$4.$Short Answer and Calculation Questions $(40$ points$)$:$1)$How does the Advanced Encryption Standard $($AES$)$ differ from DES in terms of key length and security?$2)$Explain the concept of key length in cryptography and its impact on security$\mathrm{.}3)$Calculate the number of possible keys in DES, given its $56-$bit key size$\mathrm{.}4)$How does the Vigen$$re cipher differ from the Caesar$/$shift cipher in terms of key usage and complexity?$5)$What is the purpose of cryptanalysis, and how can frequency analysis be used to break simple ciphers?