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youwin2152 avatar Crypto

THe operation proof part of paper "Why and How zhSNARK works"

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youwin2152

I'm reading the paper "Why and How zk-SNARK works" to learn zkSNARK, and I suffered some problem in section 4.4, when prove the ability of single operation.

In this section, it tries to come up with a protocol to verify that the prover have the ability of doing multiplication. It gives two number $b$ and $c$ and tries to verify the result of multiplication. The prover construct to polynomials $l(x)$ and $r(x)$ which satisfies: $l(a)=b,\ r(a)=c$ for some $a$ given by verifier, and get $o(x)$ that $o(a)=b*c$, the verifier needs to verify that $p(x) = l(x)*r(x)-o(x)$ has the zero point of $a$, which means the prover has the ability of multiplication.

While in the protocol mentioned at the end of section 4.4, there is nothing about the number $b$ and $c$, and the verifier doesn't verify the polynomial satisfies the properties like $l(a)=b$...So if I'm the prover, I can construct any polynomials if they satisfies $l(x)*r(x)-o(x) = (x-a)h(x)$, there is nothing about multiplication? I think I got something wrong but I really don't know what's it...

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