Paranormial Commitment Scheme

use pairing_ce::{
    bls12_381::{Fr, G1Affine},
    ff::{Field, PrimeField}, CurveAffine, GenericCurveProjective,
};
use paranormial::{Polynomial, Setup};
use primitive_types::U256;
use rand::{OsRng, Rng};
use std::{
    fs::File,
    io::Read,
};

const DEGREE: usize = 256;
const ALPHA: &str = "1337133713371337133713371337133713371337133713371337133713371337133713371337";  

const NUM_POINTS: usize = 512;
const PARANOMIAL_RATE: u32 = 3;

fn main() {
    let setup_path = std::env::args().nth(1).expect("no output file given");
    let flag_path = std::env::args().nth(2).expect("no flag file given");
    let output_path = std::env::args().nth(3).expect("no output file given");

    let f = File::open(setup_path).unwrap();
    let setup: Setup = serde_json::from_reader(f).expect("error deserializing setup");
    let mut poly = Polynomial::rand(DEGREE);

    let mut f = File::open(flag_path).unwrap();
    let mut flag = [0u8; 32];
    f.read(&mut flag).expect("error reading flag file");

    let flag = U256::from_big_endian(&flag);
    let mut offset = Fr::from_str(&flag.to_string()).unwrap();

    let alpha = Fr::from_str(ALPHA).unwrap();
    offset.sub_assign(&poly.evaluate(alpha));
    poly.add_scalar(offset);

    let com = poly.commit(&setup);
    let f = File::create(output_path).unwrap();

    let mut values = Vec::with_capacity(NUM_POINTS);
    for i in 0..NUM_POINTS {
        let z = Fr::from_str(&i.to_string()).unwrap();
        let (mut y, mut proof) = poly.prove(&setup, z);

        let mut rng = OsRng::new().unwrap();
        if rng.gen_weighted_bool(PARANOMIAL_RATE) {
            println!("paranormial activity occured");
            y = rng.gen::<Fr>();
            proof = G1Affine::one().mul(rng.gen::<Fr>()).into_affine();
        }
        values.push((y, proof));
    }

    serde_json::to_writer(f, &(com, values)).expect("serialization failed");
}

use paranormial::Setup;
use std::fs::File;

const DEGREE: usize = 256;

fn main() {
    let output_path = std::env::args().nth(1).expect("no output path given");  
    let setup = Setup::rand(DEGREE);
    let f = File::create(output_path).unwrap();
    serde_json::to_writer(f, &setup).expect("error serializing setup");
}

use pairing_ce::{
    bls12_381::{Fr, G1Affine, G2Affine},
    ff::Field,
    GenericCurveAffine, GenericCurveProjective,
};
use rand::{OsRng, Rng};
use serde::{Deserialize, Serialize};

#[derive(Clone, Debug, Serialize, Deserialize)]
pub struct Setup {
    pub g1_basis: Vec<G1Affine>,
    pub g2_base: G2Affine,
}

impl Setup {
    pub fn new(degree: usize, secret: Fr) -> Self {
        let mut cur = G1Affine::one();
        let mut g1_basis = Vec::with_capacity(degree);
        for _ in 0..=degree {
            g1_basis.push(cur);
            cur = cur.mul(secret).into_affine();
        }
        let g2_base = G2Affine::one().mul(secret).into_affine();
        Self { g1_basis, g2_base }
    }

    pub fn rand(degree: usize) -> Self {
        let mut rng = OsRng::new().unwrap();
        let secret = rng.gen::<Fr>();
        Self::new(degree, secret)
    }
}

#[derive(Clone, Debug, Serialize, Deserialize)]
pub struct Polynomial {
    coefficients: Vec<Fr>,
}

impl Polynomial {
    pub fn new(coefficients: Vec<Fr>) -> Self {
        Polynomial { coefficients }
    }

    pub fn rand(degree: usize) -> Self {
        let mut rng = OsRng::new().unwrap();
        let coefficients = std::iter::from_fn(|| Some(rng.gen::<Fr>()))
            .take(degree)
            .collect();
        Polynomial { coefficients }
    }

    pub fn evaluate(&self, x: Fr) -> Fr {
        let mut res = Fr::zero();
        let mut cur = Fr::one();
        for coeff in self.coefficients.iter() {
            let mut term = cur;
            term.mul_assign(coeff);
            res.add_assign(&term);
            cur.mul_assign(&x);
        }
        res
    }

    pub fn commit(&self, setup: &Setup) -> G1Affine {
        let mut res = <G1Affine as GenericCurveAffine>::Projective::zero();
        for (coeff, b) in self.coefficients.iter().zip(setup.g1_basis.iter()) {  
            let term = b.mul(*coeff);
            res.add_assign(&term);
        }
        res.into_affine()
    }

    pub fn add_scalar(&mut self, scalar: Fr) {
        self.coefficients[0].add_assign(&scalar)
    }

    pub fn divide(&self, divisor: &Self) -> Self {
        let mut dividend = self.coefficients.clone();
        let mut coefficients = vec![];

        let mut dividend_pos = dividend.len() - 1;
        let divisor_pos = divisor.coefficients.len() - 1;
        let mut difference = dividend_pos as isize - divisor_pos as isize;

        while difference >= 0 {
            let mut term_quotient = dividend[dividend_pos];
            term_quotient.mul_assign(
                &divisor.coefficients[divisor_pos]
                    .inverse()
                    .expect("zero encountered"),
            );
            coefficients.push(term_quotient);

            for i in (0..=divisor_pos).rev() {
                let difference = difference as usize;
                let mut y = divisor.coefficients[i];
                y.mul_assign(&term_quotient);
                let mut z = dividend[difference + i];
                z.sub_assign(&y);
                dividend[difference + i] = z;
            }

            dividend_pos -= 1;
            difference -= 1;
        }

        coefficients.reverse();
        Polynomial { coefficients }
    }

    pub fn prove(&self, setup: &Setup, z: Fr) -> (Fr, G1Affine) {
        let y = self.evaluate(z);
        let mut negz = z;
        negz.negate();
        let divisor = Self::new(vec![negz, Fr::one()]);
        let quo = self.divide(&divisor);
        let proof = quo.commit(setup);
        (y, proof)
    }
}

#!/bin/bash

cargo run --release --bin setup setup.json
cargo run --release --bin paranormial setup.json flag.txt output.json  

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 

use paranormial::Setup;
use std::fs::File;

const DEGREE: usize = 256;

fn main() {
    let output_path = std::env::args().nth(1).expect("no output path given");  
    let setup = Setup::rand(DEGREE);
    let f = File::create(output_path).unwrap();
    serde_json::to_writer(f, &setup).expect("error serializing setup");
}

impl Setup {
    pub fn new(degree: usize, secret: Fr) -> Self {
        let mut cur = G1Affine::one();
        let mut g1_basis = Vec::with_capacity(degree);
        for _ in 0..=degree {
            g1_basis.push(cur);
            cur = cur.mul(secret).into_affine();
        }
        let g2_base = G2Affine::one().mul(secret).into_affine();  
        Self { g1_basis, g2_base }
    }

    pub fn rand(degree: usize) -> Self {
        let mut rng = OsRng::new().unwrap();
        let secret = rng.gen::<Fr>();
        Self::new(degree, secret)
    }
}

fn main() {
    let setup_path = std::env::args().nth(1).expect("no output file given");
    let flag_path = std::env::args().nth(2).expect("no flag file given");
    let output_path = std::env::args().nth(3).expect("no output file given");

    let f = File::open(setup_path).unwrap();
    let setup: Setup = serde_json::from_reader(f).expect("error deserializing setup");  

    let mut poly = Polynomial::rand(DEGREE);  

    let mut f = File::open(flag_path).unwrap();
    let mut flag = [0u8; 32];
    f.read(&mut flag).expect("error reading flag file");

    let flag = U256::from_big_endian(&flag);
    let mut offset = Fr::from_str(&flag.to_string()).unwrap();  

    let alpha = Fr::from_str(ALPHA).unwrap();  
    offset.sub_assign(&poly.evaluate(alpha));
    poly.add_scalar(offset);

    let com = poly.commit(&setup);  

    let mut values = Vec::with_capacity(NUM_POINTS);
    for i in 0..NUM_POINTS {
        let z = Fr::from_str(&i.to_string()).unwrap();
        let (mut y, mut proof) = poly.prove(&setup, z);

        let mut rng = OsRng::new().unwrap();
        if rng.gen_weighted_bool(PARANOMIAL_RATE) {
            println!("paranormial activity occured");
            y = rng.gen::<Fr>();
            proof = G1Affine::one().mul(rng.gen::<Fr>()).into_affine();  
        }
        values.push((y, proof));
    }

    serde_json::to_writer(f, &(com, values)).expect("serialization failed");  

    pub fn commit(&self, setup: &Setup) -> G1Affine {
        let mut res = <G1Affine as GenericCurveAffine>::Projective::zero();
        for (coeff, b) in self.coefficients.iter().zip(setup.g1_basis.iter()) {  
            let term = b.mul(*coeff);
            res.add_assign(&term);
        }
        res.into_affine()
    }

    pub fn prove(&self, setup: &Setup, z: Fr) -> (Fr, G1Affine) {  
        let y = self.evaluate(z);
        let mut negz = z;
        negz.negate();
        let divisor = Self::new(vec![negz, Fr::one()]);
        let quo = self.divide(&divisor);
        let proof = quo.commit(setup);
        (y, proof)
    }

fn get_valid(com: G1Affine, values: Vec<(Fr, G1Affine)>, g2_base: G2Affine) -> (Vec<Fr>, Vec<Fr>) {  
    let (mut zs, mut ys) = (vec![], vec![]);

    for (i, (y, proof)) in values.iter().enumerate() {
        let z = Fr::from_str(&i.to_string()).unwrap();

        let (g1, g2) = (G1Affine::one(), G2Affine::one());

        let mut com_y_g1_proj = G1::from(com);
        let y_g1_proj = g1.mul(*y);
        com_y_g1_proj.sub_assign(&y_g1_proj);
        let com_y_g1 = com_y_g1_proj.into_affine();

        let mut s_g2_z_g2_proj = G2::from(g2_base);
        let z_g2_proj = G2::from(g2.mul(z));
        s_g2_z_g2_proj.sub_assign(&z_g2_proj);
        let s_g2_z_g2 = s_g2_z_g2_proj.into_affine();

        if Bls12::pairing(com_y_g1, g2) == Bls12::pairing(*proof, s_g2_z_g2) {
            zs.push(z);
            ys.push(*y);
        }
    }

    (zs, ys)
}

fn interpolate(xs: Vec<Fr>, ys: Vec<Fr>, alpha: Fr) -> Fr {
    let mut result = Fr::zero();

    for i in 0..xs.len() {
        let mut term = ys[i];

        for j in 0..xs.len() {
            if j != i {
                let mut div = xs[i];
                div.sub_assign(&xs[j]);
                let mut tmp = alpha;
                tmp.sub_assign(&xs[j]);
                term.mul_assign(&tmp);
                term.mul_assign(&div.inverse().expect("zero encountered"));  
            }
        }

        result.add_assign(&term);
    }

    result
}

fn main() {
    let setup_path = std::env::args().nth(1).expect("no setup file given");
    let output_path = std::env::args().nth(2).expect("no output file given");

    let setup_file = File::open(setup_path).expect("setup file not found");
    let output_file = File::open(output_path).expect("output file not found");

    let setup: Setup =
        serde_json::from_reader(BufReader::new(setup_file)).expect("failed to deserialize setup");
    let (com, values): (G1Affine, Vec<(Fr, G1Affine)>) =
        serde_json::from_reader(BufReader::new(output_file)).expect("failed to deserialize output");  

    let (zs, ys) = get_valid(com, values, setup.g2_base);

    let alpha = Fr::from_str(ALPHA).unwrap();
    let flag_fr = interpolate(zs, ys, alpha);

    let mut flag_hex: String = flag_fr.to_string().chars().skip(5).collect();
    flag_hex.truncate(flag_hex.len() - 1);

    let flag: Vec<u8> = Vec::from_hex(flag_hex).expect("Error decoding hex");

    print!("{}", String::from_utf8_lossy(&flag));
}

$ cargo run --release --bin solve setup.json output.json
    Finished release [optimized] target(s) in 0.01s
     Running `target/release/solve setup.json output.json`  
PCTF{k4t3_d3t3cts_paran0rm1als}