Answer Happy

INSTRUCTIONS: You must write GOOD mathematics; clear, meaningful, consistent. Show each step of your work. If you use a programming platform for a computation, write the set of commands that produced the result. Upload a SINGLE PDF file. It must be readable. 1. There are cipher texts at the end of the document. Decrypt your own cipher text obtained from a Substitution Cipher. Note that there may be meaningless words at the beginning or at the end since the plaintext is divided into equal parts. 2. Find the S-Box output of the input which you will obtain by following the steps: (a) Take the last & digits of Special number (190201967), and take mod 2 of each digit. (b) Convert row number (140), to binary string of length 8 (by padding the first digits with O's if needed). (c) XOR these two binary strings. (d) Find this binary string's correspondent polynomial in the filed F2 8 = F2[x]<x8 + x 4 + x3 + x +1> (e) Find the inverse of this polynomial in F2 8 and convert it to binary 3 Prime number p (941). (a) Consider the multiplicative group F .p and find a generator (primitive root) of it. Hint: F. p has o(p) =P - 1 elements and the order of an element must divide the order of group. (b) Use the extended Euclidean Algorithm to compute the inverse of 5 mod p. 4 Prime number (211). (a) Consider the multiplicative group F and find a generator (primitive root) of it. (b) Show the steps of the Diffie-Hellman between Alice and Bob such that they choose the secret values as a = 32 and b = 64. What are the values of A=ga and B=gb. What is the agreed key? (c) Use Fermat's Little Theorem to compute the inverse of 7 mod q.
*NOTE* *Role no: 140 * Special Numbers: 190201967 *Prime Numbers p and q which will be used in problems; P: (941) :(211) *Cipher texts which will be used to solve the problem BXZXTFXRIMAXRIQUWBPWOXJUBRTBIWBXEQZDAX RHEXZDXPHEXZDVIWHEW QKBPWOXJUBRTBIWFXRIMNWEXUQZMHIQJWTWVIQ WMEXWHDWTIABPHBBPWD TAVPXZEHQMQZHTHBPWTXKKWZMWMBXZWPOZXHJ JXRZBQZDKXTBHEBWEEQZ DPWTBRTBIWEXRVFQIIAXRXIMKWIIXFBPWOXJUBRT BIWEQDPWMMWWVIAHZ MNWDHZQZHSXQJWEXOWBQOWEJPXUWMFQBPEXN EBXEQZDBPQENWHRBQKRIE XRVEXTQJPHZMDTWWZFHQBQZDQZHPXBBRTWWZFP XKXTERJPMHQZBQWEFXR IMZXBEBXXVEXRVXKBPWWSWZQZDNWHRBQKRIEX RVEXRVXKBPWWSWZQZDNW HRBQKRIEXRVNWHRXXBQKRIEXXXXVNWHRXXBQK RIEXXXXVEXXXXVXKBPWW WwSWZQZDNWHRBQKRINWHRBQKRIEXRVNWHRBQ KRIEXRVFPXJHTWEKXTKQE PDHOWXTHZAXBPWTMQEPFPXFXRIMZXBDQSWHIIWI EWKXTBFXVWZZAFXTBP XZIAXKNWHRBQKRIEXRVVWZZAFXTBPXZIAXKNWH RBQKRIEXRVNWHRXXBQK RIEXXXXVNWHRXXBQKRIE