CYB $3363$: Data Security and Cryptography

Homework $3$ Assignment

Please follow the requirements and due date specified in the Syllabus to submit your work. Please also include a comment to tell me:

How much time did you spend on this assignment?

Problem $1(20$ points$)$:

Please list all the primitive roots of $5$ and justify your answer. $($You can create a table like primitive roots of $19$ shown in slide $18$ of Module $08.)$

Problem $2$ Calculations $(25$ points$)$:

$($a$)$ Please use a theorem that we learned in the Module $08($CYB $3363\_$Module$\_08\_1.$pptx$)$ to calculate $\backslash (\backslash$mathbf$\{3\}^\{\backslash$mathbf$\{203\}\}\backslash$bmod $11\backslash ).$ Please provide the basic steps of your calculation and mention the theorem used. $(15$ points$)$

$($b$)$ Two discrete logarithm calculations $(10$ points$)$:

$\backslash (\backslash$operatorname$\{$dlog$\}\_\{15,19\}11=\backslash )$

$\backslash (\backslash$operatorname$\{$dlog$\}\_\{3,19\}4=\backslash )$