Chapter 8, Problem P8P

a.

Explanation of Solution

Given,

p = 5 and q = 11

n is calculated using the formula $\text{p}\text{×}\text{q}$

Substitute, “5” for “p” and 11” for “q”:

Thus, $\text{n}\text{=}\text{5}\text{×}\text{11}\text{=}\text{55}$.

z is calculated using the formula $\left(\text{p}\text{–}\text{1}\right)\text{×}(\text{q}$

b.

Explanation of Solution

Given,

p = 5, q = 11 and e = 3

z is calculated using the formula $\left(\text{p}\text{–}\text{1}\right)\text{×}\left(\text{q}\text{–}\text{1}\right)$

Substitute, “5” for “p” and 11” for “q”:

Thus, $\text{z}\text{=}(\text{5}$

c.

Explanation of Solution

Given,

p = 5, q = 11 and e = 3

z is calculated using the formula $\left(\text{p}\text{–}\text{1}\right)\text{×}\left(\text{q}\text{–}\text{1}\right)$.

Substitute, “5” for “p” and 11” for “q”:

Thus, $\text{z}\text{=}\left(\text{5}\text{–}\text{1}\right)\text{×}\left(\text{11}\text{-}\text{1}\right)$

c.

Explanation of Solution

Given,

p = 5, q = 11 and e = 3

n is calculated using the formula $\text{p}\text{×}\text{q}$.

Substitute, “5” for “p” and 11” for “q”:

Thus, $\text{n}\text{=}\text{5}\text{×}\text{11}\text{=}\text{55}$.

We have m = 8, then $\text{me}\text{=}{\text{8}}^{\text{3}}\text{=}\text{512}$

Cipher text $\text{c}$