Problem $4(1$ point$).$ Assume we have a sequence of $100$ characters, the frequency distribution of different characters is listed below, compute the $($approximate$)$ index of coincidence $($IC$)$ of this sequence.Problem $5(1$ point$).$ An adversary analyzes a sequence of $($ciphertext$)$ characters, which is encrypted by Vigenere Cipher, using Kasishis method. In addition, it knows the key length is at least $2.$ If it can find a sub$-$string edlt, which is repeated twice in the sequence, and the distance between the two repeated sub$-$strings is $12,$ what are the possible key length of this Vigenere Cipher?$2$Problem $6(1$ point$).$ Assume an attacker knows the index of coincidence in plaintext is ICplain $=0\mathrm{.}234.$ Given a long sequence of $($ciphertext$)$ characters, e$.$g$.,$c$1$c$2$c$3$c$4$c$5$c$6$c$7$c$8$c$9.........$which is encrypted by Vigenere Cipher, explain how to calculate$/$estimate the key length by using the index of coincidence.