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davidnevadoc avatar davidnevadoc commented on September 25, 2024 1

Can we mark this as solved? @CPerezz

from halo2curves.

davidnevadoc avatar davidnevadoc commented on September 25, 2024

I see the source of the confusion. This trait is meant to be used for the implementation of efficient endomorphisms:

 /// The presence of this element allows you to perform (certain types of)
 /// endomorphisms on some elliptic curves.

In the case of bn and many other curves we are interested in the cubic endomorphism, hence we look for an element of order 3: zeta. The subgroup generated by this element is the small group this trait refers to, which has order N=3.

With regards to the actual ZETA, notice that this can be any generator of the subgroup, so it can be either zeta or zeta^2. AFAIK different versions of Sage may output one or the other so that may be the source of the discrepancy.

from halo2curves.

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