We prove that g^(a^2) cannot be computed efficiently from g^a under the Diffie-Hellman (DH) assumption. More rigorously, the following statement holds:
Let G be a cyclic group and g be a generater of G.
Given an oracle which can compute g^(a^2) from a given g^a for any integer a,
there exists a polynomial time algorithm which computes g^(xy) from g^x and g^y for any integers x and y.