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对于plonk系列第三章(置换证明)中置换协议的推导,建议补充过程? #39

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EricDecen opened this issue Oct 18, 2023 · 1 comment

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@EricDecen
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(1)在Grand Product中,证明的目标是:L0(X)⋅(r(X)−1)+α⋅(q(X)⋅r(X)−r(ω⋅X))=h(X)⋅zH(X)。
而后,推导至完整的置换协议中,证明的目标是:f(X)=L0(X)(z(X)−1)+α⋅(z(ω⋅X)(b(X)+β⋅σ(X)+γ)−z(X)(a(X)+β⋅id(X)+γ))
由Grand Product推导至置换协议中的式子,能否补充一下中间的步骤?(我自己后来再推导了一下,推出来了,不过如果有中间过程,可能会对新手更友好一些)
(2)有一个很小的问题:在GrandProduct中,使用的名词代号是rk+1=qkrk,而在置换协议zi+1=ziqi (且用qi来指代,qi实际上是下面式子的右边)。
image
如果文章能从头到尾连贯使用r、q这个名称代号,可能会一致性更好。另外,使用z,也容易和zH(X)这里的z混淆。
(也可能这个不算是问题,对于非初学者是很容易理解的。若有可能吹毛求疵了,请海涵!)

@EricDecen
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rk+1=qk × rk,zi+1=zi × qi,漏了一个乘号。

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