$[$Maximum mark: $7]$

$[3]$

"Password entropy" is a measure of the predictability of a com The higher the entropy, the more difficult it is to gu

number of guesses, $G,$ requirsord entropy, $p,($measured in bits$)$ and the $0\mathrm{.}301p=lo{g}_{10}G.$

$($a$)$ Calculate the value of $p$ for a password that takes $5000$ guesses to decode.

$0\mathrm{.}301p=lo{g}_{10}5000$

$0\mathrm{.}301P=3\mathrm{.}698$

$($b$)$ Write down $G$ as a function of $p.G={10}^{0\mathrm{.}301p}P=12\mathrm{.}3$ bits

$[1]$

$($c$)$ Find the number of guesses required to decode a password that has an entropy of $28$ bits. Write your answer in the form $a{10}^k,$ where kinZ$\mathrm{.}0\mathrm{.}30128=lo{g}_{10}G8\mathrm{.}428=lo{g}_{10}G={10}^{8\mathrm{.}428}=267$

There is a point on the graph of the function $G(p)$ with coordinates $(0,1).=2\mathrm{.}6$

$($d$)$ Explain what these coordinate values mean in the context of computer passwords.