INSTRUCTIONS: You must write GOOD mathematics; clear, meaningful, consistent. Show each step of your work to receive full credit. You will not receive any points for answers that are not clearly explained. Upload a SINGLE PDF file. It must be readable. No late homework is accepted.

$1.(30$ points$)$ There are ciphertexts in the attached pdf file. Look at your row number $(1$ to $40)$ in the Table and find your own ciphertext in the attached file. Decrypt your own ciphertext obtained from a Vigenere Cipher.

Note that there may be meaningless words at the beginning or at the end since the plaintext is divided into equal parts.

$2.(30$ points$)$ Find the S$-$Box output of the input which you will obtain by following the steps:

$($a$)$ Take the last $8$ digits of your student number and take mod $2$ of each digit.

$($b$)$ Convert your row number $(1$ to $40)$ to binary string of length $8($by padding the first digits with $0\text{'}$s if needed$).$

$($c$)$ XOR these two binary strings.

$($d$)$ Find this binary string's correspondent polynomial in the filed $\backslash (\backslash$mathbb$\{$F$\}\_\{2^\{8\}\}=\backslash$mathbb$\{$F$\}\_\{2\}[$x$]/\backslash ).$

$($e$)$ Find the inverse of this polynomial in $\backslash (\backslash$mathbb$\{$F$\}\_\{2^\{8\}\}\backslash )$ and convert it to binary.

$11$

UNMKTZVNGKLFQLBGAJJOYGORKHFTLKJY$$OBKNYLUTUGHPKGNCMQEEGEIISZPVIFFYA KCVQKIJDYKUZVCHIZPZPAXGZVYIWYMKJUSKDVTNMUCXJNYNMGQIWIPZNXKUZZPYAKZ NCMXUADCFGGAKJCXHMWQLJTMMGLFTLZFYHRIIGCYYBFQVFJBYCNNZQJCMXNMJCCIZP VUYBUZUUBJXNF$$NXRGGRYIGVUKHFTWKJYWSWDGHYYXCCMYYPVYUXAXK@BJXKYKHN TARNNBGBVTBJXNZTMYOLVCQFYBYCNXNMYCXXUUVJIBLICNYSOVKQNMKAVCUSJQEVB FZKRUYNIIEIIGGKBDSWGgCYUDYPVUUNJBFJYWYMCHUGOKVJUIHMVPNTZPVUYFYQUGI SIMZPBJXTZHYFTLYCXHUUVVIYNRXGHJXICEISITLUCTTBYCNBNAIGPJXGFWATZWFPN MKMEIFNYPTQUXZGFWZNTLRFORHMIQZGGBYKHLSITJCSKAZPNMKAVCKTSMTJCQJZVPX NHOZPANTBYGMFTLNKNRCWFFYSYXRFYXZPVPUWUEFHFTJOZPAMUCJGMFTLSGBNTLKJ YRGZRKFBGGJVUYOWEJIBKDVTMMKAFGHRGLVGOYZPRVM NJCHNAYGBFJEVRNBNLEUBJCIJFCSKNVGNMOOYKQNYPZJUITBTTCJJAFOOHNARKXFR QTGUXYPVUGFSISGOYZZFKHLZWWKHINMIYUDUCKKMMGTCDYUAVZUBJJNFTCYTWNKMZV XFUYGEJVKHLJZFYHJJQEOSTCVKGUWYBYCNBOTCDYFWCVGLYNGEINTHUJWLJNWNGFJ XMMGLDZPZPANYYLGYWZWUCSOAAKVBJTAYGBJGZUUIRKBYKHLYXCCMMOVXCVTABZPN MKXFQFFRQKVFJCIFQZKGVUUBJYEROHJGZVTNTSIBGIZZEYCNNZERUUYLQIUNXNRKJI ZMPKKNRAAKDYFCICTOXUZYKJUUXFVURAASWNYNMEUBJXMDGGGKZVFBTCADCFQYPVY UXTWNCHIYPVUITTURFYTABKJUYOBNCMTTTFCGTAAVVBFZPRFYGOXGGXNTTZMYMKZJG FKCWLNXNZJVQZFTGLUYSUEKJIZMPKCFNIMKQUUKIBVIYNQJOIZYMVXYWEBYKHLOAJQ IZZWWVBJCIPFIBTPVTYYNIKKMYUCCFNMOVBXYWETZMYQEQKEUSZICMUYGVPTUYKBYG LJYVFJUWSQEVLDOVXUIXNMSGAFTWDQOXKLFAIZQVFYNKKERAIZZ