Diffie-Hellman, decision Diffie-Hellman, and discrete logarithms

Let G be a cyclic group of order n. With respect to polynomial-time non-uniform generic reductions, the Diffie-Hellman problem and the discrete logarithm problem are equivalent in G if and only if n contains no multiple large prime factors. The Diffie-Hellman decision problem is equivalent to the Diffie-Hellman problem in G if and only if all prime factors of n are small.