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use super::{scalar::maybe_equal, AllocatedScalar};
use alloc::vec::Vec;
use dusk_bytes::Serializable;
use dusk_plonk::prelude::*;
fn range_proof(composer: &mut StandardComposer, value: AllocatedScalar, num_bits: u64) -> Variable {
let (is_equal, _value_bits) = scalar_decomposition_gadget(composer, num_bits as usize, value);
is_equal
}
pub fn range_check(
composer: &mut StandardComposer,
min_range: BlsScalar,
max_range: BlsScalar,
witness: AllocatedScalar,
) -> Variable {
let (y1, num_bits_pow_2) = max_bound(composer, max_range, witness);
let y2 = min_bound(composer, min_range, witness, num_bits_pow_2);
composer.mul(BlsScalar::one(), y1, y2, BlsScalar::zero(), None)
}
fn min_bound(
composer: &mut StandardComposer,
min_range: BlsScalar,
witness: AllocatedScalar,
num_bits: u64,
) -> Variable {
let x_min_a_var = {
let q_l_a = (BlsScalar::one(), witness.var);
let q_r_b = (BlsScalar::zero(), witness.var);
let q_c = -min_range;
composer.add(q_l_a, q_r_b, q_c, None)
};
let x_min_a_scalar = witness.scalar - min_range;
let x_min_a = AllocatedScalar {
var: x_min_a_var,
scalar: x_min_a_scalar,
};
range_proof(composer, x_min_a, num_bits)
}
pub fn max_bound(
composer: &mut StandardComposer,
max_range: BlsScalar,
witness: AllocatedScalar,
) -> (Variable, u64) {
let max_range = max_range - BlsScalar::one();
let num_bits_pow_2 = num_bits_closest_power_of_two(max_range);
let b_minus_x_var = {
let q_l_a = (-BlsScalar::one(), witness.var);
let q_r_b = (BlsScalar::zero(), witness.var);
let q_c = max_range;
composer.add(q_l_a, q_r_b, q_c, None)
};
let b_minus_x_scalar = max_range - witness.scalar;
let b_prime_plus_x = AllocatedScalar {
var: b_minus_x_var,
scalar: b_minus_x_scalar,
};
(
range_proof(composer, b_prime_plus_x, num_bits_pow_2),
num_bits_pow_2,
)
}
fn scalar_decomposition_gadget(
composer: &mut StandardComposer,
num_bits: usize,
witness: AllocatedScalar,
) -> (Variable, Vec<Variable>) {
let scalar_bits = scalar_to_bits(&witness.scalar);
let scalar_bits_var: Vec<Variable> = scalar_bits
.iter()
.map(|bit| composer.add_input(BlsScalar::from(*bit as u64)))
.collect();
let scalar_bits_var = scalar_bits_var[..num_bits].to_vec();
let mut accumulator = AllocatedScalar {
var: composer.add_witness_to_circuit_description(BlsScalar::zero()),
scalar: BlsScalar::zero(),
};
for (power, bit) in scalar_bits_var.iter().enumerate() {
composer.boolean_gate(*bit);
let two_pow = BlsScalar::from(2).pow(&[power as u64, 0, 0, 0]);
let q_l_a = (two_pow, *bit);
let q_r_b = (BlsScalar::one(), accumulator.var);
let q_c = BlsScalar::zero();
accumulator.var = composer.add(q_l_a, q_r_b, q_c, None);
accumulator.scalar += two_pow * BlsScalar::from(scalar_bits[power] as u64);
}
let is_equal = maybe_equal(composer, accumulator, witness);
(is_equal, scalar_bits_var)
}
fn scalar_to_bits(scalar: &BlsScalar) -> [u8; 256] {
let mut res = [0u8; 256];
let bytes = scalar.to_bytes();
for (byte, bits) in bytes.iter().zip(res.chunks_mut(8)) {
bits.iter_mut()
.enumerate()
.for_each(|(i, bit)| *bit = (byte >> i) & 1)
}
res
}
fn bits_count(mut scalar: BlsScalar) -> u64 {
scalar = scalar.reduce();
let mut counter = 1u64;
while scalar > BlsScalar::one().reduce() {
scalar.divn(1);
counter += 1;
}
counter
}
fn num_bits_closest_power_of_two(scalar: BlsScalar) -> u64 {
let num_bits = bits_count(scalar);
let closest_pow_of_two = BlsScalar::pow_of_2(num_bits);
bits_count(closest_pow_of_two)
}
#[cfg(test)]
mod tests {
use super::*;
use alloc::vec;
#[test]
fn counting_scalar_bits() {
assert_eq!(bits_count(BlsScalar::zero()), 1);
assert_eq!(bits_count(BlsScalar::one()), 1);
assert_eq!(bits_count(BlsScalar::from(3u64)), 2);
let two_pow_128 = BlsScalar::from(2u64).pow(&[128u64, 0, 0, 0]);
assert_eq!(bits_count(two_pow_128), 129);
}
#[test]
fn scalar_decomposition_test() -> Result<(), Error> {
let pub_params = PublicParameters::setup(1 << 11, &mut rand::thread_rng())?;
let (ck, vk) = pub_params.trim(1 << 10)?;
let mut prover = Prover::new(b"testing");
let witness = AllocatedScalar::allocate(prover.mut_cs(), -BlsScalar::from(100));
let (is_eq, _) = scalar_decomposition_gadget(prover.mut_cs(), 8, witness);
prover
.mut_cs()
.constrain_to_constant(is_eq, BlsScalar::zero(), None);
let proof = prover.prove(&ck)?;
let mut verifier = Verifier::new(b"testing");
let witness = AllocatedScalar::allocate(verifier.mut_cs(), BlsScalar::from(1));
let (is_eq, _) = scalar_decomposition_gadget(verifier.mut_cs(), 8, witness);
verifier
.mut_cs()
.constrain_to_constant(is_eq, BlsScalar::zero(), None);
verifier.preprocess(&ck)?;
verifier.verify(&proof, &vk, &vec![BlsScalar::zero()])
}
}