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Since the designs with automorphisms of odd prime orders have been constructed previously, we are left with the construction of the designs with automorphisms of order 2.
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Therefore, (P_{1}cap N=1) and (N) is of prime order.
In this paper two new posibilities for implementing HVE in prime order fields are presented.
Denote G 1 and G 2 to be cyclic groups of prime order q.
Choose a group G 1 of prime order p according to the security parameter.
It first chooses a group G 1 of prime order p, a generator P ∈ G 1.
Before starting these processes, the server generates a cyclic group G, of a large prime order q with generator g.
Choose an additive group G with a prime order q and a generator P∈G defined on an elliptic curve.
We obtain a bound on the number of distinct vertex-transitive self-complementary graphs of prime order p≡1(mod4), up to isomorphism.
Another advantage is that these require implementation of elliptic curves over prime order field which improve the computation speed over composite ones.
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