mirror of https://github.com/zcash/orchard.git
mul::incomplete.rs: Decompose q_mul into binary selectors.
Previously, q_mul was a non-binary selector that could be set to
1, 2, or 3. We now decompose it into three binary selectors
q_mul_{1,2,3}.
This commit is contained in:
therealyingtong
parent
f6c951d975
commit
f532ecec10
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@ -88,9 +88,9 @@ pub struct EccConfig {
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pub q_add: Selector,
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/// Variable-base scalar multiplication (hi half)
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pub q_mul_hi: Column<Fixed>,
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pub q_mul_hi: (Selector, Selector, Selector),
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/// Variable-base scalar multiplication (lo half)
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pub q_mul_lo: Column<Fixed>,
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pub q_mul_lo: (Selector, Selector, Selector),
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/// Selector used to enforce boolean decomposition in variable-base scalar mul
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pub q_mul_decompose_var: Selector,
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/// Selector used to enforce switching logic on LSB in variable-base scalar mul
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@ -196,8 +196,8 @@ impl EccChip {
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fixed_z: meta.fixed_column(),
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q_add_incomplete: meta.selector(),
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q_add: meta.selector(),
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q_mul_hi: meta.fixed_column(),
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q_mul_lo: meta.fixed_column(),
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q_mul_hi: (meta.selector(), meta.selector(), meta.selector()),
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q_mul_lo: (meta.selector(), meta.selector(), meta.selector()),
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q_mul_decompose_var: meta.selector(),
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q_mul_overflow: meta.selector(),
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q_mul_lsb: meta.selector(),
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@ -5,17 +5,18 @@ use super::{INCOMPLETE_HI_RANGE, INCOMPLETE_LO_RANGE, X, Y, Z};
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use ff::Field;
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use halo2::{
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circuit::Region,
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plonk::{Advice, Column, ConstraintSystem, Error, Expression, Fixed, VirtualCells},
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plonk::{Advice, Column, ConstraintSystem, Error, Expression, Selector, VirtualCells},
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poly::Rotation,
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};
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use pasta_curves::{arithmetic::FieldExt, pallas};
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#[derive(Copy, Clone)]
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pub(super) struct Config {
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// Number of bits covered by this incomplete range.
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num_bits: usize,
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// Selector used to constrain the cells used in incomplete addition.
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pub(super) q_mul: Column<Fixed>,
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// Selectors used to constrain the cells used in incomplete addition.
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pub(super) q_mul: (Selector, Selector, Selector),
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// Cumulative sum used to decompose the scalar.
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pub(super) z: Column<Advice>,
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// x-coordinate of the accumulator in each double-and-add iteration.
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@ -85,130 +86,115 @@ impl Deref for LoConfig {
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impl Config {
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// Gate for incomplete addition part of variable-base scalar multiplication.
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pub(super) fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
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meta.create_gate("Incomplete addition for variable-base scalar mul", |meta| {
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let q_mul = meta.query_fixed(self.q_mul, Rotation::cur());
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// Closure to compute x_{R,i} = λ_{1,i}^2 - x_{A,i} - x_{P,i}
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let x_r = |meta: &mut VirtualCells<pallas::Base>, rotation: Rotation| {
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let x_a = meta.query_advice(self.x_a, rotation);
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let x_p = meta.query_advice(self.x_p, rotation);
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let lambda_1 = meta.query_advice(self.lambda1, rotation);
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lambda_1.square() - x_a - x_p
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};
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// Useful constants
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// Closure to compute y_{A,i} = (λ_{1,i} + λ_{2,i}) * (x_{A,i} - x_{R,i}) / 2
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let y_a = |meta: &mut VirtualCells<pallas::Base>, rotation: Rotation| {
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let x_a = meta.query_advice(self.x_a, rotation);
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let lambda_1 = meta.query_advice(self.lambda1, rotation);
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let lambda_2 = meta.query_advice(self.lambda2, rotation);
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(lambda_1 + lambda_2) * (x_a - x_r(meta, rotation)) * pallas::Base::TWO_INV
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};
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// Constraints used for q_mul_{2, 3} == 1
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let for_loop = |meta: &mut VirtualCells<pallas::Base>,
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q_mul: Expression<pallas::Base>,
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y_a_next: Expression<pallas::Base>| {
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let one = Expression::Constant(pallas::Base::one());
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let two = Expression::Constant(pallas::Base::from_u64(2));
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let three = Expression::Constant(pallas::Base::from_u64(3));
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// Closures for expressions that are derived multiple times
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// x_{R,i} = λ_{1,i}^2 - x_{A,i} - x_{P,i}
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let x_r = |meta: &mut VirtualCells<pallas::Base>, rotation| {
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let x_a = meta.query_advice(self.x_a, rotation);
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let x_p = meta.query_advice(self.x_p, rotation);
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let lambda_1 = meta.query_advice(self.lambda1, rotation);
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lambda_1.square() - x_a - x_p
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};
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// z_i
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let z_cur = meta.query_advice(self.z, Rotation::cur());
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// z_{i+1}
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let z_prev = meta.query_advice(self.z, Rotation::prev());
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// x_{A,i}
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let x_a_cur = meta.query_advice(self.x_a, Rotation::cur());
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// x_{A,i-1}
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let x_a_next = meta.query_advice(self.x_a, Rotation::next());
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// x_{P,i}
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let x_p_cur = meta.query_advice(self.x_p, Rotation::cur());
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// y_{P,i}
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let y_p_cur = meta.query_advice(self.y_p, Rotation::cur());
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// λ_{1,i}
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let lambda1_cur = meta.query_advice(self.lambda1, Rotation::cur());
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// λ_{2,i}
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let lambda2_cur = meta.query_advice(self.lambda2, Rotation::cur());
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// y_{A,i} = (λ_{1,i} + λ_{2,i}) * (x_{A,i} - x_{R,i}) / 2
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let y_a = |meta: &mut VirtualCells<pallas::Base>, rotation: Rotation| {
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let x_a = meta.query_advice(self.x_a, rotation);
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let lambda_1 = meta.query_advice(self.lambda1, rotation);
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let lambda_2 = meta.query_advice(self.lambda2, rotation);
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let y_a_cur = y_a(meta, Rotation::cur());
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(lambda_1 + lambda_2) * (x_a - x_r(meta, rotation)) * pallas::Base::TWO_INV
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};
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// The current bit in the scalar decomposition, k_i = z_i - 2⋅z_{i+1}.
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// Recall that we assigned the cumulative variable `z_i` in descending order,
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// i from n down to 0. So z_{i+1} corresponds to the `z_prev` query.
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let k = z_cur - z_prev * pallas::Base::from_u64(2);
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// Check booleanity of decomposition.
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let bool_check = k.clone() * (one.clone() - k.clone());
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// λ_{1,i}⋅(x_{A,i} − x_{P,i}) − y_{A,i} + (2k_i - 1) y_{P,i} = 0
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let gradient_1 = lambda1_cur * (x_a_cur.clone() - x_p_cur) - y_a_cur.clone()
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+ (k * pallas::Base::from_u64(2) - one) * y_p_cur;
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// λ_{2,i}^2 − x_{A,i-1} − x_{R,i} − x_{A,i} = 0
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let secant_line = lambda2_cur.clone().square()
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- x_a_next.clone()
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- x_r(meta, Rotation::cur())
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- x_a_cur.clone();
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// λ_{2,i}⋅(x_{A,i} − x_{A,i-1}) − y_{A,i} − y_{A,i-1} = 0
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let gradient_2 = lambda2_cur * (x_a_cur - x_a_next) - y_a_cur - y_a_next;
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std::iter::empty()
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.chain(Some(("bool_check", q_mul.clone() * bool_check)))
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.chain(Some(("gradient_1", q_mul.clone() * gradient_1)))
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.chain(Some(("secant_line", q_mul.clone() * secant_line)))
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.chain(Some(("gradient_2", q_mul * gradient_2)))
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};
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// q_mul_1 == 1 checks
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meta.create_gate("q_mul_1 == 1 checks", |meta| {
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let q_mul_1 = meta.query_selector(self.q_mul.0);
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let y_a_next = y_a(meta, Rotation::next());
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let y_a_witnessed = meta.query_advice(self.lambda1, Rotation::cur());
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vec![("init y_a", q_mul_1 * (y_a_witnessed - y_a_next))]
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});
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// q_mul_2 == 1 checks
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meta.create_gate("q_mul_2 == 1 checks", |meta| {
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let q_mul_2 = meta.query_selector(self.q_mul.1);
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let y_a_next = y_a(meta, Rotation::next());
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// q_mul == 1
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let q_mul_one_checks = {
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let q_mul_is_one =
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q_mul.clone() * (two.clone() - q_mul.clone()) * (three.clone() - q_mul.clone());
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let y_a_witnessed = meta.query_advice(self.lambda1, Rotation::cur());
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let y_a = y_a_next.clone();
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Some(("init y_a", q_mul_is_one * (y_a_witnessed - y_a)))
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};
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// x_{P,i}
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let x_p_cur = meta.query_advice(self.x_p, Rotation::cur());
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// x_{P,i-1}
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let x_p_next = meta.query_advice(self.x_p, Rotation::next());
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// y_{P,i}
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let y_p_cur = meta.query_advice(self.y_p, Rotation::cur());
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// y_{P,i-1}
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let y_p_next = meta.query_advice(self.y_p, Rotation::next());
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// Constraints used for q_mul in {2, 3}
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let for_loop = |meta: &mut VirtualCells<pallas::Base>,
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q_mul: Expression<pallas::Base>,
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y_a_next: Expression<pallas::Base>| {
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// z_i
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let z_cur = meta.query_advice(self.z, Rotation::cur());
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// z_{i+1}
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let z_prev = meta.query_advice(self.z, Rotation::prev());
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// x_{A,i}
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let x_a_cur = meta.query_advice(self.x_a, Rotation::cur());
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// x_{A,i-1}
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let x_a_next = meta.query_advice(self.x_a, Rotation::next());
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// x_{P,i}
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let x_p_cur = meta.query_advice(self.x_p, Rotation::cur());
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// y_{P,i}
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let y_p_cur = meta.query_advice(self.y_p, Rotation::cur());
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// λ_{1,i}
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let lambda1_cur = meta.query_advice(self.lambda1, Rotation::cur());
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// λ_{2,i}
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let lambda2_cur = meta.query_advice(self.lambda2, Rotation::cur());
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let y_a_cur = y_a(meta, Rotation::cur());
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// The current bit in the scalar decomposition, k_i = z_i - 2⋅z_{i+1}.
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// Recall that we assigned the cumulative variable `z_i` in descending order,
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// i from n down to 0. So z_{i+1} corresponds to the `z_prev` query.
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let k = z_cur - z_prev * pallas::Base::from_u64(2);
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// Check booleanity of decomposition.
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let bool_check = k.clone() * (one.clone() - k.clone());
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// λ_{1,i}⋅(x_{A,i} − x_{P,i}) − y_{A,i} + (2k_i - 1) y_{P,i} = 0
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let gradient_1 = lambda1_cur * (x_a_cur.clone() - x_p_cur) - y_a_cur.clone()
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+ (k * pallas::Base::from_u64(2) - one.clone()) * y_p_cur;
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// λ_{2,i}^2 − x_{A,i-1} − x_{R,i} − x_{A,i} = 0
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let secant_line = lambda2_cur.clone().square()
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- x_a_next.clone()
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- x_r(meta, Rotation::cur())
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- x_a_cur.clone();
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// λ_{2,i}⋅(x_{A,i} − x_{A,i-1}) − y_{A,i} − y_{A,i-1} = 0
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let gradient_2 = lambda2_cur * (x_a_cur - x_a_next) - y_a_cur - y_a_next;
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std::iter::empty()
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.chain(Some(("bool_check", q_mul.clone() * bool_check)))
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.chain(Some(("gradient_1", q_mul.clone() * gradient_1)))
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.chain(Some(("secant_line", q_mul.clone() * secant_line)))
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.chain(Some(("gradient_2", q_mul * gradient_2)))
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};
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// q_mul == 2
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let q_mul_two_checks = {
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let q_mul_is_two =
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q_mul.clone() * (one.clone() - q_mul.clone()) * (three - q_mul.clone());
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// x_{P,i}
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let x_p_cur = meta.query_advice(self.x_p, Rotation::cur());
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// x_{P,i-1}
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let x_p_next = meta.query_advice(self.x_p, Rotation::next());
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// y_{P,i}
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let y_p_cur = meta.query_advice(self.y_p, Rotation::cur());
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// y_{P,i-1}
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let y_p_next = meta.query_advice(self.y_p, Rotation::next());
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// The base used in double-and-add remains constant. We check that its
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// x- and y- coordinates are the same throughout.
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let x_p_check = x_p_cur - x_p_next;
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let y_p_check = y_p_cur - y_p_next;
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std::iter::empty()
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.chain(Some(("x_p_check", q_mul_is_two.clone() * x_p_check)))
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.chain(Some(("y_p_check", q_mul_is_two.clone() * y_p_check)))
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.chain(for_loop(meta, q_mul_is_two, y_a_next))
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};
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// q_mul == 3
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let q_mul_three_checks = {
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let q_mul_is_three = q_mul.clone() * (one.clone() - q_mul.clone()) * (two - q_mul);
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let y_a_final = meta.query_advice(self.lambda1, Rotation::next());
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for_loop(meta, q_mul_is_three, y_a_final)
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};
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// The base used in double-and-add remains constant. We check that its
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// x- and y- coordinates are the same throughout.
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let x_p_check = x_p_cur - x_p_next;
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let y_p_check = y_p_cur - y_p_next;
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std::iter::empty()
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.chain(q_mul_one_checks)
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.chain(q_mul_two_checks)
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.chain(q_mul_three_checks)
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.chain(Some(("x_p_check", q_mul_2.clone() * x_p_check)))
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.chain(Some(("y_p_check", q_mul_2.clone() * y_p_check)))
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.chain(for_loop(meta, q_mul_2, y_a_next))
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});
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// q_mul_3 == 1 checks
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meta.create_gate("q_mul_3 == 1 checks", |meta| {
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let q_mul_3 = meta.query_selector(self.q_mul.2);
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let y_a_final = meta.query_advice(self.lambda1, Rotation::next());
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for_loop(meta, q_mul_3, y_a_final)
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});
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}
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@ -248,32 +234,17 @@ impl Config {
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// Set q_mul values
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{
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// q_mul = 1 on offset 0
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region.assign_fixed(
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|| "q_mul = 1",
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self.q_mul,
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offset,
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|| Ok(pallas::Base::one()),
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)?;
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// q_mul_1 = 1 on offset 0
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self.q_mul.0.enable(region, offset)?;
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let offset = offset + 1;
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// q_mul = 2 on all rows after offset 0, excluding the last row.
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// q_mul_2 = 1 on all rows after offset 0, excluding the last row.
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for idx in 0..(self.num_bits - 1) {
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region.assign_fixed(
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|| "q_mul = 2",
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self.q_mul,
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offset + idx,
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|| Ok(pallas::Base::from_u64(2)),
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)?;
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self.q_mul.1.enable(region, offset + idx)?;
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}
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// q_mul = 3 on the last row.
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region.assign_fixed(
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|| "q_mul = 3",
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self.q_mul,
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offset + self.num_bits - 1,
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|| Ok(pallas::Base::from_u64(3)),
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)?;
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// q_mul_3 = 1 on the last row.
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self.q_mul.2.enable(region, offset + self.num_bits - 1)?;
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}
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// Initialise double-and-add
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@ -491,7 +491,7 @@ pub mod tests {
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Err(vec![
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VerifyFailure::ConstraintNotSatisfied {
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constraint: (
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(12, "Short fixed-base mul gate").into(),
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(16, "Short fixed-base mul gate").into(),
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0,
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"last_window_check"
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)
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@ -523,13 +523,13 @@ pub mod tests {
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prover.verify(),
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Err(vec![
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VerifyFailure::ConstraintNotSatisfied {
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constraint: ((12, "Short fixed-base mul gate").into(), 1, "sign_check")
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constraint: ((16, "Short fixed-base mul gate").into(), 1, "sign_check")
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.into(),
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row: 26
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},
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VerifyFailure::ConstraintNotSatisfied {
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constraint: (
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(12, "Short fixed-base mul gate").into(),
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(16, "Short fixed-base mul gate").into(),
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3,
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"negation_check"
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)
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