<p>Seeing an example can be more helpful. Let’s say that&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="p=7">\(p=7\)</span> and
<span class="ltx_Math" contenteditable="false" data-equation="q=17">\(q=17\)</span>, <span class="ltx_Math" contenteditable="false" data-equation="n">\(n\)</span> can be computed by <span class="ltx_Math" contenteditable="false" data-equation="pq">\(pq\)</span>&nbsp;and in our case <span class="ltx_Math" contenteditable="false" data-equation="pq=119">\(pq=119\)</span>. To calculate <span class="ltx_Math" contenteditable="false" data-equation="\phi n">\(\phi n\)</span> we do <span class="ltx_Math" contenteditable="false" data-equation="\left(7-1\right)\left(17-1\right)">\(\left(7-1\right)\left(17-1\right)\)</span>,
<span class="ltx_Math" contenteditable="false" data-equation="\phi n=\left(6\cdot16\right)=96">\(\phi n=\left(6\cdot16\right)=96\)</span>. Next, <span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span> will be chosen. Keep in mind that <span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span> must be relatively prime
to <span class="ltx_Math" contenteditable="false" data-equation="\phi n">\(\phi n\)</span>. In our case lets say <span class="ltx_Math" contenteditable="false" data-equation="d=5">\(d=5\)</span>. We now can plug this onto our equation to find
the value of <span class="ltx_Math" contenteditable="false" data-equation="e">\(e\)</span>. In our case <span class="ltx_Math" contenteditable="false" data-equation="5e+96f=1">\(5e+96f=1\)</span>&nbsp;. We can see that <span class="ltx_Math" contenteditable="false" data-equation="e=19">\(e=19\)</span> and <span class="ltx_Math" contenteditable="false" data-equation="f=-1">\(f=-1\)</span>&nbsp;in order to satisfy our equation. Now in order to encrypt the message we take
our message <span class="ltx_Math" contenteditable="false" data-equation="M">\(M\)</span> and raise it to the <span class="ltx_Math" contenteditable="false" data-equation="e">\(e\)</span> power (mod <span class="ltx_Math" contenteditable="false" data-equation="n">\(n\)</span>), in this case lets say we
want to send the message <span class="ltx_Math" contenteditable="false" data-equation="2">\(2\)</span>, so we can encrpty by saying <span class="ltx_Math" contenteditable="false" data-equation="2^{19}">\(2^{19}\)</span>&nbsp;(mod <span class="ltx_Math" contenteditable="false" data-equation="119">\(119\)</span>) which
equals&nbsp;<span class="ltx_Math" contenteditable="false" data-equation="93">\(93\)</span>. In order for someone to decrypt the message they will take the value
<span class="ltx_Math" contenteditable="false" data-equation="C">\(C\)</span> and raise it to the <span class="ltx_Math" contenteditable="false" data-equation="d">\(d\)</span> power (mod <span class="ltx_Math" contenteditable="false" data-equation="n">\(n\)</span>), <span class="ltx_Math" contenteditable="false" data-equation="93^5">\(93^5\)</span>(mod <span class="ltx_Math" contenteditable="false" data-equation="119">\(119\)</span>) .<br></p><div><br></div>