Zero knowledge proof

1. prover commit to \(f(x)\)

$$f(X)=f_E(X^2)+X\cdot f_O(X^2)$$

if we take an intermediate variant \(Y\) to replace the \(X^2\)

With a fixed \(Y\), then \(f(x)\) can be considered as one degree polynomial for \(X\), as

$$f(X)=f_E(Y)+X\cdot f_O(Y)$$

and for a given \(y\), it determineds a unique line (one degree polynomial)

and the …

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 …

Plonk argument of knowledge can be described in 5 steps in a high level:

1. Computation
2. Arithmetic circuit
3. Constrain System
4. Transfer the constrain system to polynomial
5. Prove gate constraints are satisfied.
6. Prove permutation constraints are satisfied.

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Question 1:

There are two list \((a_1, a_2, a_3,…a_n)\) and \((b_1,b_2,b_3,…,b_n)\)

how can we prove they contain the same element? (now we only consider to have the same elements, permutation comes in next question) This question would help …

Definition of Arithmetic Circuit

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