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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Cognitive security modeling of biometric system of neural network cryptography*</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alexey Vulfin</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Vladimir Vasilyev</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Anastasia Kirillova</string-name>
          <email>kirillova.andm@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andrey Nikonov</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Ufa State Aviation Technical University</institution>
          ,
          <addr-line>12, K. Marks st., Ufa, 450008, Russian Federation</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>The object of the research is a biometric authentication system based on neural network transformation of features into a cryptographic key. The analysis of the security of such systems is carried out using the methods of cognitive modeling. The use of the neural network transformation “biometrics-key” can significantly reduce the likelihood of a number of attacks by external intruders due to the distributed storage of the base of biometric images and allows the use of a secret cryptographic key generated on the basis of the image as the output vector of the neural network. To assess the security of the biometric system based on the ML model, an analysis of current threats, vulnerabilities and potential attack vectors was carried out. A fuzzy gray cognitive map is built for modeling and assessing local relative risks of information security in the event of an attacker without using and using the architecture of the ML model of the neural network transformation “biometrics-key”. The indicators of the local relative risk of a system malfunction and refusal to use it (breach of integrity) and modification of the base and ML model (breach of confidentiality) decreased by 45%.</p>
      </abstract>
      <kwd-group>
        <kwd>Biometric authentication system</kwd>
        <kwd>Fuzzy gray cognitive map</kwd>
        <kwd>Biometrics-key</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        Currently, traditional authentication methods (passwords and IDs) are no longer
sufficient to ensure security - they have been replaced by integrated biometric systems
embedded in an increasing number of devices (for example, FaceID and TouchID
technologies in mobile devices). Today, there are two main areas of application of
biometric methods: solving the problem of user authentication and their integration
with cryptographic systems [
        <xref ref-type="bibr" rid="ref1 ref2 ref3">1-3</xref>
        ]. Cryptographic systems are much more secure than
traditional biometric systems. One of their main disadvantages is the problem of
ensuring reliable storage and correct use of secret cryptographic keys [1; 4].
      </p>
      <p>
        Biometric authentication systems based on the use of artificial intelligence and
machine learning technologies approximate a nonlinear functional display that allows the
recognized biometric image to be attributed to one of the predefined classes. The
machine learning models (ML models) used to solve this problem are very sensitive
to changes in input data, which allows an attacker in some cases to influence the
result of the biometric system by modifying the presented biometric images. A
significant number of services operate on the basis of ML models that process biometric
images, which is an important problem in ensuring information security of the system
as a whole [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p>The purpose of the work is to provide a cognitive analysis of the security of a
biometric authentication system based on a neural network transformation of biometric
features into a cryptographic key.</p>
      <p>To achieve the purpose, the following tasks were set:
─ analysis of existing biometric cryptographic systems;
─ security assessment of the neural network biometric authentication system based
on cognitive modeling technologies.
2</p>
    </sec>
    <sec id="sec-2">
      <title>Analysis of existing biometric cryptographic systems and methods for processing facial images</title>
      <p>Existing biometric cryptographic systems using facial images as primary biometric
features can be divided into three categories according to the nature of the
cryptographic key processing (Table 1).</p>
      <p>
        For the subsequent analysis and application of the ML model in solving the
problem of image classification, it is necessary to extract the vector of primary features
from the generated biometric templates [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. A possible taxonomy of methods for
constructing vectors of primary formal features with an analysis of advantages and
disadvantages is presented in Table 2.
Histogram
oriented
gradients [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]
Support vector high speed of work sensitive to noise in the
machine [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] training set
Algorithm for good generalizing ability; the possibility of
retrainenhancing the simplicity of software ing; great computational
composition of implementation; high complexity
classifiers recognition accuracy
Methods Using high recognition accuracy; it is necessary to select the
Hidden Markov the possibility of compli- model parameters for each
Models cating the model; database; inability to track
the internal state of the
model
      </p>
      <p>
        To generate keys based on biometric images, two main tools are used (Table 3)
that meet the requirements of modern cryptography and have an acceptable estimate
of the magnitude of the second type error [
        <xref ref-type="bibr" rid="ref12 ref13 ref14 ref15 ref16 ref17 ref18">12-18</xref>
        ]:
─ neural network converter “biometrics-code” (Fig. 1, a);
─ fuzzy extractors (Fig. 1, b).
key, any other vector (“alien”) into a
random signal.
      </p>
      <p>GOST R 52633-2006†: protection
against attacks on the “last bit” of the
decision rule.</p>
      <p>Advantages the length of the generated key is
specified as an algorithm parameter;
no need to store a private key, but
storage of auxiliary data is required;
allows to get a single key from one
set of biometric data
Disadvantages Training requires significant comput- the quality of work corresponds to
ing resources and makes high demands the quality of the applied error
coron the quality of the training sample. rection codes; fuzzy extractors are
susceptible to the same classes of
attacks as fuzzy containers
Fig. 1. The scheme of the neural network converter “biometrics-code” (a) and the fuzzy
extractor (b).
† GOST R 52633-2006 З Information protection. Information protection technology.</p>
      <p>Requirements for the means of high-reliability biometric authentication,
http://docs.cntd.ru/document/1200048922, last accessed 2021/01/10.</p>
      <p>X – the biometric template used during registration, F – the quantization function, R –
the random noise introduced into the construction of the secure sketch, P – the
generated secure sketch, Y – the biometric template used in the user authentication process.</p>
      <p>A generalized scheme of the neural network system of biometric identification and
authentication (NSBIA) of a person is shown in Fig. 2 and reflects the main stages of
processing biometric information.</p>
      <p>
        To store the database of biometric formed, the parameters of the neural network
connection weights are used, which makes it possible to ensure the confidentiality of
the biometric network system, since even a compromise of the neural network
connection weights will not give the intruder information either about the users of the
system, or the system itself. The only vulnerable element of the system is the output
vector generated by the neural network, which makes it possible to assign the
presented biometric image to one of the known classes. This type of attack on a
biometric system is called an attack on the “last bit” of the decision rule [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ], when an
attacker presents an output vector to the information system, in which a unit in a
specific line position indicates the class of a legitimate user of the system registered in
the NSBIA. An attacker will gain access to the system under the guise of an existing
user. A diagram of such an attack is shown in Fig. 3.
      </p>
      <p>Consequently, the use of biometric systems based on this class of neural networks
and other ML models with an open vector encoding the belonging of the input image
to a certain class becomes problematic in open and weakly protected information
systems.</p>
      <p>The key for biometric identification and authentication systems are falsification of
biometric data presented through the user interface and leakage from the database of
biometric images‡. Vulnerabilities in the implementations of biometric identification
and authentication systems can be divided into:
─ vulnerabilities in used libraries and plug-ins;
─ vulnerabilities in the program code;
─ architectural vulnerabilities.
─ Attacks on biometric images presented through the system user interface can be
divided into two groups:
─ non-targeted attack (a general type of attack when the main target is an incorrect
classification result);
─ targeted attack (the goal is to obtain a label of the required class for a given input
image§).
─ For systems using machine learning methods and technologies, there are two types
of AML attacks (adversarial machine learning)**:
─ evasion – an attacker causes the model to behave incorrectly. The system is viewed
by the attacker as a black box. This type of attack is considered the most common
‡ How vulnerable are biometric Big Data systems: causes of errors and their
measurement metrics,
https://www.bigdataschool.ru/blog/biometrics-vulnerabilities-bigdata-ml.html
§ Attacks on biometric systems,
https://www.itsec.ru/articles/ataka-nabiometricheskie-sistemy
** How to deceive a neural network or what is an Adversarial attack,
https://chernobrovov.ru/articles/kak-obmanut-nejroset-ili-chto-takoe-adversarialattack.html
and includes spoofing attacks on biometric systems, when an attacker tries to
disguise himself as another person.
─ poisoning – an attacker seeks to gain access to the data and learning process of the
ML model in order to disrupt the learning process. Poisoning can be thought of as
malicious infection of training data. The attacker possesses information about the
system (Adversarial Knowledge, AK): sources and algorithms for processing data
for training, training algorithms and resulting parameters.
3</p>
    </sec>
    <sec id="sec-3">
      <title>Security assessment of the authentication system with neural network conversion of biometric parameters into a cryptographic “private” key</title>
      <p>The final structure of the identification and authentication system with neural network
conversion of biometric parameters into a cryptographic "private" key is shown in
Fig. 4.</p>
      <p>
        To assess the security of the system shall use the methodology for analyzing
information security and cybersecurity based on fuzzy gray cognitive maps, detailed in
[
        <xref ref-type="bibr" rid="ref21">21</xref>
        ].
      </p>
      <p>
        Fuzzy gray cognitive map (FGCM) is a directed graph defined using a tuple of sets
[
        <xref ref-type="bibr" rid="ref21">21</xref>
        ]:
      </p>
      <p>Where C – a set of concepts, which are significant factors (graph vertices), F – a
set of connections between concepts (directed arcs), and W – a set of weights of
FGCM connections, which can be both positive and negative for “strengthening” and
“weakening” the influence of the concept, respectively.</p>
      <p>The use of the algebra of “gray” numbers when specifying the set W allows the use
of a fuzzy linguistic scale, considering the degree of confidence of the expert in the
current assessment (Table 4). The state of concepts X will also be defined as a “gray”
number at an arbitrary discrete moment in time t  N  0 :</p>
      <p>FGCM = 〈C, F, W〉,
(1)</p>
      <p>Where X i t  and X i t  1 – the values of the concept state variable at times t
and t  1 , n – number of concepts in FGCM, f () – nonlinear concept function
(hyperbolic tangent).
†† Database of information security threats FSTEC, https://bdu.fstec.ru/threat, last
accessed 2021/01/10.</p>
      <p>In Table 6, the main vulnerabilities correspond to the C7 – C9 FGCM concepts.
Threats C2 – C6 correspond to scenarios of exposure to an external attacker in the
course of exploiting one or more system vulnerabilities. The assessment of local
relative risks of violation of information security and cybersecurity of the NSBIA system
was carried out for the most likely attack vectors. The corresponding FGCM is shown
in Fig. 5.</p>
      <p>Fig. 5. Fuzzy cognitive map for assessing local relative risks of information security and
cybersecurity breach NSBIA.</p>
      <p>Concept
ExtAt1</p>
      <p>C2
C3
C4
С5
С6
C7
C8
C9
C10
C11
C12
C13
C14</p>
      <p>Let us consider the scenario of an attacker's impact with and without using a
countermeasure based on a neural network transformation “biometrics-key” to ensure
information security and cybersecurity of the NSBIA.</p>
      <p>Fig. 6 andFig. 7 below show the process of changing the state of FGCM concepts
in the event of an attacker without using and using the implementation of the neural
network transformation “biometrics-key” to ensure information security and
cybersecurity of NSBIA as a defensive countermeasure.
Fig. 6. Change in time of the state of (a) “grayness” – the spread of the assessment, (b)
“bleached” – the central meaning of the gray assessment) of concepts under the influence
of an attacker without using the implementation of the neural network transformation
“biometrics-key”.</p>
      <p>Local relative risk indicators for target concepts C13, C14 are shown in Table 7.
Violation of the system's performance
and refusal to use it (breach of integrity)
Modification of the base and ML model
(breach of confidentiality)
without the use of
neural network
transformation “biometrics-key”
[0.0162; 0.4156]
after applying the neural
network transformation
“biometrics-key”
[0.0442; 0.2560]</p>
    </sec>
    <sec id="sec-4">
      <title>Discussion</title>
      <p>The use of cognitive analysis in the task of assessing information security and
cybersecurity risks allows us to consider the range of opinions of experts, as well as the
inaccuracy and incompleteness of the data collected during the audit on the state and
properties of the information system. Cognitive models allow one to formalize the
mutual influence of system elements and the destabilizing effects of internal and
external abusers who exploit vulnerabilities of software and hardware components,
which are a significant decision-making tool in the process of qualitative and
quantitative assessments. Scenarios for modeling the impact of an attacker using a gray
fuzzy cognitive map built based on expert data make it possible to assess the
effectiveness of the applied protection tools and select the optimal combination of applied
solutions, considering the identified threats and potential attack vectors on NSBIA,
including ML models for processing biometric data.
5</p>
    </sec>
    <sec id="sec-5">
      <title>Conclusion</title>
      <p>The paper proposes an approach to the analysis of the security of integrated biometric
authentication and identification systems based on gray fuzzy cognitive maps. A
feature of the biometric system is the use of a neural network transformation
“biometrics-key”, which provides distributed storage of the base of biometric images and
allows the use of a secret cryptographic key generated based on the image as an
output of the neural network.</p>
      <p>To assess the security of biometric authentication and identification systems using
ML models, an analysis of current threats, vulnerabilities and potential attack vectors
was carried out, on the basis of which a fuzzy gray cognitive map was built to assess
local relative risks of ensuring information security and cybersecurity in the event of
an attacker without using and using neural network transformation “biometrics-key”.
Local relative risk indicators for key information resources decreased by 45%.
6</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>The reported study was funded by Ministry of Science and Higher Education of the
Russian Federation (information security) as part of research project № 1/2020.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          1.
          <string-name>
            <surname>Vasilyev</surname>
            ,
            <given-names>V.I.</given-names>
          </string-name>
          :
          <article-title>Intelligent information security systems</article-title>
          .
          <source>2nd edn. M.:Mashinostroenie</source>
          ,
          <volume>199</volume>
          (
          <year>2012</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          2.
          <string-name>
            <surname>Kulikova</surname>
            ,
            <given-names>O.V.</given-names>
          </string-name>
          :
          <article-title>Biometric cryptographic systems and their applications</article-title>
          .
          <source>Bezopasnost' informacionnyh tehnologij</source>
          ,
          <volume>16</volume>
          (
          <issue>3</issue>
          ),
          <fpage>53</fpage>
          -
          <lpage>58</lpage>
          (
          <year>2009</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          3.
          <string-name>
            <surname>Merkushev</surname>
            ,
            <given-names>O. Yu.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Sidorkina</surname>
            ,
            <given-names>I.G.</given-names>
          </string-name>
          :
          <article-title>Use of biometric cryptography in a control system of access</article-title>
          .
          <source>Software &amp; System</source>
          ,
          <volume>4</volume>
          ,
          <fpage>172</fpage>
          -
          <lpage>175</lpage>
          (
          <year>2012</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          4.
          <string-name>
            <given-names>Abu</given-names>
            <surname>Elreesh</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.Y.</given-names>
            ,
            <surname>Abu-Naser</surname>
          </string-name>
          ,
          <string-name>
            <surname>S.S.</surname>
          </string-name>
          <article-title>Cloud Network Security Based on Biometrics Cryptography Intelligent Tutoring System</article-title>
          .
          <source>International Journal of Academic Information Systems Research (IJAISR)</source>
          ,
          <volume>3</volume>
          (
          <issue>3</issue>
          ),
          <fpage>37</fpage>
          -
          <lpage>70</lpage>
          (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          5.
          <string-name>
            <surname>Barreno</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          et al.:
          <article-title>The security of machine learning</article-title>
          .
          <source>Machine Learning</source>
          ,
          <volume>81</volume>
          (
          <issue>2</issue>
          ),
          <fpage>121</fpage>
          -
          <lpage>148</lpage>
          (
          <year>2010</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          6.
          <string-name>
            <surname>Turk</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Pentland</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          :
          <article-title>Face recognition using eigenfaces</article-title>
          .
          <source>In Journal of Cognitive Neuroscience</source>
          ,
          <volume>3</volume>
          ,
          <issue>7286</issue>
          (
          <year>2001</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          7.
          <string-name>
            <surname>Wiskott</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          et al.:
          <article-title>Face recognition by elastic bunch graph matching</article-title>
          .
          <source>IEEE Transactions on pattern analysis and machine intelligence</source>
          ,
          <volume>19</volume>
          (
          <issue>7</issue>
          ),
          <fpage>775</fpage>
          -
          <lpage>779</lpage>
          (
          <year>1997</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          8.
          <string-name>
            <surname>Wagner</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          et al.:
          <article-title>Toward a practical face recognition system: Robust alignment and illumination by sparse representation</article-title>
          .
          <source>IEEE transactions on pattern analysis and machine intelligence</source>
          ,
          <volume>34</volume>
          (
          <issue>2</issue>
          ),
          <fpage>372</fpage>
          -
          <lpage>386</lpage>
          (
          <year>2011</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          9.
          <string-name>
            <surname>Paul</surname>
            ,
            <given-names>L.C.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Al</surname>
            <given-names>Sumam A.</given-names>
          </string-name>
          :
          <article-title>Face recognition using principal component analysis method</article-title>
          .
          <source>International Journal of Advanced Research in Computer Engineering &amp; Technology (IJARCET)</source>
          ,
          <volume>1</volume>
          (
          <issue>9</issue>
          ),
          <fpage>135</fpage>
          -
          <lpage>139</lpage>
          (
          <year>2012</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          10.
          <string-name>
            <surname>Bhele</surname>
            ,
            <given-names>S.G.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Mankar</surname>
            ,
            <given-names>V.H.:</given-names>
          </string-name>
          <article-title>A review paper on face recognition techniques</article-title>
          .
          <source>International Journal of Advanced Research in Computer Engineering &amp; Technology (IJARCET)</source>
          ,
          <volume>1</volume>
          (
          <issue>8</issue>
          ),
          <fpage>339</fpage>
          -
          <lpage>346</lpage>
          (
          <year>2012</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          11.
          <string-name>
            <surname>Ding</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          et al.:
          <article-title>Evolutionary artificial neural networks: a review</article-title>
          .
          <source>Artificial Intelligence Review</source>
          ,
          <volume>39</volume>
          (
          <issue>3</issue>
          ),
          <fpage>251</fpage>
          -
          <lpage>260</lpage>
          (
          <year>2013</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          12.
          <string-name>
            <surname>Dodis</surname>
            ,
            <given-names>Y.</given-names>
          </string-name>
          et al.:
          <article-title>Robust fuzzy extractors and authenticated key agreement from close secrets</article-title>
          . In: Dwork C. (Ed.)
          <source>Annual International Cryptology Conference CRYPTO</source>
          <year>2006</year>
          , LNCS
          <volume>4117</volume>
          ,
          <fpage>232</fpage>
          -
          <lpage>250</lpage>
          . Springer, Berlin, Heidelberg, (
          <year>2006</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          13.
          <string-name>
            <surname>Boyen</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          et al.:
          <article-title>Secure remote authentication using biometric data</article-title>
          . In: Cramer,
          <string-name>
            <surname>R</surname>
          </string-name>
          . (Ed.)
          <source>Annual International Conference on the Theory and Applications of Cryptographic Techniques EUROCRYPT</source>
          <year>2005</year>
          , LNCS
          <volume>3494</volume>
          ,
          <fpage>147</fpage>
          -
          <lpage>163</lpage>
          , Springer, Berlin, Heidelberg (
          <year>2005</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          14.
          <string-name>
            <surname>Sahai</surname>
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Waters</surname>
            <given-names>B.</given-names>
          </string-name>
          :
          <article-title>Fuzzy identity-based encryption</article-title>
          . In: Cramer,
          <string-name>
            <surname>R</surname>
          </string-name>
          . (Ed.)
          <source>Annual International Conference on the Theory and Applications of Cryptographic Techniques EUROCRYPT</source>
          <year>2005</year>
          , LNCS
          <volume>3494</volume>
          ,
          <fpage>457</fpage>
          -
          <lpage>473</lpage>
          , Springer, Berlin, Heidelberg (
          <year>2005</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          15.
          <string-name>
            <surname>Baek</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Susilo</surname>
            ,
            <given-names>W.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zhou</surname>
          </string-name>
          , J.:
          <article-title>New constructions of fuzzy identity-based encryption</article-title>
          .
          <source>In: Proceedings of the 2nd ACM symposium on Information, computer and communications security</source>
          ,
          <fpage>368</fpage>
          -
          <lpage>370</lpage>
          , ACM New York. NY, USA (
          <year>2007</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          16.
          <string-name>
            <surname>Fang</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          et al.:
          <article-title>Chosen-Ciphertext Secure Fuzzy Identity-Based Key Encapsulation without ROM</article-title>
          .
          <source>IACR Cryptology ePrint Archive</source>
          <year>2008</year>
          ,
          <fpage>139</fpage>
          -
          <lpage>151</lpage>
          (
          <year>2008</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          17.
          <string-name>
            <surname>Fang</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Xia</surname>
          </string-name>
          , J.:
          <source>Full Security: Fuzzy Identity Based Encryption. IACR Cryptology ePrint Archive</source>
          ,
          <volume>307</volume>
          (
          <year>2008</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          18.
          <string-name>
            <surname>Yang</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Cao</surname>
            ,
            <given-names>Z.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Dong</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          :
          <article-title>Fuzzy Identity Based Signature</article-title>
          .
          <source>IACR Cryptology EPrint Archive</source>
          ,
          <volume>2</volume>
          (
          <year>2008</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          19.
          <string-name>
            <surname>Vasilyev</surname>
            ,
            <given-names>V.I.</given-names>
          </string-name>
          et al.:
          <article-title>Analysis of confidential data protection in critical information infrastructure and the use of biometric, neural network and cryptographic algorithms (standards review and perspectives)</article-title>
          .
          <source>Informacionnye tehnologii i sistemy</source>
          ,
          <fpage>193</fpage>
          -
          <lpage>197</lpage>
          (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          20.
          <string-name>
            <surname>Juels</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Sudan</surname>
            ,
            <given-names>M.:</given-names>
          </string-name>
          <article-title>A fuzzy vault scheme</article-title>
          .
          <source>Designs, Codes and Cryptography</source>
          ,
          <volume>38</volume>
          (
          <issue>2</issue>
          ),
          <fpage>237</fpage>
          -
          <lpage>257</lpage>
          (
          <year>2006</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          21.
          <string-name>
            <surname>Salmeron</surname>
            ,
            <given-names>J.L.</given-names>
          </string-name>
          :
          <article-title>A Fuzzy Grey Cognitive Maps-based intelligent security system</article-title>
          .
          <source>2015 IEEE International Conference on Grey Systems and Intelligent Services (GSIS)</source>
          . IEEE,
          <fpage>29</fpage>
          -
          <lpage>32</lpage>
          (
          <year>2015</year>
          ).
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>