Why do we need the random number in Pinochioo protocol compared with GGPR

Wang Linger

4/27/24, 8:05 AM

I find it hard to fully grasp the whole Pinocchio protocol .

I understand that the $\alpha$ s are for restricting the prover to compute only the corresponding set-up values.

But it's not clear for me to pick up $\gamma$ for the consistent(same) witness check.

From what I can tell, this protocol cleverly embedded different $r_v,r_w,r_y$ s to generators, $g_v,g_w,g_y$. An insightful improvement on GGPR. By generating generators in this way, different $r$ s have already been encoded into the equation. All we need is another random number, $\beta$ to mitigate the malleability problem mentioned in this manual script zksnark explain.

So, why do we need another randomness $\theta$ in Pinocchio protocol? (Compared with the GGPR protocol)

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Elon Musk

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EN: Why do we need the random number in Pinochioo protocol compared with GGPR

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