### Building blocks

Vector Commitment on elliptic curve, useful for its additive homomorphic

### Statement

$$\{(\textbf{g,h}\in \mathbb{G}^n, P \in \mathbb{G}, c \in \mathbb{Z}_p; \textbf{a,b}\in \mathbb{Z}_p^n): P=\textbf{g}^{\textbf{a}}\textbf{h}^{\textbf{b}} \wedge c=<\textbf{a},\textbf{b}>\}$$

### Proving

the strategy is recursive proof. For every recursive step, keep the public statement in the same format, but the vector length, together with …