Score:3

Decisional Diffie-Hellman Assumption on Pairing Friendly Curves

yt flag

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?

ckamath avatar
ag flag
Isn't this the Decisional Bilinear DH (DBDH) assumption? (See, e.g., [this](https://eprint.iacr.org/2012/687) paper.)
Sean avatar
yt flag
Fantastic. Thanks for the information!
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