$G$ a finite cyclic group of order n, g is the generator

Computational Diffie-Hellman Assumption

Comp. DH (CDH) assumption holds in G if $g, g^a, g^b \nRightarrow g^{ab}$

i.e. for all efficient algo. $\mathcal A$:
Pr[$\mathcal A(g, g^a, g^b) = g^{ab}$] < negligible
where a, b $ \leftarrow Z_n$ .

Hash Diffie-Hellman Assumption(HDH)

$H: G_2→ K$ a hash function
Def: Hash-DH (HDH) assumption holds for (G, H) if:
$(g, g^a, g^b, H(g^a, g^b)) \approx (g, g^a, g^b, R_{andom})$

Interactive Diffie-Hellman Assumption(IDH)