CYB $710$ Module $2$: Homework

This problem coborems binary repersentatioes. Complete the follow$-$

ing, in each case describing how you arrive at your answer.

$($a$)$ How many integers can be represented using nibe binary digits?

$($b$)$ What is the smallest nine$-$bit integer? What is the largest nibs$-$

bit integer?

$($c$)$ What is the minimum mumber of binary digits nosded to represent

the integer $250000?($boce: you can answer this without finding the full

binary representation of $250000)$

$($a$)$ Given that the cipbertext EBO was encrypted using a shift$($n$)$

cipher and that the plaintext bs an Englibh word, if you use a brute

force hay search to try to decrypt it$,$ you will run into an ambiguity.

Describe what the issase is$.$

$($b$)$ Is the isene in part $($a$)$ resolved if you find out that the plaintest

is a proper first name ratber than a word? Explain.

$($c$)$ Compare and contrist the docryption of this message with the

decryption you did in the Module $1$ discussion. For example, you might

focus on the process you used for each, the difficulties encountered, etc.

In our lecture botes we used the initial state $s_0{s}_1{s}_2=011$ and

recursbon

$s_m=s_{m-1}+s_{m-1}(mod2)$

to extend this kxy stream to $011101.$

$($a$)$ Continuse to extend this stream until you see a repeating pattern.

What block of digits is contimually repoated?

$($b$)$ Describe how you cas use what you found in part $($a$)$ to predict

the lary stream that would result from starting with the initial state

$s_0{s}_1{s}_2=010.$

$($c$)$ Repeat $($a$)$ with the mecursion

$s_e=s_{m-1}+s_{m-1},(mod2)$

and initial state $s_0{s}_1{s}_2{s}_2=1000.$

Suppose you are nsing a variable shift cipher shi $ft(n_1,n_2,$dots,$n_f)$ to

encrypt messages and you wish to thwart Oroar, who his the following

capahilitios. $(1)$ he can figure ont the value of $l$ that you are using, and

$(2)$ be has the capacity to perform a brute force bey search oner one

billion bays.

To give yourself a monsure of security, you would liloe Oscar's ex$-$

pected average sararch length to be at least one trillion trials. What is

the minimun value of $t$ requirorl? Explain carcfully how you arrive at

your answer.