poly_proto_poly_comm.tex

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\subsection{Polynomial Protocols and Polynomial Commitments}
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In order to prove the security of our custom SNARKs, we start by defining custom vector-based conditional NP relations and we describe for each of them a ranged polynomial protocol. 
Extending the notion introduced in PLONK~\cite{plonk}, we give an updated definition of ranged polynomial protocols in Section~\ref{supplementary_poly_protocols_appendix} of the appendix/supplementary material. 
We also use KZG polynomial commitments \cite{KZG_10}, their batched version and their security definitions as described in PLONK, Section 3. 
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