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create new ark-group crate about algebra HOT 1 OPEN

mmaker avatar mmaker commented on August 15, 2024 1
create new ark-group crate

from algebra.

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mmaker avatar mmaker commented on August 15, 2024

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

from algebra.

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