Please help me to solve these questions. They are very tough though!

1.The method of using exponentiation to conduct an encryption or a decryption is determined by the use of logarithms to conduct attacks resulting to efficient results. True or false?

2.The Non - primitive root of a group is one that has the elements the same as the order of the group having the assumption of G = . Determine the truth value of this statement.

3.Given a group G = containing of 20, 50, 17 and 38, determine the values that lack primitive roots.

4.Determine the primitive roots given a group represented by G = .

5.How can the order of the group represented by G = be determined? Give the order.

6.Determine whether there is any truth where equations are said to lack solution or they have exactly three incongruent solutions.

7.Given x2 2 mod 11. Determine the solution.

8.Given a set - Z13* = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12}, determine the set of quadratic residues that is present in the set.

9.Determine the solution of x2 16 mod 23.

10.It is determined that (p - 1)/2 elements are QR and (p - 1)/2 elements are QNR. This is in reference to Zp* with (p-1) elements. Is it a true determination?