mirror of https://github.com/zcash/halo2.git
661 lines
25 KiB
Rust
661 lines
25 KiB
Rust
use std::convert::TryInto;
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use super::super::{EccPoint, EccScalarFixedShort, FixedPoints, L_SCALAR_SHORT, NUM_WINDOWS_SHORT};
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use crate::{ecc::chip::MagnitudeSign, utilities::bool_check};
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use halo2_proofs::{
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circuit::{Layouter, Region},
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plonk::{ConstraintSystem, Constraints, 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, Debug, Eq, PartialEq)]
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pub struct Config<Fixed: FixedPoints<pallas::Affine>> {
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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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super_config: super::Config<Fixed>,
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}
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impl<Fixed: FixedPoints<pallas::Affine>> Config<Fixed> {
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pub(crate) fn configure(
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meta: &mut ConstraintSystem<pallas::Base>,
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super_config: super::Config<Fixed>,
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) -> Self {
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let config = Self {
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q_mul_fixed_short: meta.selector(),
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super_config,
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};
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config.create_gate(meta);
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config
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}
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fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
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// Gate contains the following constraints:
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// - https://p.z.cash/halo2-0.1:ecc-fixed-mul-short-msb
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// - https://p.z.cash/halo2-0.1:ecc-fixed-mul-short-conditional-neg
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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.add_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 = k_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 = bool_check(last_window);
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// Check that sign is either 1 or -1.
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let sign_check = sign.clone().square() - 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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//
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// This constraint is redundant / unnecessary, because `sign` is constrained
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// to -1 or 1 by `sign_check`, and `negation_check` therefore permits a strict
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// subset of the cases that this constraint permits.
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let y_check = (y_p.clone() - y_a.clone()) * (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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Constraints::with_selector(
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q_mul_fixed_short,
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[
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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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)
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});
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}
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/// Constraints `magnitude` to be at most 66 bits.
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///
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/// The final window is separately constrained to be a single bit, which completes the
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/// 64-bit range constraint.
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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: MagnitudeSign,
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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 running_sum = self.super_config.running_sum_config.copy_decompose(
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region,
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offset,
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magnitude.clone(),
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true,
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L_SCALAR_SHORT,
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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: Some((*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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scalar: &EccScalarFixedShort,
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base: &<Fixed as FixedPoints<pallas::Affine>>::ShortScalar,
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) -> Result<(EccPoint, EccScalarFixedShort), Error>
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where
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<Fixed as FixedPoints<pallas::Affine>>::ShortScalar:
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super::super::FixedPoint<pallas::Affine>,
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{
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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 = match scalar.running_sum {
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None => self.decompose(
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&mut region,
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offset,
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(scalar.magnitude.clone(), scalar.sign.clone()),
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),
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Some(_) => todo!("unimplemented for halo2_gadgets v0.1.0"),
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}?;
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let (acc, mul_b) = self
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.super_config
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.assign_region_inner::<_, NUM_WINDOWS_SHORT>(
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&mut region,
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offset,
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&(&scalar).into(),
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base,
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self.super_config.running_sum_config.q_range_check(),
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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.clone().into(),
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&acc.clone().into(),
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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 = scalar.sign.copy_advice(
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|| "sign",
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&mut region,
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self.super_config.window,
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offset,
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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.as_ref().unwrap()[21].clone();
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z_21.copy_advice(|| "last_window", &mut region, self.super_config.u, offset)?;
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// Conditionally negate `y`-coordinate
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let y_val = sign.value().and_then(|sign| {
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if sign == &-pallas::Base::one() {
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-magnitude_mul.y.value()
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} else {
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magnitude_mul.y.value().cloned()
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}
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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.add_config.y_p,
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offset,
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|| y_val,
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)?;
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Ok(EccPoint::from_coordinates_unchecked(magnitude_mul.x, y_var))
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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 super::super::FixedPoint;
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use group::{ff::PrimeField, Curve};
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scalar
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.magnitude
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.value()
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.zip(scalar.sign.value())
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.zip(result.point())
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.assert_if_known(|((magnitude, sign), result)| {
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let magnitude_is_valid =
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magnitude <= &&pallas::Base::from(0xFFFF_FFFF_FFFF_FFFFu64);
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let sign_is_valid = sign.square() == pallas::Base::one();
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// Only check the result if the magnitude and sign are valid.
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!(magnitude_is_valid && sign_is_valid) || {
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let scalar = {
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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 = pallas::Scalar::from_repr(magnitude.to_repr()).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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let real_mul = base.generator() * scalar;
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&real_mul.to_affine() == result
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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::{ff::PrimeField, Curve};
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use halo2_proofs::{
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arithmetic::CurveAffine,
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circuit::{AssignedCell, Chip, Layouter, Value},
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plonk::{Any, Error},
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};
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use pasta_curves::pallas;
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use crate::{
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ecc::{
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chip::{EccChip, FixedPoint, MagnitudeSign},
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tests::{Short, TestFixedBases},
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FixedPointShort, NonIdentityPoint, Point, ScalarFixedShort,
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},
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utilities::{lookup_range_check::LookupRangeCheckConfig, UtilitiesInstructions},
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};
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#[allow(clippy::op_ref)]
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pub(crate) fn test_mul_fixed_short(
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chip: EccChip<TestFixedBases>,
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mut layouter: impl Layouter<pallas::Base>,
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) -> Result<(), Error> {
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// test_short
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let base_val = Short.generator();
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let test_short = FixedPointShort::from_inner(chip.clone(), Short);
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fn load_magnitude_sign(
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chip: EccChip<TestFixedBases>,
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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<MagnitudeSign, Error> {
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let column = chip.config().advices[0];
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let magnitude = chip.load_private(
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layouter.namespace(|| "magnitude"),
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column,
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Value::known(magnitude),
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)?;
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let sign =
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chip.load_private(layouter.namespace(|| "sign"), column, Value::known(sign))?;
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Ok((magnitude, sign))
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}
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fn constrain_equal_non_id(
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chip: EccChip<TestFixedBases>,
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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<TestFixedBases>>,
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) -> Result<(), Error> {
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let expected = NonIdentityPoint::new(
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chip,
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layouter.namespace(|| "expected point"),
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Value::known((base_val * scalar_val).to_affine()),
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)?;
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result.constrain_equal(layouter.namespace(|| "constrain result"), &expected)
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}
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let magnitude_signs = [
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("random [a]B", pallas::Base::from(rand::random::<u64>()), {
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let mut random_sign = pallas::Base::one();
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if rand::random::<bool>() {
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random_sign = -random_sign;
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}
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random_sign
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}),
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(
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"[2^64 - 1]B",
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pallas::Base::from(0xFFFF_FFFF_FFFF_FFFFu64),
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pallas::Base::one(),
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),
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(
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"-[2^64 - 1]B",
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pallas::Base::from(0xFFFF_FFFF_FFFF_FFFFu64),
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-pallas::Base::one(),
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),
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// There is a single canonical sequence of window values for which a doubling occurs on the last step:
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// 1333333333333333333334 in octal.
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// [0xB6DB_6DB6_DB6D_B6DC] B
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(
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"mul_with_double",
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pallas::Base::from(0xB6DB_6DB6_DB6D_B6DCu64),
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pallas::Base::one(),
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),
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(
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"mul_with_double negative",
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pallas::Base::from(0xB6DB_6DB6_DB6D_B6DCu64),
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-pallas::Base::one(),
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),
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];
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for (name, magnitude, sign) in magnitude_signs.iter() {
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let (result, _) = {
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let magnitude_sign = load_magnitude_sign(
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chip.clone(),
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layouter.namespace(|| *name),
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*magnitude,
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*sign,
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)?;
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let by = ScalarFixedShort::new(
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chip.clone(),
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layouter.namespace(|| "signed short scalar"),
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magnitude_sign,
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)?;
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test_short.mul(layouter.namespace(|| *name), by)?
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};
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// Move from base field into scalar field
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let scalar = {
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let magnitude = pallas::Scalar::from_repr(magnitude.to_repr()).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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constrain_equal_non_id(
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chip.clone(),
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layouter.namespace(|| *name),
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base_val,
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scalar,
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result,
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)?;
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}
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let zero_magnitude_signs = [
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("mul by +zero", pallas::Base::zero(), pallas::Base::one()),
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("mul by -zero", pallas::Base::zero(), -pallas::Base::one()),
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];
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for (name, magnitude, sign) in zero_magnitude_signs.iter() {
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let (result, _) = {
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let magnitude_sign = load_magnitude_sign(
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chip.clone(),
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layouter.namespace(|| *name),
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*magnitude,
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*sign,
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)?;
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let by = ScalarFixedShort::new(
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chip.clone(),
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layouter.namespace(|| "signed short scalar"),
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magnitude_sign,
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)?;
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test_short.mul(layouter.namespace(|| *name), by)?
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};
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result
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.inner()
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.is_identity()
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.assert_if_known(|is_identity| *is_identity);
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}
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Ok(())
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}
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#[test]
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fn invalid_magnitude_sign() {
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use crate::{
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ecc::chip::{EccConfig, FixedPoint},
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utilities::UtilitiesInstructions,
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};
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use halo2_proofs::{
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circuit::{Layouter, SimpleFloorPlanner},
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dev::{FailureLocation, MockProver, VerifyFailure},
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plonk::{Circuit, ConstraintSystem, Error},
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};
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#[derive(Default)]
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struct MyCircuit {
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magnitude: Value<pallas::Base>,
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sign: Value<pallas::Base>,
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// For test checking
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magnitude_error: Value<pallas::Base>,
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}
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impl UtilitiesInstructions<pallas::Base> for MyCircuit {
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type Var = AssignedCell<pallas::Base, pallas::Base>;
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}
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impl Circuit<pallas::Base> for MyCircuit {
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type Config = EccConfig<TestFixedBases>;
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type FloorPlanner = SimpleFloorPlanner;
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fn without_witnesses(&self) -> Self {
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Self::default()
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}
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fn configure(meta: &mut ConstraintSystem<pallas::Base>) -> Self::Config {
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let advices = [
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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meta.advice_column(),
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];
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let lookup_table = meta.lookup_table_column();
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let lagrange_coeffs = [
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meta.fixed_column(),
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meta.fixed_column(),
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meta.fixed_column(),
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meta.fixed_column(),
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meta.fixed_column(),
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meta.fixed_column(),
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meta.fixed_column(),
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meta.fixed_column(),
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];
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// Shared fixed column for loading constants
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let constants = meta.fixed_column();
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meta.enable_constant(constants);
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let range_check = LookupRangeCheckConfig::configure(meta, advices[9], lookup_table);
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EccChip::<TestFixedBases>::configure(meta, advices, lagrange_coeffs, range_check)
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}
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fn synthesize(
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&self,
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config: Self::Config,
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mut layouter: impl Layouter<pallas::Base>,
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) -> Result<(), Error> {
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let column = config.advices[0];
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let short_config = config.mul_fixed_short.clone();
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let magnitude_sign = {
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let magnitude = self.load_private(
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layouter.namespace(|| "load magnitude"),
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column,
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self.magnitude,
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)?;
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let sign =
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self.load_private(layouter.namespace(|| "load sign"), column, self.sign)?;
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ScalarFixedShort::new(
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EccChip::construct(config),
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layouter.namespace(|| "signed short scalar"),
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(magnitude, sign),
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)?
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};
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short_config.assign(layouter, &magnitude_sign.inner, &Short)?;
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Ok(())
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}
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}
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// Copied from halo2_proofs::dev::util
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fn format_value(v: pallas::Base) -> String {
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use ff::Field;
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if v.is_zero_vartime() {
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"0".into()
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} else if v == pallas::Base::one() {
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"1".into()
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} else if v == -pallas::Base::one() {
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"-1".into()
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} else {
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// Format value as hex.
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let s = format!("{:?}", v);
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// Remove leading zeroes.
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let s = s.strip_prefix("0x").unwrap();
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let s = s.trim_start_matches('0');
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format!("0x{}", s)
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}
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}
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// Magnitude larger than 64 bits should fail
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{
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let circuits = [
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// 2^64
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MyCircuit {
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magnitude: Value::known(pallas::Base::from_u128(1 << 64)),
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sign: Value::known(pallas::Base::one()),
|
|
magnitude_error: Value::known(pallas::Base::from(1 << 1)),
|
|
},
|
|
// -2^64
|
|
MyCircuit {
|
|
magnitude: Value::known(pallas::Base::from_u128(1 << 64)),
|
|
sign: Value::known(-pallas::Base::one()),
|
|
magnitude_error: Value::known(pallas::Base::from(1 << 1)),
|
|
},
|
|
// 2^66
|
|
MyCircuit {
|
|
magnitude: Value::known(pallas::Base::from_u128(1 << 66)),
|
|
sign: Value::known(pallas::Base::one()),
|
|
magnitude_error: Value::known(pallas::Base::from(1 << 3)),
|
|
},
|
|
// -2^66
|
|
MyCircuit {
|
|
magnitude: Value::known(pallas::Base::from_u128(1 << 66)),
|
|
sign: Value::known(-pallas::Base::one()),
|
|
magnitude_error: Value::known(pallas::Base::from(1 << 3)),
|
|
},
|
|
// 2^254
|
|
MyCircuit {
|
|
magnitude: Value::known(pallas::Base::from_u128(1 << 127).square()),
|
|
sign: Value::known(pallas::Base::one()),
|
|
magnitude_error: Value::known(
|
|
pallas::Base::from_u128(1 << 95).square() * pallas::Base::from(2),
|
|
),
|
|
},
|
|
// -2^254
|
|
MyCircuit {
|
|
magnitude: Value::known(pallas::Base::from_u128(1 << 127).square()),
|
|
sign: Value::known(-pallas::Base::one()),
|
|
magnitude_error: Value::known(
|
|
pallas::Base::from_u128(1 << 95).square() * pallas::Base::from(2),
|
|
),
|
|
},
|
|
];
|
|
|
|
for circuit in circuits.iter() {
|
|
let prover = MockProver::<pallas::Base>::run(11, circuit, vec![]).unwrap();
|
|
circuit.magnitude_error.assert_if_known(|magnitude_error| {
|
|
assert_eq!(
|
|
prover.verify(),
|
|
Err(vec![
|
|
VerifyFailure::ConstraintNotSatisfied {
|
|
constraint: (
|
|
(17, "Short fixed-base mul gate").into(),
|
|
0,
|
|
"last_window_check",
|
|
)
|
|
.into(),
|
|
location: FailureLocation::InRegion {
|
|
region: (3, "Short fixed-base mul (most significant word)")
|
|
.into(),
|
|
offset: 1,
|
|
},
|
|
cell_values: vec![(
|
|
((Any::Advice, 5).into(), 0).into(),
|
|
format_value(*magnitude_error),
|
|
)],
|
|
},
|
|
VerifyFailure::Permutation {
|
|
column: (Any::Fixed, 9).into(),
|
|
location: FailureLocation::OutsideRegion { row: 0 },
|
|
},
|
|
VerifyFailure::Permutation {
|
|
column: (Any::Advice, 4).into(),
|
|
location: FailureLocation::InRegion {
|
|
region: (2, "Short fixed-base mul (incomplete addition)")
|
|
.into(),
|
|
offset: 22,
|
|
},
|
|
},
|
|
])
|
|
);
|
|
true
|
|
});
|
|
}
|
|
}
|
|
|
|
// Sign that is not +/- 1 should fail
|
|
{
|
|
let magnitude_u64 = rand::random::<u64>();
|
|
let circuit = MyCircuit {
|
|
magnitude: Value::known(pallas::Base::from(magnitude_u64)),
|
|
sign: Value::known(pallas::Base::zero()),
|
|
magnitude_error: Value::unknown(),
|
|
};
|
|
|
|
let negation_check_y = {
|
|
*(Short.generator() * pallas::Scalar::from(magnitude_u64))
|
|
.to_affine()
|
|
.coordinates()
|
|
.unwrap()
|
|
.y()
|
|
};
|
|
|
|
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
|
|
assert_eq!(
|
|
prover.verify(),
|
|
Err(vec![
|
|
VerifyFailure::ConstraintNotSatisfied {
|
|
constraint: ((17, "Short fixed-base mul gate").into(), 1, "sign_check")
|
|
.into(),
|
|
location: FailureLocation::InRegion {
|
|
region: (3, "Short fixed-base mul (most significant word)").into(),
|
|
offset: 1,
|
|
},
|
|
cell_values: vec![(((Any::Advice, 4).into(), 0).into(), "0".to_string())],
|
|
},
|
|
VerifyFailure::ConstraintNotSatisfied {
|
|
constraint: (
|
|
(17, "Short fixed-base mul gate").into(),
|
|
3,
|
|
"negation_check"
|
|
)
|
|
.into(),
|
|
location: FailureLocation::InRegion {
|
|
region: (3, "Short fixed-base mul (most significant word)").into(),
|
|
offset: 1,
|
|
},
|
|
cell_values: vec![
|
|
(
|
|
((Any::Advice, 1).into(), 0).into(),
|
|
format_value(negation_check_y),
|
|
),
|
|
(
|
|
((Any::Advice, 3).into(), 0).into(),
|
|
format_value(negation_check_y),
|
|
),
|
|
(((Any::Advice, 4).into(), 0).into(), "0".to_string()),
|
|
],
|
|
}
|
|
])
|
|
);
|
|
}
|
|
}
|
|
}
|