Open mmaker opened 1 year ago
In #577, @Pratyush suggests basing PairingOutput
over MultiplicativeGroup
. However, this would break some arguments and I'd rather vouch for it being AdditiveGroup
. For instance. in a sumcheck-based argument for proving $\langle A, B \rangle$ with $A$, $B$ resp. in $\mathbb{G}_1$, $\mathbb{G}_2$, the sumcheck messages will be polynomials in the target group, and we'd expect to manipulate them just as sumcheck messages from $\langle a, b\rangle$ (with $a$, $b$ in $\mathbb{F}$), which are in $\mathbb{G}_1$, that is solely AdditiveGroup
. This part requires some more thought
As we try to implement some generic arguments, like generic inner-products, we must share common traits between
Field
andCurveGroup
. This issue is meant to track the status of it, and the abstractions done overAdditiveGroup
. This issue is a spin-off of #577ark-group
traitAdditiveGroup
thereThe new crate
ark-group
should also supportMultiplicativeGroup
, for multiplicative groups used over fields (and overPairingOutput
?)MultiplicativeGroup
using the template ofAdditiveGroup
and baseField
it