For one of my projects, I need a pairing group which holds the External co-Diffie-Hellman assumption. I am trying to implement it using Charm crypto python modules which provides support for MNT curves. According to Wikipedia:

In practice, it is believed that the XDH assumption may hold in certain subgroups of MNT elliptic curves.

On searching a little bit more on the web about this assumption, I encountered the following statement in the book, Applied Cryptography and Network Security:

bilinear maps based on MNT curves, where G1 $\neq$ G2, the XDH assumption is believed to hold.

As one can see, when Wikipedia says that the assumption may hold only for certain MNT curves, the book says it is assumed to hold for all the MNT. curves. However, Charm Crypto provides modules for only certain MNT curves and therefore, I need to know for sure whether this assumption actually holds for all the MNT curves or not. If someone can provide me with some clarity on this, it would be great.


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