How to calculate the integration equation?












0














I am newbie in this forum, thus I have not been allowed to paste image in this question. Hopefully the readers can click to the link to view the equations.
I have a few of integration equations.
The first equation is the error probability of authentication in normal operation, $P_{e}^{Auth,normal}$:



normal operation



The $P_{e}^{Auth,normal}$ can be calculated using the equation:



Error probability in normal equation



The second equation is the error probability of authentication under MIM attack, $P_{e}^{Auth,MIM}$:



MIM attack



My question is how to calculate $P_{e}^{Auth,MIM}$ since the calculation of error probability in MIM attack was not given. The only equation that I have is error probability in normal equation.



Supposedly, the graph of the integration equation will be shown like this:



Graph of normal & MIM attack



$P_{e}^{Auth,normal}$ - blue line



$P_{e}^{Auth,MIM}$ - red line



Differences between two error probabilities - green line



I hope that anyone may help me to solve this problem.



Thank you.










share|cite|improve this question



























    0














    I am newbie in this forum, thus I have not been allowed to paste image in this question. Hopefully the readers can click to the link to view the equations.
    I have a few of integration equations.
    The first equation is the error probability of authentication in normal operation, $P_{e}^{Auth,normal}$:



    normal operation



    The $P_{e}^{Auth,normal}$ can be calculated using the equation:



    Error probability in normal equation



    The second equation is the error probability of authentication under MIM attack, $P_{e}^{Auth,MIM}$:



    MIM attack



    My question is how to calculate $P_{e}^{Auth,MIM}$ since the calculation of error probability in MIM attack was not given. The only equation that I have is error probability in normal equation.



    Supposedly, the graph of the integration equation will be shown like this:



    Graph of normal & MIM attack



    $P_{e}^{Auth,normal}$ - blue line



    $P_{e}^{Auth,MIM}$ - red line



    Differences between two error probabilities - green line



    I hope that anyone may help me to solve this problem.



    Thank you.










    share|cite|improve this question

























      0












      0








      0







      I am newbie in this forum, thus I have not been allowed to paste image in this question. Hopefully the readers can click to the link to view the equations.
      I have a few of integration equations.
      The first equation is the error probability of authentication in normal operation, $P_{e}^{Auth,normal}$:



      normal operation



      The $P_{e}^{Auth,normal}$ can be calculated using the equation:



      Error probability in normal equation



      The second equation is the error probability of authentication under MIM attack, $P_{e}^{Auth,MIM}$:



      MIM attack



      My question is how to calculate $P_{e}^{Auth,MIM}$ since the calculation of error probability in MIM attack was not given. The only equation that I have is error probability in normal equation.



      Supposedly, the graph of the integration equation will be shown like this:



      Graph of normal & MIM attack



      $P_{e}^{Auth,normal}$ - blue line



      $P_{e}^{Auth,MIM}$ - red line



      Differences between two error probabilities - green line



      I hope that anyone may help me to solve this problem.



      Thank you.










      share|cite|improve this question













      I am newbie in this forum, thus I have not been allowed to paste image in this question. Hopefully the readers can click to the link to view the equations.
      I have a few of integration equations.
      The first equation is the error probability of authentication in normal operation, $P_{e}^{Auth,normal}$:



      normal operation



      The $P_{e}^{Auth,normal}$ can be calculated using the equation:



      Error probability in normal equation



      The second equation is the error probability of authentication under MIM attack, $P_{e}^{Auth,MIM}$:



      MIM attack



      My question is how to calculate $P_{e}^{Auth,MIM}$ since the calculation of error probability in MIM attack was not given. The only equation that I have is error probability in normal equation.



      Supposedly, the graph of the integration equation will be shown like this:



      Graph of normal & MIM attack



      $P_{e}^{Auth,normal}$ - blue line



      $P_{e}^{Auth,MIM}$ - red line



      Differences between two error probabilities - green line



      I hope that anyone may help me to solve this problem.



      Thank you.







      integration






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Dec 28 '18 at 14:17









      Afir Afir

      12




      12






















          0






          active

          oldest

          votes











          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "69"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3054930%2fhow-to-calculate-the-integration-equation%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes
















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.





          Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


          Please pay close attention to the following guidance:


          • Please be sure to answer the question. Provide details and share your research!

          But avoid



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3054930%2fhow-to-calculate-the-integration-equation%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          Human spaceflight

          Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

          File:DeusFollowingSea.jpg