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<title>Axiom Documentation</title>
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<div align="center"><img align="middle" src="doctitle.png"/></div>
<hr/>
<center>
<h2>RCM3720 Cryptography, Network and Computer Security</h2>
<h3>Laboratory Class 6: Digital Signatures</h3>
</center>
<hr/>
You will need to read in the <a href="rcm3720.input">rcm3720.input</a>
file for the <tt>str2num</tt> and <tt>num2str</tt> procedures.
<br/>
<b>NOTE:</b> To save typing in all the messages and long signature
numbers, just copy them from <a href="signatures.txt">signatures.txt</a>
<ul>
<li> For an RSA signature scheme, I provide the public key <i>(n,e)</i>, where
<pre>
137
n=2 -1, e=17
</pre>
</li>
<li> This value <tt>n</tt> has two large prime factors.
Use my public key to verify my signature of the following message:
<pre>
This is my text.
68767027465671577191073128495082795700768
</pre>
</li>
<li> Now try with the public key
<pre>
67
n=(6 - 1)/5, e=17
</pre>
</li>
<li> to verify my signature:
<pre>
Please feed my dog!
1703215098456351993605104919259566435843590978852633
</pre>
</li>
<li> For a Rabin signature scheme, I provide the public key
<pre>
74
N=(7 -1)/6,
</pre>
which I know can be factorized into two large primes.
</li>
<li> Check the following message and signature:
<pre>
Arrive Thursday.
189479723122534414019783447271411895509
</pre>
</li>
<li> For an El Gamal signature scheme, I choose the next prime after
<pre>
150
2
</pre>
which has a primitive root <tt>a=2</tt>. My public key is
<pre>
B=1369851585774063312693119161120024351761244461
</pre>
</li>
<li> Verify the signature
<pre>
Leave AT ONCE!,
1389080525305754392111976715361069425353578198
1141326468070168229982976133801721430306004477
</pre>
</li>
<li> For a DSS signature, choose <tt>p</tt> to be the next prime after
<pre>
170
2 and q=143441505468590696209
</pre>
</li>
<li> Verify that <tt>q</tt> is a divisor of <tt>p-1</tt>.
A primitive root of <tt>p</tt> is <tt>a=3</tt>.
Use this primitive root to determine
<pre>
(p-1)/q
g = a mod p
</pre>
</li>
<li> The public key value is
<pre>
B=1394256880659595564848116770226045673904445792389839.
</pre>
</li>
<li> Now using these values, verify this signature:
<pre>
Now's your chance!
64609209464638355801
13824808741200493330
</pre>
</li>
<li> Now exchange some public keys with a friend, and sign messages to each
other. Then verify the signatures you have been sent. Make sure you try
each of
<ul>
<li> RSA signatures,</li>
<li> Rabin signatures,</li>
<li> El Gamal signatures,</li>
<li> DSS.</li>
</ul>
</li>
</ul>
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