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create new ark-group crate #591

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mmaker opened this issue Jan 26, 2023 · 1 comment · May be fixed by #665
Open
3 tasks

create new ark-group crate #591

mmaker opened this issue Jan 26, 2023 · 1 comment · May be fixed by #665

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@mmaker
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mmaker commented Jan 26, 2023

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
@mmaker
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mmaker commented Jan 26, 2023

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

@Pratyush Pratyush linked a pull request Sep 6, 2023 that will close this issue
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