I am doing some research on the BLS12-381 (https://hackmd.io/@benjaminion/bls12-381) and trying to understand if there are endomorphisms that are efficient. Of course, I am looking at this to explore faster multi scalar multiplications :)

I came across this post on Koblitz curves do koblitz curves over $\mathbb{F}_{P}$ as generalized in SEC2 always have $a$ as 0?

The case of interest for me is when the Koblitz curve is defined over prime order fields.

It does appear that the BLS12-381 has some similarities to the above. From what I understand, in the case of BLS12-381, There also exists a zero trace-subgroup which probably has a Frobenius automorphism.

Does there exist a construction for BLS12-381 on a zero trace subgroup (not sure if this makes sense), and if so does it have an efficiently computable endomorphism?

I am a bit new to this, so I am not sure if I phrased it effectively. I would appreciate any feedback/references. Thanks!



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