$2.$ Use the Mandylion "Brute Force Attack Estimator" Excel spreadsheet $($a slightly modified version$).$ Suppose you want a password that requires the rest of your life for a PC to crack. You have $50$ years to live. How many days $($live each to the fullest$)$ is that? In the spreadsheet, consider passwords consisting of numerals $("$Numbers$")$ only.

a$)$ the length of the numbers$-$only password that requires at least $50$ years to crack, according to the spreadsheet, is $\_\_\_\_\_\_\_\_\_$ characters?

b$)$ account for Moore's law. It says computing power doubles every $2$ years. The spreadsheet is dated. It reflects the computing power of $10$ years ago $.$ For today, you need to increase its computing power assumptions by a factor of $32($having doubled $5$ times over the $10$ years$).$ Do so by entering $32$ as the "Special factor" in cell G$1($which is applied in the "computing power" cell, E$24,$ as a multiplier$).$ Thus, with today's computing power, the length of the numerals$-$only password that requires at least the rest of your life to crack is $\_\_\_\_\_\_\_\_\_\_$ characters.

c$)$ account for Moore's law's continued operation. Let's assume Moore's law doesn't stop. $($There$\text{'}$s debate about that. But let's set it aside because if Moore's law's potential to continue raising cracking power is blunted, GPU advances or specialized cracking silicon may more than fill the gap.$)$ Then today's isn't the right computing power for the upcoming $50$ years' calculations. I say that on average $($less near term, more far term$)$ the upcoming power is $2\mathrm{.}5$ million times today's $($approximately$).$ Using $2\mathrm{.}5$ million as your future computing power, the length of the password that requires at least $50$ years to crack becomes $\_\_\_\_\_\_\_\_\_\_$ characters. $($Multipy the current special factor by yet a further $2\mathrm{.}5$x$10^6)$

d$)$ if you then made the one change of allowing mixed random characters $($spreadsheet$\text{'}$s "PURELY Random Combo of Alpha$/$Numeric$/$Special$")$ instead of confining your password to numerals only you should be able to use a shorter password with equal effect. The shortest "mixed character" password that'll last $50$ years is $\_\_\_\_\_\_\_\_\_\_$ characters.