• cqplus
  • Run and build documentation
  • Run an example
  • Contents
  • Some modifications to the paper
  • TODOs

cqplus

Run and build documentation

• To build the library, run make or run cargo build
• To build the documentation (with latex supported), run make d or run RUSTDOCFLAGS="--html-in-header katex-header.html" cargo doc --no-deps --open

Run an example

• To run an example, first clone this repository and clone a testcq repository (in a same folder), then go to testcq directory and run cargo run

git clone https://github.com/HuyHung0/cqplus.git
git clone https://github.com/HuyHung0/testcq.git
cd testcq
cargo run

We can put two repository in different place, but make sure to add the path of the library cqplus in the Cargo.toml file of testcq

Contents

• The notation of functions and variables in this project are based on the notation of the figure 1, page 19 of the paper in https://eprint.iacr.org/2023/1518.
  • The formulas of each calculated polynomial are written in comments before the function
• Some functions was implemented in this repository https://github.com/geometryresearch/cq
  • create srs (which is in utils.rs of the cq repository)
  • create table (which is in table.rs of the cq repository)
  • create commitments of polynomial (which is in kzg.rs of the cq repository)
  • For the rest, I implemented from beginning
• The structures of the codes as follows:
  • First is srs.rs and table.rs to create Srs and table structure
  • polynomials.rs contains some basic polynomials for computation such as Lagrange basic, vanishing polynomial on a set,...
  • kzg.rs contains function to compute the commitment to a polynomial
  • After that
    • derive.rs: implement the derive function
    • prover.rs: implement the prove function
    • verifier.rs: implement the verify function
    • data_structures.rs contains the structures of the return of function derive() and prove()

Some modifications to the paper

• In derive() function,
  • there is a typo in the formula of $T(X)$.
  • when compute the commitment of $\nu_K(s)U(s)$ in $G_2$, we need a condition about the degree of this polynomial and the length of srs in $G_2$. More specific, we need $(N-1)+(N_1-N+2) < N_2$ ,i.e., we need $N_1+2 \geq N_2$
• In prove() function,
  • Need to modify the input
    • when compute $[B(s)]_1$, we need to evaluation $\rho_B(X)$ at $s$. Hence, the secret s should be in the input
    • the input notation $e{N,n}$ should be the same as the output $e_{t,n}$ of derive() function
• In verify() function:
  • It written that computing $[D(s)]_1$, however, we don't know the components. I guess that this should be computed in prove() function and the result should added to the return of prove()
  • We need $[U(X)]_2$. Hence, I guess that It should also include in the return of derive().
  • The same for $c_t$. We need $[c_t]_2$ but in derive(), we only have $[c_t]_1$
  • The same for $[B_\gamma]_1$, $[X-\gamma]_2$
  • We also need some randoms value generated by prove() such as $\beta,\gamma,\eta$. Hence, it should include in the return of the prove()
  • In the end of condition i, it wrote $[x]_2$. I guess it should be $[1]_2$.

TODOs

• Remove some debug commands in the library
• Update the crate version in Cargo.toml (in the new version, the some function names are changed, some functions are removed)
• Implement the hash function which depends on all public inputs.
• If the project is corrected, public to crates.io