The

multiplicative inverse of a number Z (mod m) is a value that when multiplied mod m by Z = 1.

For simplicity, we only consider the computation overhead for generating a polynomial, restoring the constant term of a polynomial by using Lagrange interpolation, and computing the modular multiplicative inverse of L.

In the SAKDA [20], the GKD executes two modular multiplicative inverse operations by using Extended Euclidean Algorithm.

In the SAKDA [20], each member executes one modular multiplicative inverse operation and one modular exponentiation to get the group key.

Then we can say that the first and last number in each subset is the multiplicative inverse of itself modulo [2.

a) The proof for 1 as the multiplicative inverse of itself is trivial.

This should be an easy task for the students, with most of them expected to point out that the LOCK and the KEY are the

multiplicative inverses of each other.

mod N] (the multiplicative inverse of N - g), [[Beta].

As we saw above, the multiplicative inverse of 2 mod 7 is 4, and 4 is the span of the generating interval of the perfect fifth.

Therefore 5, the

multiplicative inverse of 3 (mod 7), is also a primitive root (mod 7) and these are the only distinct residues which are primitive roots (mod 7).