Cryptography Assignment on Math Foundations 1. Use the Euclidean Algorithm to calculate gcd(798, 111) 2. Use the Extended Euclidean Algorithm find x and y such that gcd(798,111)=798x+111y 3. Use the Euclidean Algorithm to calculate the inverse 271mod131. 4. Let f(x)=x6+x3+x2+x+1 and g(x)=x4+x3+1 in GF(2)[x]. Find the quotient of f(x) : g(x) and the remainder. 5. Solve the system of modular equations: x=2mod3,x=3mod7 and x=2mod11. 6. Let Galois Field GF(24) with irreducible polynomial x4+x3+1,f(x)=x3+1, and g(x)=x+1. a. find c(x)=f(x)g(x) in GF(24) (remember to do remainder operation). b. Express the multiplication c(x)=f(x)g(x) as bit string multiplication using the quivalence ax3+bx2+cx+d==(abcd). For example, x3+1=(1001). 7. (optional - students need to look for the fast exponentiation algorithm an ddo it accordingly) Use the fast expopentiation algorithm to calculate 2369mod71