Motivation

KZG

Applications:

Polynomial

$$ f(x) = \sum_{i = 0}^{n} a_i x^i=a_0 + a_1x + ...+a_nx^n $$

Encoding data into Polynomial using Lagrange Interpolation

Given $(x_i, y_i), x_i \neq x_j, \forall i\neq j$, build a polynomial such that $f(x_i) = y_i$ and degree is $n-1$

$$ f(x)=\sum_{i=0}^{n-1}y_i \prod_{j=0, j \neq i}^{n-1} \frac{x - x_j}{x_i - x_j} $$