mirror of https://github.com/zcash/orchard.git
600 lines
23 KiB
Rust
600 lines
23 KiB
Rust
use super::super::{EccBaseFieldElemFixed, EccConfig, EccPoint, OrchardFixedBasesFull};
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use super::H_BASE;
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use crate::{
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circuit::gadget::utilities::{
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bitrange_subset, copy, decompose_running_sum::RunningSumConfig,
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lookup_range_check::LookupRangeCheckConfig, range_check, CellValue, Var,
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},
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constants::{self, T_P},
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primitives::sinsemilla,
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};
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use halo2::{
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circuit::Layouter,
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plonk::{Advice, Column, ConstraintSystem, Error, Expression, Selector},
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poly::Rotation,
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};
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use pasta_curves::{arithmetic::FieldExt, pallas};
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use std::convert::TryInto;
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pub struct Config {
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q_mul_fixed_running_sum: Selector,
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base_field_fixed_canon: Selector,
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canon_advices: [Column<Advice>; 3],
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lookup_config: LookupRangeCheckConfig<pallas::Base, { sinsemilla::K }>,
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running_sum_config: RunningSumConfig<
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pallas::Base,
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{ constants::L_ORCHARD_BASE },
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{ constants::FIXED_BASE_WINDOW_SIZE },
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{ constants::NUM_WINDOWS },
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>,
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super_config: super::Config<{ constants::NUM_WINDOWS }>,
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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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let config = Self {
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q_mul_fixed_running_sum: config.q_mul_fixed_running_sum,
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base_field_fixed_canon: config.base_field_fixed_canon,
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canon_advices: [config.advices[6], config.advices[7], config.advices[8]],
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lookup_config: config.lookup_config.clone(),
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running_sum_config: config.running_sum_full_config.clone(),
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super_config: config.into(),
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};
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let add_incomplete_advices = config.super_config.add_incomplete_config.advice_columns();
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for canon_advice in config.canon_advices.iter() {
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assert!(
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!add_incomplete_advices.contains(canon_advice),
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"Deconflict canon_advice columns with incomplete addition columns."
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);
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}
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assert_eq!(config.running_sum_config.z, config.super_config.window);
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config
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}
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}
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impl Config {
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pub fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
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// Check that each window uses the correct y_p and interpolated x_p.
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meta.create_gate("Coordinates check", |meta| {
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let q_mul_fixed_running_sum = meta.query_selector(self.q_mul_fixed_running_sum);
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let z_cur = meta.query_advice(self.super_config.window, Rotation::cur());
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let z_next = meta.query_advice(self.super_config.window, Rotation::next());
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// z_{i+1} = (z_i - a_i) / 2^3
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// => a_i = z_i - z_{i+1} * 2^3
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let word = z_cur - z_next * pallas::Base::from_u64(constants::H as u64);
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self.super_config
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.coords_check(meta, q_mul_fixed_running_sum, word)
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});
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// Check that we get z_85 = 0 as the final output of the three-bit decomposition running sum.
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// Also check that the base field element is canonical.
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meta.create_gate("Canonicity checks", |meta| {
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let base_field_fixed_canon = meta.query_selector(self.base_field_fixed_canon);
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let alpha = meta.query_advice(self.canon_advices[0], Rotation::prev());
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// z_85_alpha is constrained to be zero in this gate.
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let z_85_alpha = meta.query_advice(self.canon_advices[1], Rotation::prev());
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// The last three bits of α.
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let z_84_alpha = meta.query_advice(self.canon_advices[2], Rotation::prev());
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// Decompose α into three pieces, in little-endian order:
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// α = α_0 (252 bits) || α_1 (2 bits) || α_2 (1 bit).
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//
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// α_0 is derived, not witnessed.
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let alpha_0 = {
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let two_pow_252 = pallas::Base::from_u128(1 << 126).square();
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alpha - (z_84_alpha.clone() * two_pow_252)
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};
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let alpha_1 = meta.query_advice(self.canon_advices[1], Rotation::cur());
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let alpha_2 = meta.query_advice(self.canon_advices[2], Rotation::cur());
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let alpha_0_prime = meta.query_advice(self.canon_advices[0], Rotation::cur());
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let z_13_alpha_0_prime = meta.query_advice(self.canon_advices[0], Rotation::next());
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let z_44_alpha = meta.query_advice(self.canon_advices[1], Rotation::next());
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let z_43_alpha = meta.query_advice(self.canon_advices[2], Rotation::next());
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let decomposition_checks = {
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// Range-constrain α_1 to be 2 bits
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let alpha_1_range_check = range_check(alpha_1.clone(), 1 << 2);
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// Boolean-constrain α_2
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let alpha_2_range_check = range_check(alpha_2.clone(), 1 << 1);
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// Check that α_1 + 2^2 α_2 = z_84_alpha
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let z_84_alpha_check = z_84_alpha.clone()
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- (alpha_1.clone() + alpha_2.clone() * pallas::Base::from_u64(1 << 2));
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std::iter::empty()
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.chain(Some(("alpha_1_range_check", alpha_1_range_check)))
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.chain(Some(("alpha_2_range_check", alpha_2_range_check)))
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.chain(Some(("z_84_alpha_check", z_84_alpha_check)))
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};
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// Check α_0_prime = α_0 + 2^130 - t_p
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let alpha_0_prime_check = {
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let two_pow_130 = Expression::Constant(pallas::Base::from_u128(1 << 65).square());
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let t_p = Expression::Constant(pallas::Base::from_u128(T_P));
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alpha_0_prime - (alpha_0 + two_pow_130 - t_p)
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};
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// We want to enforce canonicity of a 255-bit base field element, α.
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// That is, we want to check that 0 ≤ α < p, where p is Pallas base
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// field modulus p = 2^254 + t_p
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// = 2^254 + 45560315531419706090280762371685220353.
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// Note that t_p < 2^130.
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//
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// α has been decomposed into three pieces in little-endian order:
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// α = α_0 (252 bits) || α_1 (2 bits) || α_2 (1 bit).
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// = α_0 + 2^252 α_1 + 2^254 α_2.
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//
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// If the MSB α_2 = 1, then:
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// - α_2 = 1 => α_1 = 0, and
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// - α_2 = 1 => α_0 < t_p. To enforce this:
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// - α_2 = 1 => 0 ≤ α_0 < 2^130
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// - alpha_0_hi_120 = 0 (constrain α_0 to be 132 bits)
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// - a_43 = 0 or 1 (constrain α_0[130..=131] to be 0)
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// - α_2 = 1 => 0 ≤ α_0 + 2^130 - t_p < 2^130
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// => 13 ten-bit lookups of α_0 + 2^130 - t_p
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// => z_13_alpha_0_prime = 0
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//
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let canon_checks = {
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// alpha_0_hi_120 = z_44 - 2^120 z_84
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let alpha_0_hi_120 = {
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let two_pow_120 =
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Expression::Constant(pallas::Base::from_u128(1 << 60).square());
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z_44_alpha.clone() - z_84_alpha * two_pow_120
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};
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// a_43 = z_43 - (2^3)z_44
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let a_43 = z_43_alpha - z_44_alpha * *H_BASE;
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std::iter::empty()
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.chain(Some(("MSB = 1 => alpha_1 = 0", alpha_2.clone() * alpha_1)))
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.chain(Some((
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"MSB = 1 => alpha_0_hi_120 = 0",
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alpha_2.clone() * alpha_0_hi_120,
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)))
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.chain(Some((
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"MSB = 1 => a_43 = 0 or 1",
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alpha_2.clone() * range_check(a_43, 2),
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)))
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.chain(Some((
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"MSB = 1 => z_13_alpha_0_prime = 0",
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alpha_2 * z_13_alpha_0_prime,
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)))
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};
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canon_checks
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.chain(decomposition_checks)
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.chain(Some(("z_85_alpha = 0", z_85_alpha)))
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.chain(Some(("alpha_0_prime check", alpha_0_prime_check)))
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.map(move |(name, poly)| (name, base_field_fixed_canon.clone() * poly))
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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: CellValue<pallas::Base>,
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base: OrchardFixedBasesFull,
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) -> Result<EccPoint, Error> {
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let (scalar, acc, mul_b) = layouter.assign_region(
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|| "Base-field elem fixed-base mul (incomplete addition)",
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|mut region| {
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let offset = 0;
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// Decompose scalar
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let scalar =
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{
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let (base_field_elem, running_sum) = self
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.running_sum_config
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.copy_decompose(&mut region, offset, scalar, true)?;
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EccBaseFieldElemFixed {
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base_field_elem,
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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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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.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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// Add to the accumulator and return the final result as `[scalar]B`.
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let result = layouter.assign_region(
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|| "Base-field elem fixed-base mul (complete addition)",
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|mut region| {
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self.super_config
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.add_config
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.assign_region(&mul_b, &acc, 0, &mut region)
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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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{
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use group::Curve;
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let base: super::OrchardFixedBases = base.into();
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let scalar = &scalar
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.base_field_elem()
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.value()
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.map(|scalar| pallas::Scalar::from_bytes(&scalar.to_bytes()).unwrap());
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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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// We want to enforce canonicity of a 255-bit base field element, α.
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// That is, we want to check that 0 ≤ α < p, where p is Pallas base
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// field modulus p = 2^254 + t_p
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// = 2^254 + 45560315531419706090280762371685220353.
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// Note that t_p < 2^130.
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//
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// α has been decomposed into three pieces in little-endian order:
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// α = α_0 (252 bits) || α_1 (2 bits) || α_2 (1 bit).
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// = α_0 + 2^252 α_1 + 2^254 α_2.
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//
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// If the MSB α_2 = 1, then:
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// - α_2 = 1 => α_1 = 0, and
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// - α_2 = 1 => α_0 < t_p. To enforce this:
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// - α_2 = 1 => 0 ≤ α_0 < 2^130
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// => 13 ten-bit lookups of α_0
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// - α_2 = 1 => 0 ≤ α_0 + 2^130 - t_p < 2^130
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// => 13 ten-bit lookups of α_0 + 2^130 - t_p
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// => z_13_alpha_0_prime = 0
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//
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let (alpha, running_sum) = (scalar.base_field_elem, &scalar.running_sum);
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let z_43_alpha = running_sum[42];
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let z_44_alpha = running_sum[43];
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let z_84_alpha = running_sum[83];
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let z_85_alpha = running_sum[84];
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// α_0 = α - z_84_alpha * 2^252
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let alpha_0 = alpha
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.value()
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.zip(z_84_alpha.value())
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.map(|(alpha, z_84_alpha)| {
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let two_pow_252 = pallas::Base::from_u128(1 << 126).square();
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alpha - z_84_alpha * two_pow_252
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});
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let (alpha_0_prime, z_13_alpha_0_prime) = {
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// alpha_0_prime = alpha + 2^130 - t_p.
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let alpha_0_prime = alpha_0.map(|alpha_0| {
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let two_pow_130 = pallas::Base::from_u128(1 << 65).square();
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let t_p = pallas::Base::from_u128(T_P);
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alpha_0 + two_pow_130 - t_p
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});
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let (alpha_0_prime, zs) = self.lookup_config.witness_check(
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layouter.namespace(|| "Lookup range check alpha_0 + 2^130 - t_p"),
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alpha_0_prime,
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13,
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false,
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)?;
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(alpha_0_prime, zs[13])
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};
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layouter.assign_region(
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|| "Canonicity checks",
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|mut region| {
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let perm = &self.super_config.perm;
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// Activate canonicity check gate
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self.base_field_fixed_canon.enable(&mut region, 1)?;
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// Offset 0
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{
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let offset = 0;
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// Copy α
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copy(
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&mut region,
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|| "Copy α",
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self.canon_advices[0],
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offset,
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&alpha,
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perm,
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)?;
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// z_85_alpha is constrained to be zero in the custom gate.
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copy(
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&mut region,
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|| "Copy z_85_alpha",
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self.canon_advices[1],
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offset,
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&z_85_alpha,
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perm,
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)?;
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// z_84_alpha = the top three bits of alpha.
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copy(
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&mut region,
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|| "Copy z_84_alpha",
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self.canon_advices[2],
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offset,
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&z_84_alpha,
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perm,
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)?;
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}
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// Offset 1
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{
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let offset = 1;
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// Copy alpha_0_prime = alpha_0 + 2^130 - t_p.
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// We constrain this in the custom gate to be derived correctly.
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copy(
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&mut region,
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|| "Copy α_0 + 2^130 - t_p",
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self.canon_advices[0],
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offset,
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&alpha_0_prime,
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perm,
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)?;
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// Decompose α into three pieces,
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// α = α_0 (252 bits) || α_1 (2 bits) || α_2 (1 bit).
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// We only need to witness α_1 and α_2. α_0 is derived in the gate.
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// Witness α_1 = α[252..=253]
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let alpha_1 = alpha.value().map(|alpha| bitrange_subset(alpha, 252..254));
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region.assign_advice(
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|| "α_1 = α[252..=253]",
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self.canon_advices[1],
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offset,
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|| alpha_1.ok_or(Error::SynthesisError),
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)?;
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// Witness the MSB α_2 = α[254]
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let alpha_2 = alpha.value().map(|alpha| bitrange_subset(alpha, 254..255));
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region.assign_advice(
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|| "α_2 = α[254]",
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self.canon_advices[2],
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offset,
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|| alpha_2.ok_or(Error::SynthesisError),
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)?;
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}
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// Offset 2
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{
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let offset = 2;
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// Copy z_13_alpha_0_prime
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copy(
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&mut region,
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|| "Copy z_13_alpha_0_prime",
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self.canon_advices[0],
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offset,
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&z_13_alpha_0_prime,
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perm,
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)?;
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// Copy z_44_alpha
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copy(
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&mut region,
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|| "Copy z_44_alpha",
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self.canon_advices[1],
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offset,
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&z_44_alpha,
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perm,
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)?;
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// Copy z_43_alpha
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copy(
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&mut region,
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|| "Copy z_43_alpha",
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self.canon_advices[2],
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offset,
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&z_43_alpha,
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perm,
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)?;
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}
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Ok(())
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},
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)?;
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Ok(result)
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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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plonk::Error,
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};
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use pasta_curves::{arithmetic::FieldExt, pallas};
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use crate::circuit::gadget::{
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ecc::{
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chip::{EccChip, OrchardFixedBasesFull},
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FixedPoint, Point,
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},
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utilities::{CellValue, UtilitiesInstructions},
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};
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use crate::constants;
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pub fn test_mul_fixed_base_field(
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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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impl UtilitiesInstructions<pallas::Base> for EccChip {
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type Var = CellValue<pallas::Base>;
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}
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// commit_ivk_r
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let commit_ivk_r = OrchardFixedBasesFull::CommitIvkR;
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test_single_base(
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chip.clone(),
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layouter.namespace(|| "commit_ivk_r"),
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FixedPoint::from_inner(chip.clone(), commit_ivk_r),
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commit_ivk_r.generator(),
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)?;
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// note_commit_r
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let note_commit_r = OrchardFixedBasesFull::NoteCommitR;
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test_single_base(
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chip.clone(),
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layouter.namespace(|| "note_commit_r"),
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FixedPoint::from_inner(chip.clone(), note_commit_r),
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note_commit_r.generator(),
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)?;
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// nullifier_k
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let nullifier_k = OrchardFixedBasesFull::NullifierK;
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test_single_base(
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chip.clone(),
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layouter.namespace(|| "nullifier_k"),
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FixedPoint::from_inner(chip.clone(), nullifier_k),
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nullifier_k.generator(),
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)?;
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// value_commit_r
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let value_commit_r = OrchardFixedBasesFull::ValueCommitR;
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test_single_base(
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chip.clone(),
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layouter.namespace(|| "value_commit_r"),
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FixedPoint::from_inner(chip.clone(), value_commit_r),
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value_commit_r.generator(),
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)?;
|
||
|
||
// spend_auth_g
|
||
let spend_auth_g = OrchardFixedBasesFull::SpendAuthG;
|
||
test_single_base(
|
||
chip.clone(),
|
||
layouter.namespace(|| "spend_auth_g"),
|
||
FixedPoint::from_inner(chip, spend_auth_g),
|
||
spend_auth_g.generator(),
|
||
)?;
|
||
|
||
Ok(())
|
||
}
|
||
|
||
#[allow(clippy::op_ref)]
|
||
fn test_single_base(
|
||
chip: EccChip,
|
||
mut layouter: impl Layouter<pallas::Base>,
|
||
base: FixedPoint<pallas::Affine, EccChip>,
|
||
base_val: pallas::Affine,
|
||
) -> Result<(), Error> {
|
||
let column = chip.config().advices[0];
|
||
fn constrain_equal(
|
||
chip: EccChip,
|
||
mut layouter: impl Layouter<pallas::Base>,
|
||
base_val: pallas::Affine,
|
||
scalar_val: pallas::Base,
|
||
result: Point<pallas::Affine, EccChip>,
|
||
) -> Result<(), Error> {
|
||
// Move scalar from base field into scalar field (which always fits for Pallas).
|
||
let scalar = pallas::Scalar::from_bytes(&scalar_val.to_bytes()).unwrap();
|
||
let expected = Point::new(
|
||
chip,
|
||
layouter.namespace(|| "expected point"),
|
||
Some((base_val * scalar).to_affine()),
|
||
)?;
|
||
result.constrain_equal(layouter.namespace(|| "constrain result"), &expected)
|
||
}
|
||
|
||
// [a]B
|
||
{
|
||
let scalar_fixed = pallas::Base::rand();
|
||
let result = {
|
||
let scalar_fixed = chip.load_private(
|
||
layouter.namespace(|| "random base field element"),
|
||
column,
|
||
Some(scalar_fixed),
|
||
)?;
|
||
base.mul_base_field_elem(layouter.namespace(|| "random [a]B"), scalar_fixed)?
|
||
};
|
||
constrain_equal(
|
||
chip.clone(),
|
||
layouter.namespace(|| "random [a]B"),
|
||
base_val,
|
||
scalar_fixed,
|
||
result,
|
||
)?;
|
||
}
|
||
|
||
// There is a single canonical sequence of window values for which a doubling occurs on the last step:
|
||
// 1333333333333333333333333333333333333333333333333333333333333333333333333333333333334 in octal.
|
||
// (There is another *non-canonical* sequence
|
||
// 5333333333333333333333333333333333333333332711161673731021062440252244051273333333333 in octal.)
|
||
{
|
||
let h = pallas::Base::from_u64(constants::H as u64);
|
||
let scalar_fixed = "1333333333333333333333333333333333333333333333333333333333333333333333333333333333334"
|
||
.chars()
|
||
.fold(pallas::Base::zero(), |acc, c| {
|
||
acc * &h + &pallas::Base::from_u64(c.to_digit(8).unwrap().into())
|
||
});
|
||
let result = {
|
||
let scalar_fixed = chip.load_private(
|
||
layouter.namespace(|| "mul with double"),
|
||
column,
|
||
Some(scalar_fixed),
|
||
)?;
|
||
base.mul_base_field_elem(layouter.namespace(|| "mul with double"), scalar_fixed)?
|
||
};
|
||
constrain_equal(
|
||
chip.clone(),
|
||
layouter.namespace(|| "mul with double"),
|
||
base_val,
|
||
scalar_fixed,
|
||
result,
|
||
)?;
|
||
}
|
||
|
||
// [0]B should return (0,0) since it uses complete addition
|
||
// on the last step.
|
||
{
|
||
let scalar_fixed = pallas::Base::zero();
|
||
let result = {
|
||
let scalar_fixed =
|
||
chip.load_private(layouter.namespace(|| "zero"), column, Some(scalar_fixed))?;
|
||
base.mul_base_field_elem(layouter.namespace(|| "mul by zero"), scalar_fixed)?
|
||
};
|
||
constrain_equal(
|
||
chip.clone(),
|
||
layouter.namespace(|| "mul by zero"),
|
||
base_val,
|
||
scalar_fixed,
|
||
result,
|
||
)?;
|
||
}
|
||
|
||
// [-1]B is the largest base field element
|
||
{
|
||
let scalar_fixed = -pallas::Base::one();
|
||
let result = {
|
||
let scalar_fixed =
|
||
chip.load_private(layouter.namespace(|| "-1"), column, Some(scalar_fixed))?;
|
||
base.mul_base_field_elem(layouter.namespace(|| "mul by -1"), scalar_fixed)?
|
||
};
|
||
constrain_equal(
|
||
chip,
|
||
layouter.namespace(|| "mul by -1"),
|
||
base_val,
|
||
scalar_fixed,
|
||
result,
|
||
)?;
|
||
}
|
||
|
||
Ok(())
|
||
}
|
||
}
|