Here we consider a method for quickly testing for group membership in the groups $G_1$, $G_2$ and $G_T$ (all of prime order $r$) as they arise on a type-3 pairing-friendly curve. As is well known endomorphisms exist for each of these groups which allows for faster point multiplication for elements of order $r$. The endomorphism applies if an element is of
order $r$. Here we show that, under relatively mild conditions, the endomorphism applies {bf if and only if} an element is of order $r$. This results in a faster method of confirming group membership. In particular we show that the conditions are met for the popular BLS family of curves.

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