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use std::{array, convert::TryInto};
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use super::super::{EccConfig, EccPoint, EccScalarFixedShort};
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use crate::{
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circuit::gadget::utilities::{copy, decompose_running_sum::RunningSumConfig, CellValue, Var},
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constants::{ValueCommitV, FIXED_BASE_WINDOW_SIZE, L_VALUE, NUM_WINDOWS_SHORT},
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};
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use halo2::{
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circuit::{Layouter, Region},
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plonk::{ConstraintSystem, Error, Expression, Selector},
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poly::Rotation,
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};
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use pasta_curves::pallas;
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#[derive(Clone)]
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pub struct Config {
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// Selector used for fixed-base scalar mul with short signed exponent.
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q_mul_fixed_short: Selector,
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q_mul_fixed_running_sum: Selector,
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running_sum_config: RunningSumConfig<pallas::Base, { FIXED_BASE_WINDOW_SIZE }>,
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super_config: super::Config<NUM_WINDOWS_SHORT>,
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}
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impl From<&EccConfig> for Config {
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fn from(config: &EccConfig) -> Self {
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Self {
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q_mul_fixed_short: config.q_mul_fixed_short,
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q_mul_fixed_running_sum: config.q_mul_fixed_running_sum,
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running_sum_config: config.running_sum_config.clone(),
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super_config: config.into(),
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}
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}
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}
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impl Config {
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pub(crate) fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
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meta.create_gate("Short fixed-base mul gate", |meta| {
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let q_mul_fixed_short = meta.query_selector(self.q_mul_fixed_short);
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let y_p = meta.query_advice(self.super_config.y_p, Rotation::cur());
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let y_a = meta.query_advice(self.super_config.add_config.y_qr, Rotation::cur());
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// z_21
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let last_window = meta.query_advice(self.super_config.u, Rotation::cur());
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let sign = meta.query_advice(self.super_config.window, Rotation::cur());
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let one = Expression::Constant(pallas::Base::one());
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// Check that last window is either 0 or 1.
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let last_window_check = last_window.clone() * (one.clone() - last_window);
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// Check that sign is either 1 or -1.
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let sign_check = sign.clone() * sign.clone() - one;
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// `(x_a, y_a)` is the result of `[m]B`, where `m` is the magnitude.
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// We conditionally negate this result using `y_p = y_a * s`, where `s` is the sign.
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// Check that the final `y_p = y_a` or `y_p = -y_a`
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let y_check = q_mul_fixed_short.clone()
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* (y_p.clone() - y_a.clone())
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* (y_p.clone() + y_a.clone());
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// Check that the correct sign is witnessed s.t. sign * y_p = y_a
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let negation_check = sign * y_p - y_a;
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array::IntoIter::new([
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("last_window_check", last_window_check),
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("sign_check", sign_check),
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("y_check", y_check),
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("negation_check", negation_check),
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])
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.map(move |(name, poly)| (name, q_mul_fixed_short.clone() * poly))
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});
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}
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fn decompose(
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&self,
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region: &mut Region<'_, pallas::Base>,
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offset: usize,
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magnitude_sign: (CellValue<pallas::Base>, CellValue<pallas::Base>),
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) -> Result<EccScalarFixedShort, Error> {
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let (magnitude, sign) = magnitude_sign;
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// Decompose magnitude
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let (magnitude, running_sum) = self.running_sum_config.copy_decompose(
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region,
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offset,
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magnitude,
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true,
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L_VALUE,
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NUM_WINDOWS_SHORT,
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)?;
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Ok(EccScalarFixedShort {
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magnitude,
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sign,
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running_sum: (*running_sum).as_slice().try_into().unwrap(),
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})
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}
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pub fn assign(
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&self,
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mut layouter: impl Layouter<pallas::Base>,
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magnitude_sign: (CellValue<pallas::Base>, CellValue<pallas::Base>),
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base: &ValueCommitV,
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) -> Result<(EccPoint, EccScalarFixedShort), Error> {
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let (scalar, acc, mul_b) = layouter.assign_region(
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|| "Short fixed-base mul (incomplete addition)",
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|mut region| {
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let offset = 0;
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// Decompose the scalar
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let scalar = self.decompose(&mut region, offset, magnitude_sign)?;
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let (acc, mul_b) = self.super_config.assign_region_inner(
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&mut region,
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offset,
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&(&scalar).into(),
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base.clone().into(),
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self.q_mul_fixed_running_sum,
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)?;
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Ok((scalar, acc, mul_b))
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},
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)?;
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// Last window
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let result = layouter.assign_region(
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|| "Short fixed-base mul (most significant word)",
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|mut region| {
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let offset = 0;
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// Add to the cumulative sum to get `[magnitude]B`.
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let magnitude_mul = self.super_config.add_config.assign_region(
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&mul_b,
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&acc,
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offset,
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&mut region,
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)?;
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// Increase offset by 1 after complete addition
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let offset = offset + 1;
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// Copy sign to `window` column
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let sign = copy(
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&mut region,
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|| "sign",
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self.super_config.window,
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offset,
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&scalar.sign,
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)?;
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// Copy last window to `u` column.
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// (Although the last window is not a `u` value; we are copying it into the `u`
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// column because there is an available cell there.)
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let z_21 = scalar.running_sum[20];
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copy(
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&mut region,
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|| "last_window",
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self.super_config.u,
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offset,
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&z_21,
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)?;
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// Conditionally negate `y`-coordinate
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let y_val = if let Some(sign) = sign.value() {
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if sign == -pallas::Base::one() {
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magnitude_mul.y.value().map(|y: pallas::Base| -y)
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} else {
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magnitude_mul.y.value()
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}
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} else {
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None
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};
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// Enable mul_fixed_short selector on final row
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self.q_mul_fixed_short.enable(&mut region, offset)?;
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// Assign final `y` to `y_p` column and return final point
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let y_var = region.assign_advice(
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|| "y_var",
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self.super_config.y_p,
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offset,
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|| y_val.ok_or(Error::SynthesisError),
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)?;
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Ok(EccPoint {
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x: magnitude_mul.x,
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y: CellValue::new(y_var, y_val),
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})
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},
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)?;
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#[cfg(test)]
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// Check that the correct multiple is obtained.
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// This inlined test is only done for valid 64-bit magnitudes
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// and valid +/- 1 signs.
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// Invalid values result in constraint failures which are
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// tested at the circuit-level.
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{
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use group::Curve;
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use pasta_curves::arithmetic::FieldExt;
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if let (Some(magnitude), Some(sign)) = (scalar.magnitude.value(), scalar.sign.value()) {
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let magnitude_is_valid =
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magnitude <= pallas::Base::from_u64(0xFFFF_FFFF_FFFF_FFFFu64);
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let sign_is_valid = sign * sign == pallas::Base::one();
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if magnitude_is_valid && sign_is_valid {
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let base: super::OrchardFixedBases = base.clone().into();
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let scalar = scalar.magnitude.value().zip(scalar.sign.value()).map(
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|(magnitude, sign)| {
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// Move magnitude from base field into scalar field (which always fits
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// for Pallas).
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let magnitude =
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pallas::Scalar::from_bytes(&magnitude.to_bytes()).unwrap();
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let sign = if sign == pallas::Base::one() {
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pallas::Scalar::one()
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} else {
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-pallas::Scalar::one()
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};
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magnitude * sign
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},
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);
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let real_mul = scalar.map(|scalar| base.generator() * scalar);
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let result = result.point();
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if let (Some(real_mul), Some(result)) = (real_mul, result) {
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assert_eq!(real_mul.to_affine(), result);
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}
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}
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}
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}
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Ok((result, scalar))
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}
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}
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#[cfg(test)]
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pub mod tests {
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use group::Curve;
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use halo2::{
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circuit::{Chip, Layouter},
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2021-07-20 01:22:08 -07:00
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plonk::{Any, Error},
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};
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use pasta_curves::{arithmetic::FieldExt, pallas};
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2021-07-10 08:56:24 -07:00
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use crate::circuit::gadget::{
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ecc::{chip::EccChip, FixedPointShort, Point},
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utilities::{lookup_range_check::LookupRangeCheckConfig, CellValue, UtilitiesInstructions},
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};
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use crate::constants::load::ValueCommitV;
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#[allow(clippy::op_ref)]
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pub fn test_mul_fixed_short(
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chip: EccChip,
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mut layouter: impl Layouter<pallas::Base>,
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) -> Result<(), Error> {
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// value_commit_v
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let value_commit_v = ValueCommitV::get();
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let base_val = value_commit_v.generator;
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let value_commit_v = FixedPointShort::from_inner(chip.clone(), value_commit_v);
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fn load_magnitude_sign(
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chip: EccChip,
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mut layouter: impl Layouter<pallas::Base>,
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magnitude: pallas::Base,
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sign: pallas::Base,
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) -> Result<(CellValue<pallas::Base>, CellValue<pallas::Base>), Error> {
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let column = chip.config().advices[0];
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let magnitude =
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chip.load_private(layouter.namespace(|| "magnitude"), column, Some(magnitude))?;
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let sign = chip.load_private(layouter.namespace(|| "sign"), column, Some(sign))?;
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Ok((magnitude, sign))
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}
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2021-07-08 00:06:47 -07:00
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fn constrain_equal(
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chip: EccChip,
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mut layouter: impl Layouter<pallas::Base>,
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base_val: pallas::Affine,
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scalar_val: pallas::Scalar,
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result: Point<pallas::Affine, EccChip>,
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) -> Result<(), Error> {
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let expected = Point::new(
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chip,
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layouter.namespace(|| "expected point"),
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|
|
Some((base_val * scalar_val).to_affine()),
|
|
|
|
)?;
|
|
|
|
result.constrain_equal(layouter.namespace(|| "constrain result"), &expected)
|
|
|
|
}
|
|
|
|
|
2021-07-10 08:56:24 -07:00
|
|
|
let magnitude_signs = [
|
|
|
|
("mul by +zero", pallas::Base::zero(), pallas::Base::one()),
|
|
|
|
("mul by -zero", pallas::Base::zero(), -pallas::Base::one()),
|
|
|
|
(
|
|
|
|
"random [a]B",
|
|
|
|
pallas::Base::from_u64(rand::random::<u64>()),
|
2021-07-10 18:49:23 -07:00
|
|
|
{
|
|
|
|
let mut random_sign = pallas::Base::one();
|
|
|
|
if rand::random::<bool>() {
|
|
|
|
random_sign = -random_sign;
|
|
|
|
}
|
|
|
|
random_sign
|
|
|
|
},
|
2021-07-10 08:56:24 -07:00
|
|
|
),
|
|
|
|
(
|
|
|
|
"[2^64 - 1]B",
|
|
|
|
pallas::Base::from_u64(0xFFFF_FFFF_FFFF_FFFFu64),
|
|
|
|
pallas::Base::one(),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
"-[2^64 - 1]B",
|
|
|
|
pallas::Base::from_u64(0xFFFF_FFFF_FFFF_FFFFu64),
|
|
|
|
-pallas::Base::one(),
|
|
|
|
),
|
|
|
|
// There is a single canonical sequence of window values for which a doubling occurs on the last step:
|
|
|
|
// 1333333333333333333334 in octal.
|
|
|
|
// [0xB6DB_6DB6_DB6D_B6DC] B
|
|
|
|
(
|
|
|
|
"mul_with_double",
|
|
|
|
pallas::Base::from_u64(0xB6DB_6DB6_DB6D_B6DCu64),
|
|
|
|
pallas::Base::one(),
|
|
|
|
),
|
2021-07-14 21:30:14 -07:00
|
|
|
(
|
|
|
|
"mul_with_double negative",
|
|
|
|
pallas::Base::from_u64(0xB6DB_6DB6_DB6D_B6DCu64),
|
|
|
|
-pallas::Base::one(),
|
|
|
|
),
|
2021-07-10 08:56:24 -07:00
|
|
|
];
|
|
|
|
|
|
|
|
for (name, magnitude, sign) in magnitude_signs.iter() {
|
|
|
|
let (result, _) = {
|
|
|
|
let magnitude_sign = load_magnitude_sign(
|
|
|
|
chip.clone(),
|
|
|
|
layouter.namespace(|| *name),
|
|
|
|
*magnitude,
|
|
|
|
*sign,
|
|
|
|
)?;
|
|
|
|
value_commit_v.mul(layouter.namespace(|| *name), magnitude_sign)?
|
|
|
|
};
|
|
|
|
// Move from base field into scalar field
|
|
|
|
let scalar = {
|
|
|
|
let magnitude = pallas::Scalar::from_bytes(&magnitude.to_bytes()).unwrap();
|
|
|
|
let sign = if *sign == pallas::Base::one() {
|
|
|
|
pallas::Scalar::one()
|
|
|
|
} else {
|
|
|
|
-pallas::Scalar::one()
|
|
|
|
};
|
|
|
|
magnitude * sign
|
|
|
|
};
|
2021-07-08 00:06:47 -07:00
|
|
|
constrain_equal(
|
2021-06-04 23:34:44 -07:00
|
|
|
chip.clone(),
|
2021-07-10 08:56:24 -07:00
|
|
|
layouter.namespace(|| *name),
|
2021-07-08 00:06:47 -07:00
|
|
|
base_val,
|
2021-07-10 08:56:24 -07:00
|
|
|
scalar,
|
2021-07-08 00:06:47 -07:00
|
|
|
result,
|
2021-06-04 23:34:44 -07:00
|
|
|
)?;
|
|
|
|
}
|
|
|
|
|
|
|
|
Ok(())
|
|
|
|
}
|
2021-07-10 18:49:23 -07:00
|
|
|
|
|
|
|
#[test]
|
|
|
|
fn invalid_magnitude_sign() {
|
|
|
|
use crate::circuit::gadget::{
|
|
|
|
ecc::chip::EccConfig,
|
|
|
|
utilities::{CellValue, UtilitiesInstructions},
|
|
|
|
};
|
|
|
|
use halo2::{
|
|
|
|
circuit::{Layouter, SimpleFloorPlanner},
|
|
|
|
dev::{MockProver, VerifyFailure},
|
|
|
|
plonk::{Circuit, ConstraintSystem, Error},
|
|
|
|
};
|
|
|
|
|
|
|
|
#[derive(Default)]
|
|
|
|
struct MyCircuit {
|
|
|
|
magnitude: Option<pallas::Base>,
|
|
|
|
sign: Option<pallas::Base>,
|
|
|
|
}
|
|
|
|
|
|
|
|
impl UtilitiesInstructions<pallas::Base> for MyCircuit {
|
|
|
|
type Var = CellValue<pallas::Base>;
|
|
|
|
}
|
|
|
|
|
|
|
|
impl Circuit<pallas::Base> for MyCircuit {
|
|
|
|
type Config = EccConfig;
|
|
|
|
type FloorPlanner = SimpleFloorPlanner;
|
|
|
|
|
|
|
|
fn without_witnesses(&self) -> Self {
|
|
|
|
Self::default()
|
|
|
|
}
|
|
|
|
|
|
|
|
fn configure(meta: &mut ConstraintSystem<pallas::Base>) -> Self::Config {
|
|
|
|
let advices = [
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
meta.advice_column(),
|
|
|
|
];
|
|
|
|
let lookup_table = meta.fixed_column();
|
2021-07-21 04:13:47 -07:00
|
|
|
let lagrange_coeffs = [
|
|
|
|
meta.fixed_column(),
|
|
|
|
meta.fixed_column(),
|
|
|
|
meta.fixed_column(),
|
|
|
|
meta.fixed_column(),
|
|
|
|
meta.fixed_column(),
|
|
|
|
meta.fixed_column(),
|
|
|
|
meta.fixed_column(),
|
|
|
|
meta.fixed_column(),
|
|
|
|
];
|
2021-07-15 04:52:15 -07:00
|
|
|
|
2021-07-20 01:22:08 -07:00
|
|
|
// Shared fixed column for loading constants
|
|
|
|
let constants = meta.fixed_column();
|
|
|
|
meta.enable_constant(constants);
|
|
|
|
|
2021-07-21 07:59:08 -07:00
|
|
|
let range_check = LookupRangeCheckConfig::configure(meta, advices[9], lookup_table);
|
|
|
|
EccChip::configure(meta, advices, lagrange_coeffs, range_check)
|
2021-07-10 18:49:23 -07:00
|
|
|
}
|
|
|
|
|
|
|
|
fn synthesize(
|
|
|
|
&self,
|
|
|
|
config: Self::Config,
|
|
|
|
mut layouter: impl Layouter<pallas::Base>,
|
|
|
|
) -> Result<(), Error> {
|
|
|
|
let column = config.advices[0];
|
|
|
|
|
|
|
|
let short_config: super::Config = (&config).into();
|
|
|
|
let magnitude_sign = {
|
|
|
|
let magnitude = self.load_private(
|
|
|
|
layouter.namespace(|| "load magnitude"),
|
|
|
|
column,
|
|
|
|
self.magnitude,
|
|
|
|
)?;
|
|
|
|
let sign =
|
|
|
|
self.load_private(layouter.namespace(|| "load sign"), column, self.sign)?;
|
|
|
|
(magnitude, sign)
|
|
|
|
};
|
|
|
|
|
|
|
|
short_config.assign(layouter, magnitude_sign, &ValueCommitV::get())?;
|
|
|
|
|
|
|
|
Ok(())
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Magnitude larger than 64 bits should fail
|
|
|
|
{
|
2021-07-16 09:44:56 -07:00
|
|
|
let circuits = [
|
|
|
|
// 2^64
|
|
|
|
MyCircuit {
|
|
|
|
magnitude: Some(pallas::Base::from_u128(1 << 64)),
|
|
|
|
sign: Some(pallas::Base::one()),
|
|
|
|
},
|
|
|
|
// -2^64
|
|
|
|
MyCircuit {
|
|
|
|
magnitude: Some(pallas::Base::from_u128(1 << 64)),
|
|
|
|
sign: Some(-pallas::Base::one()),
|
|
|
|
},
|
|
|
|
// 2^66
|
|
|
|
MyCircuit {
|
|
|
|
magnitude: Some(pallas::Base::from_u128(1 << 66)),
|
|
|
|
sign: Some(pallas::Base::one()),
|
|
|
|
},
|
|
|
|
// -2^66
|
|
|
|
MyCircuit {
|
|
|
|
magnitude: Some(pallas::Base::from_u128(1 << 66)),
|
|
|
|
sign: Some(-pallas::Base::one()),
|
|
|
|
},
|
|
|
|
// 2^254
|
|
|
|
MyCircuit {
|
|
|
|
magnitude: Some(pallas::Base::from_u128(1 << 127).square()),
|
|
|
|
sign: Some(pallas::Base::one()),
|
|
|
|
},
|
|
|
|
// -2^254
|
|
|
|
MyCircuit {
|
|
|
|
magnitude: Some(pallas::Base::from_u128(1 << 127).square()),
|
|
|
|
sign: Some(-pallas::Base::one()),
|
|
|
|
},
|
|
|
|
];
|
|
|
|
|
|
|
|
for circuit in circuits.iter() {
|
|
|
|
let prover = MockProver::<pallas::Base>::run(11, circuit, vec![]).unwrap();
|
|
|
|
assert_eq!(
|
|
|
|
prover.verify(),
|
|
|
|
Err(vec![
|
2021-07-19 04:57:50 -07:00
|
|
|
VerifyFailure::ConstraintNotSatisfied {
|
2021-07-16 09:44:56 -07:00
|
|
|
constraint: (
|
2021-07-23 06:10:08 -07:00
|
|
|
(16, "Short fixed-base mul gate").into(),
|
2021-07-16 09:44:56 -07:00
|
|
|
0,
|
|
|
|
"last_window_check"
|
|
|
|
)
|
|
|
|
.into(),
|
|
|
|
row: 26
|
2021-07-20 01:22:08 -07:00
|
|
|
},
|
|
|
|
VerifyFailure::Permutation {
|
2021-07-22 07:14:34 -07:00
|
|
|
column: (Any::Fixed, 9).into(),
|
2021-07-23 09:02:48 -07:00
|
|
|
row: 0
|
2021-07-20 01:22:08 -07:00
|
|
|
},
|
|
|
|
VerifyFailure::Permutation {
|
|
|
|
column: (Any::Advice, 4).into(),
|
|
|
|
row: 24
|
2021-07-16 09:44:56 -07:00
|
|
|
}
|
|
|
|
])
|
|
|
|
);
|
|
|
|
}
|
2021-07-10 18:49:23 -07:00
|
|
|
}
|
|
|
|
|
|
|
|
// Sign that is not +/- 1 should fail
|
|
|
|
{
|
|
|
|
let circuit = MyCircuit {
|
|
|
|
magnitude: Some(pallas::Base::from_u64(rand::random::<u64>())),
|
|
|
|
sign: Some(pallas::Base::zero()),
|
|
|
|
};
|
|
|
|
|
|
|
|
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
|
|
|
|
assert_eq!(
|
|
|
|
prover.verify(),
|
|
|
|
Err(vec![
|
2021-07-19 04:57:50 -07:00
|
|
|
VerifyFailure::ConstraintNotSatisfied {
|
2021-07-23 06:10:08 -07:00
|
|
|
constraint: ((16, "Short fixed-base mul gate").into(), 1, "sign_check")
|
2021-07-10 18:49:23 -07:00
|
|
|
.into(),
|
|
|
|
row: 26
|
|
|
|
},
|
2021-07-19 04:57:50 -07:00
|
|
|
VerifyFailure::ConstraintNotSatisfied {
|
2021-07-10 18:49:23 -07:00
|
|
|
constraint: (
|
2021-07-23 06:10:08 -07:00
|
|
|
(16, "Short fixed-base mul gate").into(),
|
2021-07-10 18:49:23 -07:00
|
|
|
3,
|
|
|
|
"negation_check"
|
|
|
|
)
|
|
|
|
.into(),
|
|
|
|
row: 26
|
|
|
|
}
|
|
|
|
])
|
|
|
|
);
|
|
|
|
}
|
|
|
|
}
|
2021-06-04 23:34:44 -07:00
|
|
|
}
|