mirror of https://github.com/zcash/halo2.git
615 lines
21 KiB
Rust
615 lines
21 KiB
Rust
//! Chip implementations for the ECC gadgets.
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use super::{BaseFitsInScalarInstructions, EccInstructions, FixedPoints};
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use crate::{
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sinsemilla::primitives as sinsemilla,
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utilities::{lookup_range_check::LookupRangeCheckConfig, UtilitiesInstructions},
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};
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use arrayvec::ArrayVec;
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use ff::PrimeField;
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use group::prime::PrimeCurveAffine;
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use halo2_proofs::{
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circuit::{AssignedCell, Chip, Layouter, Value},
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plonk::{Advice, Assigned, Column, ConstraintSystem, Error, Fixed},
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};
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use pasta_curves::{arithmetic::CurveAffine, pallas};
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use std::convert::TryInto;
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pub(super) mod add;
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pub(super) mod add_incomplete;
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pub mod constants;
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pub(super) mod mul;
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pub(super) mod mul_fixed;
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pub(super) mod witness_point;
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pub use constants::*;
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// Exposed for Sinsemilla.
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pub(crate) use mul::incomplete::DoubleAndAdd;
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/// A curve point represented in affine (x, y) coordinates, or the
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/// identity represented as (0, 0).
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/// Each coordinate is assigned to a cell.
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#[derive(Clone, Debug)]
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pub struct EccPoint {
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/// x-coordinate
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///
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/// Stored as an `Assigned<F>` to enable batching inversions.
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x: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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/// y-coordinate
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///
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/// Stored as an `Assigned<F>` to enable batching inversions.
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y: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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}
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impl EccPoint {
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/// Constructs a point from its coordinates, without checking they are on the curve.
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///
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/// This is an internal API that we only use where we know we have a valid curve point.
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pub(crate) fn from_coordinates_unchecked(
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x: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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y: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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) -> Self {
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EccPoint { x, y }
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}
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/// Returns the value of this curve point, if known.
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pub fn point(&self) -> Value<pallas::Affine> {
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self.x.value().zip(self.y.value()).map(|(x, y)| {
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if x.is_zero_vartime() && y.is_zero_vartime() {
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pallas::Affine::identity()
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} else {
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pallas::Affine::from_xy(x.evaluate(), y.evaluate()).unwrap()
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}
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})
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}
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/// The cell containing the affine short-Weierstrass x-coordinate,
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/// or 0 for the zero point.
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pub fn x(&self) -> AssignedCell<pallas::Base, pallas::Base> {
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self.x.clone().evaluate()
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}
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/// The cell containing the affine short-Weierstrass y-coordinate,
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/// or 0 for the zero point.
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pub fn y(&self) -> AssignedCell<pallas::Base, pallas::Base> {
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self.y.clone().evaluate()
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}
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#[cfg(test)]
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fn is_identity(&self) -> Value<bool> {
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self.x.value().map(|x| x.is_zero_vartime())
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}
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}
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/// A non-identity point represented in affine (x, y) coordinates.
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/// Each coordinate is assigned to a cell.
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#[derive(Clone, Debug)]
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pub struct NonIdentityEccPoint {
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/// x-coordinate
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///
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/// Stored as an `Assigned<F>` to enable batching inversions.
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x: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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/// y-coordinate
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///
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/// Stored as an `Assigned<F>` to enable batching inversions.
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y: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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}
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impl NonIdentityEccPoint {
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/// Constructs a point from its coordinates, without checking they are on the curve.
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///
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/// This is an internal API that we only use where we know we have a valid non-identity
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/// curve point.
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pub(crate) fn from_coordinates_unchecked(
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x: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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y: AssignedCell<Assigned<pallas::Base>, pallas::Base>,
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) -> Self {
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NonIdentityEccPoint { x, y }
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}
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/// Returns the value of this curve point, if known.
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pub fn point(&self) -> Value<pallas::Affine> {
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self.x.value().zip(self.y.value()).map(|(x, y)| {
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assert!(!x.is_zero_vartime() && !y.is_zero_vartime());
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pallas::Affine::from_xy(x.evaluate(), y.evaluate()).unwrap()
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})
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}
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/// The cell containing the affine short-Weierstrass x-coordinate.
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pub fn x(&self) -> AssignedCell<pallas::Base, pallas::Base> {
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self.x.clone().evaluate()
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}
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/// The cell containing the affine short-Weierstrass y-coordinate.
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pub fn y(&self) -> AssignedCell<pallas::Base, pallas::Base> {
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self.y.clone().evaluate()
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}
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}
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impl From<NonIdentityEccPoint> for EccPoint {
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fn from(non_id_point: NonIdentityEccPoint) -> Self {
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Self {
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x: non_id_point.x,
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y: non_id_point.y,
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}
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}
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}
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/// Configuration for [`EccChip`].
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#[derive(Clone, Debug, Eq, PartialEq)]
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#[allow(non_snake_case)]
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pub struct EccConfig<FixedPoints: super::FixedPoints<pallas::Affine>> {
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/// Advice columns needed by instructions in the ECC chip.
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pub advices: [Column<Advice>; 10],
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/// Incomplete addition
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add_incomplete: add_incomplete::Config,
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/// Complete addition
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add: add::Config,
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/// Variable-base scalar multiplication
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mul: mul::Config,
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/// Fixed-base full-width scalar multiplication
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mul_fixed_full: mul_fixed::full_width::Config<FixedPoints>,
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/// Fixed-base signed short scalar multiplication
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mul_fixed_short: mul_fixed::short::Config<FixedPoints>,
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/// Fixed-base mul using a base field element as a scalar
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mul_fixed_base_field: mul_fixed::base_field_elem::Config<FixedPoints>,
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/// Witness point
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witness_point: witness_point::Config,
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/// Lookup range check using 10-bit lookup table
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pub lookup_config: LookupRangeCheckConfig<pallas::Base, { sinsemilla::K }>,
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}
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/// A trait representing the kind of scalar used with a particular `FixedPoint`.
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///
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/// This trait exists because of limitations around const generics.
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pub trait FixedScalarKind {
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/// The number of windows that this scalar kind requires.
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const NUM_WINDOWS: usize;
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}
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/// Type marker representing a full-width scalar for use in fixed-base scalar
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/// multiplication.
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#[derive(Debug)]
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pub enum FullScalar {}
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impl FixedScalarKind for FullScalar {
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const NUM_WINDOWS: usize = NUM_WINDOWS;
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}
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/// Type marker representing a signed 64-bit scalar for use in fixed-base scalar
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/// multiplication.
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#[derive(Debug)]
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pub enum ShortScalar {}
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impl FixedScalarKind for ShortScalar {
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const NUM_WINDOWS: usize = NUM_WINDOWS_SHORT;
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}
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/// Type marker representing a base field element being used as a scalar in fixed-base
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/// scalar multiplication.
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#[derive(Debug)]
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pub enum BaseFieldElem {}
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impl FixedScalarKind for BaseFieldElem {
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const NUM_WINDOWS: usize = NUM_WINDOWS;
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}
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/// Returns information about a fixed point that is required by [`EccChip`].
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///
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/// For each window required by `Self::FixedScalarKind`, $z$ is a field element such that for
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/// each point $(x, y)$ in the window:
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/// - $z + y = u^2$ (some square in the field); and
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/// - $z - y$ is not a square.
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///
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/// TODO: When associated consts can be used as const generics, introduce a
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/// `const NUM_WINDOWS: usize` associated const, and return `NUM_WINDOWS`-sized
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/// arrays instead of `Vec`s.
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pub trait FixedPoint<C: CurveAffine>: std::fmt::Debug + Eq + Clone {
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/// The kind of scalar that this fixed point can be multiplied by.
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type FixedScalarKind: FixedScalarKind;
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/// Returns the generator for this fixed point.
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fn generator(&self) -> C;
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/// Returns the $u$ values for this fixed point.
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fn u(&self) -> Vec<[<C::Base as PrimeField>::Repr; H]>;
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/// Returns the $z$ value for this fixed point.
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fn z(&self) -> Vec<u64>;
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/// Returns the Lagrange coefficients for this fixed point.
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fn lagrange_coeffs(&self) -> Vec<[C::Base; H]> {
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compute_lagrange_coeffs(self.generator(), Self::FixedScalarKind::NUM_WINDOWS)
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}
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}
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/// An [`EccInstructions`] chip that uses 10 advice columns.
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#[derive(Clone, Debug, Eq, PartialEq)]
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pub struct EccChip<FixedPoints: super::FixedPoints<pallas::Affine>> {
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config: EccConfig<FixedPoints>,
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}
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impl<FixedPoints: super::FixedPoints<pallas::Affine>> Chip<pallas::Base> for EccChip<FixedPoints> {
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type Config = EccConfig<FixedPoints>;
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type Loaded = ();
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fn config(&self) -> &Self::Config {
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&self.config
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}
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fn loaded(&self) -> &Self::Loaded {
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&()
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}
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}
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impl<Fixed: super::FixedPoints<pallas::Affine>> UtilitiesInstructions<pallas::Base>
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for EccChip<Fixed>
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{
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type Var = AssignedCell<pallas::Base, pallas::Base>;
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}
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impl<FixedPoints: super::FixedPoints<pallas::Affine>> EccChip<FixedPoints> {
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/// Reconstructs this chip from the given config.
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pub fn construct(config: <Self as Chip<pallas::Base>>::Config) -> Self {
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Self { config }
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}
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/// # Side effects
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///
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/// All columns in `advices` will be equality-enabled.
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#[allow(non_snake_case)]
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pub fn configure(
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meta: &mut ConstraintSystem<pallas::Base>,
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advices: [Column<Advice>; 10],
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lagrange_coeffs: [Column<Fixed>; 8],
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range_check: LookupRangeCheckConfig<pallas::Base, { sinsemilla::K }>,
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) -> <Self as Chip<pallas::Base>>::Config {
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// Create witness point gate
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let witness_point = witness_point::Config::configure(meta, advices[0], advices[1]);
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// Create incomplete point addition gate
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let add_incomplete =
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add_incomplete::Config::configure(meta, advices[0], advices[1], advices[2], advices[3]);
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// Create complete point addition gate
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let add = add::Config::configure(
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meta, advices[0], advices[1], advices[2], advices[3], advices[4], advices[5],
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advices[6], advices[7], advices[8],
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);
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// Create variable-base scalar mul gates
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let mul = mul::Config::configure(meta, add, range_check, advices);
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// Create config that is shared across short, base-field, and full-width
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// fixed-base scalar mul.
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let mul_fixed = mul_fixed::Config::<FixedPoints>::configure(
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meta,
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lagrange_coeffs,
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advices[4],
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advices[5],
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add,
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add_incomplete,
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);
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// Create gate that is only used in full-width fixed-base scalar mul.
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let mul_fixed_full =
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mul_fixed::full_width::Config::<FixedPoints>::configure(meta, mul_fixed.clone());
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// Create gate that is only used in short fixed-base scalar mul.
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let mul_fixed_short =
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mul_fixed::short::Config::<FixedPoints>::configure(meta, mul_fixed.clone());
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// Create gate that is only used in fixed-base mul using a base field element.
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let mul_fixed_base_field = mul_fixed::base_field_elem::Config::<FixedPoints>::configure(
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meta,
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advices[6..9].try_into().unwrap(),
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range_check,
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mul_fixed,
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);
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EccConfig {
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advices,
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add_incomplete,
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add,
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mul,
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mul_fixed_full,
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mul_fixed_short,
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mul_fixed_base_field,
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witness_point,
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lookup_config: range_check,
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}
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}
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}
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/// A full-width scalar used for fixed-base scalar multiplication.
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/// This is decomposed into 85 3-bit windows in little-endian order,
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/// i.e. `windows` = [k_0, k_1, ..., k_84] (for a 255-bit scalar)
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/// where `scalar = k_0 + k_1 * (2^3) + ... + k_84 * (2^3)^84` and
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/// each `k_i` is in the range [0..2^3).
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#[derive(Clone, Debug)]
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pub struct EccScalarFixed {
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value: Value<pallas::Scalar>,
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/// The circuit-assigned windows representing this scalar, or `None` if the scalar has
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/// not been used yet.
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windows: Option<ArrayVec<AssignedCell<pallas::Base, pallas::Base>, { NUM_WINDOWS }>>,
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}
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// TODO: Make V a `u64`
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type MagnitudeCell = AssignedCell<pallas::Base, pallas::Base>;
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// TODO: Make V an enum Sign { Positive, Negative }
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type SignCell = AssignedCell<pallas::Base, pallas::Base>;
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type MagnitudeSign = (MagnitudeCell, SignCell);
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/// A signed short scalar used for fixed-base scalar multiplication.
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/// A short scalar must have magnitude in the range [0..2^64), with
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/// a sign of either 1 or -1.
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/// This is decomposed into 3-bit windows in little-endian order
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/// using a running sum `z`, where z_{i+1} = (z_i - a_i) / (2^3)
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/// for element α = a_0 + (2^3) a_1 + ... + (2^{3(n-1)}) a_{n-1}.
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/// Each `a_i` is in the range [0..2^3).
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///
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/// `windows` = [k_0, k_1, ..., k_21] (for a 64-bit magnitude)
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/// where `scalar = k_0 + k_1 * (2^3) + ... + k_84 * (2^3)^84` and
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/// each `k_i` is in the range [0..2^3).
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/// k_21 must be a single bit, i.e. 0 or 1.
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#[derive(Clone, Debug)]
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pub struct EccScalarFixedShort {
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magnitude: MagnitudeCell,
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sign: SignCell,
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/// The circuit-assigned running sum constraining this signed short scalar, or `None`
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/// if the scalar has not been used yet.
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running_sum:
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Option<ArrayVec<AssignedCell<pallas::Base, pallas::Base>, { NUM_WINDOWS_SHORT + 1 }>>,
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}
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/// A base field element used for fixed-base scalar multiplication.
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/// This is decomposed into 3-bit windows in little-endian order
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/// using a running sum `z`, where z_{i+1} = (z_i - a_i) / (2^3)
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/// for element α = a_0 + (2^3) a_1 + ... + (2^{3(n-1)}) a_{n-1}.
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/// Each `a_i` is in the range [0..2^3).
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///
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/// `running_sum` = [z_0, ..., z_85], where we expect z_85 = 0.
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/// Since z_0 is initialized as the scalar α, we store it as
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/// `base_field_elem`.
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#[derive(Clone, Debug)]
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struct EccBaseFieldElemFixed {
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base_field_elem: AssignedCell<pallas::Base, pallas::Base>,
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running_sum: ArrayVec<AssignedCell<pallas::Base, pallas::Base>, { NUM_WINDOWS + 1 }>,
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}
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impl EccBaseFieldElemFixed {
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#![allow(dead_code)]
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fn base_field_elem(&self) -> AssignedCell<pallas::Base, pallas::Base> {
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self.base_field_elem.clone()
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}
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}
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/// An enumeration of the possible types of scalars used in variable-base
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/// multiplication.
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#[derive(Clone, Debug)]
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pub enum ScalarVar {
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/// An element of the elliptic curve's base field, that is used as a scalar
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/// in variable-base scalar mul.
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///
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/// It is not true in general that a scalar field element fits in a curve's
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/// base field, and in particular it is untrue for the Pallas curve, whose
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/// scalar field `Fq` is larger than its base field `Fp`.
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///
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/// However, the only use of variable-base scalar mul in the Orchard protocol
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/// is in deriving diversified addresses `[ivk] g_d`, and `ivk` is guaranteed
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/// to be in the base field of the curve. (See non-normative notes in
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/// [4.2.3 Orchard Key Components][orchardkeycomponents].)
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///
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/// [orchardkeycomponents]: https://zips.z.cash/protocol/protocol.pdf#orchardkeycomponents
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BaseFieldElem(AssignedCell<pallas::Base, pallas::Base>),
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/// A full-width scalar. This is unimplemented for halo2_gadgets v0.1.0.
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FullWidth,
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}
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impl<Fixed: FixedPoints<pallas::Affine>> EccInstructions<pallas::Affine> for EccChip<Fixed>
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where
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<Fixed as FixedPoints<pallas::Affine>>::Base:
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FixedPoint<pallas::Affine, FixedScalarKind = BaseFieldElem>,
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<Fixed as FixedPoints<pallas::Affine>>::FullScalar:
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FixedPoint<pallas::Affine, FixedScalarKind = FullScalar>,
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<Fixed as FixedPoints<pallas::Affine>>::ShortScalar:
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FixedPoint<pallas::Affine, FixedScalarKind = ShortScalar>,
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{
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type ScalarFixed = EccScalarFixed;
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type ScalarFixedShort = EccScalarFixedShort;
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type ScalarVar = ScalarVar;
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type Point = EccPoint;
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type NonIdentityPoint = NonIdentityEccPoint;
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type X = AssignedCell<pallas::Base, pallas::Base>;
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type FixedPoints = Fixed;
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fn constrain_equal(
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&self,
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layouter: &mut impl Layouter<pallas::Base>,
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a: &Self::Point,
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b: &Self::Point,
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) -> Result<(), Error> {
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layouter.assign_region(
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|| "constrain equal",
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|mut region| {
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// Constrain x-coordinates
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region.constrain_equal(a.x().cell(), b.x().cell())?;
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// Constrain x-coordinates
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region.constrain_equal(a.y().cell(), b.y().cell())
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},
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)
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}
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fn witness_point(
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&self,
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layouter: &mut impl Layouter<pallas::Base>,
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value: Value<pallas::Affine>,
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) -> Result<Self::Point, Error> {
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let config = self.config().witness_point;
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layouter.assign_region(
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|| "witness point",
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|mut region| config.point(value, 0, &mut region),
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)
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}
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fn witness_point_non_id(
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&self,
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layouter: &mut impl Layouter<pallas::Base>,
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value: Value<pallas::Affine>,
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) -> Result<Self::NonIdentityPoint, Error> {
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let config = self.config().witness_point;
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layouter.assign_region(
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|| "witness non-identity point",
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|mut region| config.point_non_id(value, 0, &mut region),
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)
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}
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fn witness_scalar_var(
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&self,
|
||
_layouter: &mut impl Layouter<pallas::Base>,
|
||
_value: Value<pallas::Scalar>,
|
||
) -> Result<Self::ScalarVar, Error> {
|
||
// This is unimplemented for halo2_gadgets v0.1.0.
|
||
todo!()
|
||
}
|
||
|
||
fn witness_scalar_fixed(
|
||
&self,
|
||
_layouter: &mut impl Layouter<pallas::Base>,
|
||
value: Value<pallas::Scalar>,
|
||
) -> Result<Self::ScalarFixed, Error> {
|
||
Ok(EccScalarFixed {
|
||
value,
|
||
// This chip uses lazy witnessing.
|
||
windows: None,
|
||
})
|
||
}
|
||
|
||
fn scalar_fixed_from_signed_short(
|
||
&self,
|
||
_layouter: &mut impl Layouter<pallas::Base>,
|
||
(magnitude, sign): MagnitudeSign,
|
||
) -> Result<Self::ScalarFixedShort, Error> {
|
||
Ok(EccScalarFixedShort {
|
||
magnitude,
|
||
sign,
|
||
// This chip uses lazy constraining.
|
||
running_sum: None,
|
||
})
|
||
}
|
||
|
||
fn extract_p<Point: Into<Self::Point> + Clone>(point: &Point) -> Self::X {
|
||
let point: EccPoint = (point.clone()).into();
|
||
point.x()
|
||
}
|
||
|
||
fn add_incomplete(
|
||
&self,
|
||
layouter: &mut impl Layouter<pallas::Base>,
|
||
a: &Self::NonIdentityPoint,
|
||
b: &Self::NonIdentityPoint,
|
||
) -> Result<Self::NonIdentityPoint, Error> {
|
||
let config = self.config().add_incomplete;
|
||
layouter.assign_region(
|
||
|| "incomplete point addition",
|
||
|mut region| config.assign_region(a, b, 0, &mut region),
|
||
)
|
||
}
|
||
|
||
fn add<A: Into<Self::Point> + Clone, B: Into<Self::Point> + Clone>(
|
||
&self,
|
||
layouter: &mut impl Layouter<pallas::Base>,
|
||
a: &A,
|
||
b: &B,
|
||
) -> Result<Self::Point, Error> {
|
||
let config = self.config().add;
|
||
layouter.assign_region(
|
||
|| "complete point addition",
|
||
|mut region| {
|
||
config.assign_region(&(a.clone()).into(), &(b.clone()).into(), 0, &mut region)
|
||
},
|
||
)
|
||
}
|
||
|
||
fn mul(
|
||
&self,
|
||
layouter: &mut impl Layouter<pallas::Base>,
|
||
scalar: &Self::ScalarVar,
|
||
base: &Self::NonIdentityPoint,
|
||
) -> Result<(Self::Point, Self::ScalarVar), Error> {
|
||
let config = self.config().mul;
|
||
match scalar {
|
||
ScalarVar::BaseFieldElem(scalar) => config.assign(
|
||
layouter.namespace(|| "variable-base scalar mul"),
|
||
scalar.clone(),
|
||
base,
|
||
),
|
||
ScalarVar::FullWidth => {
|
||
todo!()
|
||
}
|
||
}
|
||
}
|
||
|
||
fn mul_fixed(
|
||
&self,
|
||
layouter: &mut impl Layouter<pallas::Base>,
|
||
scalar: &Self::ScalarFixed,
|
||
base: &<Self::FixedPoints as FixedPoints<pallas::Affine>>::FullScalar,
|
||
) -> Result<(Self::Point, Self::ScalarFixed), Error> {
|
||
let config = self.config().mul_fixed_full.clone();
|
||
config.assign(
|
||
layouter.namespace(|| format!("fixed-base mul of {:?}", base)),
|
||
scalar,
|
||
base,
|
||
)
|
||
}
|
||
|
||
fn mul_fixed_short(
|
||
&self,
|
||
layouter: &mut impl Layouter<pallas::Base>,
|
||
scalar: &Self::ScalarFixedShort,
|
||
base: &<Self::FixedPoints as FixedPoints<pallas::Affine>>::ShortScalar,
|
||
) -> Result<(Self::Point, Self::ScalarFixedShort), Error> {
|
||
let config = self.config().mul_fixed_short.clone();
|
||
config.assign(
|
||
layouter.namespace(|| format!("short fixed-base mul of {:?}", base)),
|
||
scalar,
|
||
base,
|
||
)
|
||
}
|
||
|
||
fn mul_fixed_base_field_elem(
|
||
&self,
|
||
layouter: &mut impl Layouter<pallas::Base>,
|
||
base_field_elem: AssignedCell<pallas::Base, pallas::Base>,
|
||
base: &<Self::FixedPoints as FixedPoints<pallas::Affine>>::Base,
|
||
) -> Result<Self::Point, Error> {
|
||
let config = self.config().mul_fixed_base_field.clone();
|
||
config.assign(
|
||
layouter.namespace(|| format!("base-field elem fixed-base mul of {:?}", base)),
|
||
base_field_elem,
|
||
base,
|
||
)
|
||
}
|
||
}
|
||
|
||
impl<Fixed: FixedPoints<pallas::Affine>> BaseFitsInScalarInstructions<pallas::Affine>
|
||
for EccChip<Fixed>
|
||
where
|
||
<Fixed as FixedPoints<pallas::Affine>>::Base:
|
||
FixedPoint<pallas::Affine, FixedScalarKind = BaseFieldElem>,
|
||
<Fixed as FixedPoints<pallas::Affine>>::FullScalar:
|
||
FixedPoint<pallas::Affine, FixedScalarKind = FullScalar>,
|
||
<Fixed as FixedPoints<pallas::Affine>>::ShortScalar:
|
||
FixedPoint<pallas::Affine, FixedScalarKind = ShortScalar>,
|
||
{
|
||
fn scalar_var_from_base(
|
||
&self,
|
||
_layouter: &mut impl Layouter<pallas::Base>,
|
||
base: &Self::Var,
|
||
) -> Result<Self::ScalarVar, Error> {
|
||
Ok(ScalarVar::BaseFieldElem(base.clone()))
|
||
}
|
||
}
|