this course Applied Cryptography Question $2(11$ points$)$:

Assume an attacker knows that a user's password is either $"$wxyz$"$ or $"$bddf$".$ Say the user encrypts his

password using:

a$)$ The substitution cipher,

b$)$ The Vigen$$re cipher using period $2,$ or

c$)$ The Vigen$$re cipher using period $3$

and the attacker sees the resulting ciphertext. Show how the attacker can determine the user's

password, or explain why this is not possible.Question $2(11$ points$)$: Assume an attacker knows that a user's password is either $"$wxyz$"$ or $"$bddf$".$ Say the user encrypts his password using: a$)$ The substitution cipher, b$)$ The Vigen$$re cipher using period $2,$ or c$)$ The Vigen$$re cipher using period $3$ and the attacker sees the resulting ciphertext. Show how the attacker can determine the user's password, or explain why this is not possible. Question $3(6$ points$)$: Suppose we have a computer with a $4\mathrm{.}2$GHz$16-$core processor that executes $4\mathrm{.}2\backslash$times $10^(9)$ cycles per second per core. Considering that it can test $20$ keys per CPU cycle, calculate: a$)$ The average time $($in years$)$ to find a key by the brute$-$force attack if the key size is $56$ bits. b$)$ The average time $($in years$)$ to find a key by the brute$-$force attack if the key size is $128$ bits Question $4(16$ points$)$: Answer each of the following without using a calculator. a$)3-11($mod$9)=$ b$)15\backslash$times $29($mod$13)=$ c$)-(12)/(35)($mod$19)=$ d$)$ Are $172$ and $68$ co$-$prime numbers?