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As we try to implement some generic arguments, like generic inner-products, we must share common traits between Field and CurveGroup. This issue is meant to track the status of it, and the abstractions done over AdditiveGroup. This issue is a spin-off of #577
create new ark-group trait
move AdditiveGroup there
The new crate ark-group should also support MultiplicativeGroup, for multiplicative groups used over fields (and over PairingOutput?)
create MultiplicativeGroup using the template of AdditiveGroup and base Field it
The text was updated successfully, but these errors were encountered:
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
itThe text was updated successfully, but these errors were encountered: