# Decisional Diffie-Hellman Assumption on Pairing Friendly Curves

It is known that the Decision Diffie-Hellman (DDH) problem can be easily solved over groups on pairing friendly curves (that is: one can use pairing to tell if $$g^x$$ and $$g^y$$ and $$g^z$$ forms a DH tuple such that $$z = x*y$$). What about the "tripartite" case where one has the tuple ($$g^x$$, $$g^y$$, $$g^z$$ and $$g^u$$) and need to tell if $$u= x*y*z$$. Would that be easy?

It looks like not an easy problem to me, as pairing can only be applied once?

• Isn't this the Decisional Bilinear DH (DBDH) assumption? (See, e.g., this paper.) Jul 28 '21 at 14:54
• Fantastic. Thanks for the information!
– Sean
Jul 28 '21 at 15:03