCI, which were produced in the reporting
period on the order of foreign states or
international organizations—30; 2) “completely
secret” (or CS): the total number of MCCI as of the
end of the reporting period: a total of 10,
including which arrived in the reporting
period—5; the number of MCCI, which were
produced in the reporting period on the order of
foreign states or international organizations—5.</p>
        <p>
          (23)
where sU  i  sU (i = 1, k9 ) is ith identifier of the
access restriction vultures of the former USSR,
and k9 is their number. According to [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ], they
are as follows: “secret” (or S), “top secret” (or TS),
and “of special importance” (or SI), so at k9 = 3
(i = 1,3) formula (23) looks like:
        </p>
        <p>3
sU = { sU  i} = {sU 1, sU  2 , sU  3} =
i=1</p>
        <p>= {“С”, “СС”, “ОВ”}.</p>
        <p>
          k9 k10
IS 4.10 = nMu = {{ nMu i. j}} = {{nMu1.1},...,{nMu i. j},...,{nMu k9.k10 }},
i=1 j=1
(24)
where nMu i. j  nM (i = 1, k9 , j = 1, k10 ) is jth
identifier of the number of MCCI with access
restriction vultures of the former USSR, and k10
is their number for each k9 , i.e. for a specific ith
vulture of access restriction of the former USSR
(for example, taking into account [
          <xref ref-type="bibr" rid="ref13">14</xref>
          ],  = 1 for
k9 = 2 (i = 1,2), k10 = 2 ( j = 1,2) , then (24) will
be as:
        </p>
        <p>2 2
1 = {⋃ ⋃ 
 =1  =1

= {{  1.1,   1.2}, {  2.1,   2.2}} =</p>
        <p>= {{“14”, “17”}, {“8”, “3”}},
i.e., in NAU, the number of MCCI with access
restriction stamps of the former USSR is as
follows: 1) “secret” (or S): the total number of
MCCI as of the end of the reporting period
(without taking into account interstate
standards of limited distribution of the former
USSR) is 14, the total number of copies of
interstate standards of restricted distribution
of the former USSR—17; 2) “top secret” (or
TS): the total number of MCCI as of the end of
the reporting period (not including interstate
standards of limited distribution of the former
USSR) is 8, the total number of copies of
interstate standards of limited distribution of
the former USSR is 3.</p>
        <p>The developed model's general hierarchical
structure (considering the given examples) is
presented in Fig. 1
IS</p>
        <p>IS 1
IS 2</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>4. Conclusions</title>
      <p>A tuple model was developed, which, due to the
set-theoretic representation of sets of tuple
models of the integrated representation of the
internal parameters of the state of provision of
PSS, which reflect the values of the reporting
period as a set characterizing the MCCI and the
number of employees with access and admission
to the PSS, etc., allows determining the required
number of initial values to form a database, keep
statistics and improve the formalization of the
process of assessing damage (damages) from the
loss of SS to the national security of Ukraine, both
at the level of the state and the level of its regions,
territorial communities following the legislation
of Ukraine.</p>
      <p>In the future, to implement the evaluation
process, it is necessary to continue the
development of a tuple model for the formation
of a database of secondary parameters to
improve the Method following domestic
regulatory requirements, and in the future,
taking into account the legislation of NATO
member countries and the European Union.
cherez-rozgholoshennya-derzhavnoitaiemnytsi/
[17] O. Korchenko, Y. Dreis, L. Derkach, A
Theoretical-Multiple Approach to
Assessing Damage to the National
Security of Ukraine in the Event of a Leak
of Information Constituting a State
Secret, Guidelines (2021).
[18] O. Korchenko, Y. Dreis, Tuple Model for
Forming a Database of Primary
Parameters for Assessing the State
Secret Protection Status, Ukrainian Sci. J.
Inf. Secur. 28(1) (2022) 35–42. doi:
10.18372/2225-5036.28.16911.
[19] YouControl is a Counterparty
Verification Service, a Catalogue of Court
Decisions. URL: https://youcontrol.com.
ua/catalog/court-document/10172467
6/
[20] National Aviation University (NAU).</p>
      <p>URL: https://nau.edu.ua.https://nau.
edu.ua/download/buhgalteriya/2021/S
htatnij2021.pdf</p>
    </sec>
  </body>
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