QAP Assignment

Calculate QAP step by step for the given equation. Fill in the values in this markdown to complete the assignment

$$ x^2-x-42 == 0 $$

Gates

[Add the gates here]

Symbols

symbols = [~one, x, ?, ?, ?, ?]

Solution Vector

$\vec{s}$ = [1, 7, ?, ?, ?]

R1CS

Gate #1

$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$

Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$

Gate #2

$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$

Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$

Gate #3

$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$

Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$

Gate #4

$$ \vec{a} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{b} = [?, ?, ?, ?, ?, ?] $$

$$ \vec{c} = [?, ?, ?, ?, ?, ?] $$

Verify $$\vec{a}.\vec{s} * \vec{b}.\vec{s} - \vec{c}.\vec{s} == 0$$

Constraint Matrices

$$ A = \begin{bmatrix} ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ \end{bmatrix} $$

$$ B = \begin{bmatrix} ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ \end{bmatrix} $$

$$ C = \begin{bmatrix} ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ ? & ? & ? & ? & ? & ? \\ \end{bmatrix} $$

QAP

$$ A(x) = \begin{bmatrix} ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ \end{bmatrix} $$

$$ B(x) = \begin{bmatrix} ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ \end{bmatrix} $$

$$ C(x) = \begin{bmatrix} ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ ?x^3 + ?x^2 + ?x + ? \\ \end{bmatrix} $$

$$A(x).\vec{s} = ?$$ $$B(x).\vec{s} = ?$$ $$C(x).\vec{s} = ?$$

$$A(x).\vec{s} * B(x).\vec{s} - C(x).\vec{s} = ?$$

Since the above polynomial is equal to $H(x).Z(x)$ it should have roots at x = 1, 2, 3, 4. Verify the same by pasting the polynomial here.

Evaluation

• Clone this repo.

  git clone CLONE_URL
  

• Create a new branch with your name. You can use the following command

  git checkout -b my-name
  

• Fill in the values in this file with your solution

• Create a pull request from your branch to the main branch of the repo

• Since this assignment is manually evaluated we will provide feedback on your solution in form of pull request comments