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mul::incomplete.rs: Constrain first and last y_a values. 

Co-authored-by: Jack Grigg <jack@electriccoin.co>
This commit is contained in:
therealyingtong 2021-07-02 16:41:18 +08:00
parent b363492a35
commit 4d69dec00f
5 changed files with 201 additions and 115 deletions
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8
src/circuit/gadget/ecc/chip.rs
View File

@ -88,9 +88,9 @@ pub struct EccConfig {
pub q_add: Selector,
/// Variable-base scalar multiplication (hi half)
pub q_mul_hi: Selector,
pub q_mul_hi: Column<Fixed>,
/// Variable-base scalar multiplication (lo half)
pub q_mul_lo: Selector,
pub q_mul_lo: Column<Fixed>,
/// Selector used to enforce boolean decomposition in variable-base scalar mul
pub q_mul_decompose_var: Selector,
/// Selector used to enforce switching logic on LSB in variable-base scalar mul
@ -179,8 +179,8 @@ impl EccChip {
fixed_z: meta.fixed_column(),
q_add_incomplete: meta.selector(),
q_add: meta.selector(),
q_mul_hi: meta.selector(),
q_mul_lo: meta.selector(),
q_mul_hi: meta.fixed_column(),
q_mul_lo: meta.fixed_column(),
q_mul_decompose_var: meta.selector(),
q_mul_overflow: meta.selector(),
q_mul_lsb: meta.selector(),

19
src/circuit/gadget/ecc/chip/mul.rs
View File

@ -39,8 +39,6 @@ const COMPLETE_RANGE: Range<usize> = INCOMPLETE_LEN..(INCOMPLETE_LEN + NUM_COMPL
pub struct Config {
// Fixed column used to constrain the initialization of the running sum to be zero.
constants: Column<Fixed>,
// Selector used to check z_i = 2*z_{i+1} + k_i
q_mul_decompose_var: Selector,
// Selector used to check switching logic on LSB
q_mul_lsb: Selector,
// Permutation
@ -61,7 +59,6 @@ impl From<&EccConfig> for Config {
fn from(ecc_config: &EccConfig) -> Self {
let config = Self {
constants: ecc_config.constants,
q_mul_decompose_var: ecc_config.q_mul_decompose_var,
q_mul_lsb: ecc_config.q_mul_lsb,
perm: ecc_config.perm.clone(),
add_config: ecc_config.into(),
@ -180,26 +177,23 @@ impl Config {
Z(CellValue::new(z_cell, Some(z_val)))
};
// Increase the offset by 1 after initializing `z`.
let offset = offset + 1;
// Double-and-add (incomplete addition) for the `hi` half of the scalar decomposition
let (x_a, y_a, zs_incomplete_hi) = self.hi_config.double_and_add(
&mut region,
offset,
&base,
bits_incomplete_hi,
(X(acc.x), Y(acc.y.value()), z_init),
(X(acc.x), Y(acc.y), z_init),
)?;
// Double-and-add (incomplete addition) for the `lo` half of the scalar decomposition
let z = &zs_incomplete_hi[zs_incomplete_hi.len() - 1];
let z = &zs_incomplete_hi.last().expect("should not be empty");
let (x_a, y_a, zs_incomplete_lo) = self.lo_config.double_and_add(
&mut region,
offset,
&base,
bits_incomplete_lo,
(x_a, y_a, *z),
(x_a, y_a, **z),
)?;
// Move from incomplete addition to complete addition.
@ -299,9 +293,6 @@ impl Config {
|| z_0_val.ok_or(Error::SynthesisError),
)?;
// Check that z_0 was properly derived from z_1.
self.q_mul_decompose_var.enable(region, offset)?;
Z(CellValue::new(z_0_cell, z_0_val))
};
@ -387,9 +378,9 @@ impl<F: FieldExt> Deref for X<F> {
#[derive(Copy, Clone, Debug)]
// `y`-coordinate of the accumulator.
struct Y<F: FieldExt>(Option<F>);
struct Y<F: FieldExt>(CellValue<F>);
impl<F: FieldExt> Deref for Y<F> {
type Target = Option<F>;
type Target = CellValue<F>;
fn deref(&self) -> &Self::Target {
&self.0

13
src/circuit/gadget/ecc/chip/mul/complete.rs
View File

@ -102,17 +102,16 @@ impl Config {
)?;
// Assign final `y_a` output from incomplete addition
let y_a_cell = region.assign_advice(
|| "y_a",
let y_a = copy(
region,
|| "y_a output from incomplete addition",
self.add_config.y_qr,
offset,
|| y_a.ok_or(Error::SynthesisError),
&y_a.0,
&self.perm,
)?;
EccPoint {
x: x_a,
y: CellValue::<pallas::Base>::new(y_a_cell, *y_a),
}
EccPoint { x: x_a, y: y_a }
};
// Copy running sum `z` from incomplete addition

273
src/circuit/gadget/ecc/chip/mul/incomplete.rs
View File

@ -1,11 +1,13 @@
use std::{array, ops::Deref};
use std::ops::Deref;
use super::super::{copy, CellValue, EccConfig, EccPoint, Var};
use super::{INCOMPLETE_HI_RANGE, INCOMPLETE_LO_RANGE, X, Y, Z};
use ff::Field;
use halo2::{
circuit::Region,
plonk::{Advice, Column, ConstraintSystem, Error, Expression, Permutation, Selector},
plonk::{
Advice, Column, ConstraintSystem, Error, Expression, Fixed, Permutation, VirtualCells,
},
poly::Rotation,
};
@ -15,7 +17,7 @@ pub(super) struct Config {
// Number of bits covered by this incomplete range.
num_bits: usize,
// Selector used to constrain the cells used in incomplete addition.
pub(super) q_mul: Selector,
pub(super) q_mul: Column<Fixed>,
// Cumulative sum used to decompose the scalar.
pub(super) z: Column<Advice>,
// x-coordinate of the accumulator in each double-and-add iteration.
@ -90,74 +92,128 @@ impl Config {
// Gate for incomplete addition part of variable-base scalar multiplication.
pub(super) fn create_gate(&self, meta: &mut ConstraintSystem<pallas::Base>) {
meta.create_gate("Incomplete addition for variable-base scalar mul", |meta| {
let q_mul = meta.query_selector(self.q_mul);
let z_cur = meta.query_advice(self.z, Rotation::cur());
let z_prev = meta.query_advice(self.z, Rotation::prev());
let x_a_cur = meta.query_advice(self.x_a, Rotation::cur());
let x_a_next = meta.query_advice(self.x_a, Rotation::next());
let x_p_cur = meta.query_advice(self.x_p, Rotation::cur());
let x_p_next = meta.query_advice(self.x_p, Rotation::next());
let y_p_cur = meta.query_advice(self.y_p, Rotation::cur());
let y_p_next = meta.query_advice(self.y_p, Rotation::next());
let lambda1_cur = meta.query_advice(self.lambda1, Rotation::cur());
let lambda2_cur = meta.query_advice(self.lambda2, Rotation::cur());
let lambda1_next = meta.query_advice(self.lambda1, Rotation::next());
let lambda2_next = meta.query_advice(self.lambda2, Rotation::next());
let q_mul = meta.query_fixed(self.q_mul, Rotation::cur());
// The current bit in the scalar decomposition, k_i = z_i - 2⋅z_{i+1}.
// Recall that we assigned the cumulative variable `z_i` in descending order,
// i from n down to 0. So z_{i+1} corresponds to the `z_prev` query.
let k = z_cur - Expression::Constant(pallas::Base::from_u64(2)) * z_prev;
// Useful constants
let one = Expression::Constant(pallas::Base::one());
let two = Expression::Constant(pallas::Base::from_u64(2));
let three = Expression::Constant(pallas::Base::from_u64(3));
// y_{A,i} = (λ_{1,i} + λ_{2,i})
// * (x_{A,i} - (λ_{1,i}^2 - x_{A,i} - x_{P,i})) / 2
let y_a_cur = (lambda1_cur.clone() + lambda2_cur.clone())
* (x_a_cur.clone()
- (lambda1_cur.clone() * lambda1_cur.clone()
- x_a_cur.clone()
- x_p_cur.clone()))
* pallas::Base::TWO_INV;
// y_{A,i+1} = (λ_{1,i+1} + λ_{2,i+1})
// * (x_{A,i+1} - (λ_{1,i+1}^2 - x_{A,i+1} - x_{P,i+1})) / 2
let y_a_next = (lambda1_next.clone() + lambda2_next)
* (x_a_next.clone()
- (lambda1_next.clone() * lambda1_next - x_a_next.clone() - x_p_next.clone()))
* pallas::Base::TWO_INV;
// Check booleanity of decomposition.
let bool_check = k.clone() * (k.clone() + Expression::Constant(-pallas::Base::one()));
// The base used in double-and-add remains constant. We check that its
// x- and y- coordinates are the same throughout.
let x_p_check = x_p_cur.clone() - x_p_next;
let y_p_check = y_p_cur.clone() - y_p_next;
// λ_{1,i}⋅(x_{A,i} − x_{P,i}) − y_{A,i} + (2k_i - 1) y_{P,i} = 0
let poly1 = lambda1_cur.clone() * (x_a_cur.clone() - x_p_cur.clone()) - y_a_cur.clone()
+ (k * pallas::Base::from_u64(2) + Expression::Constant(-pallas::Base::one()))
* y_p_cur;
// (λ_{1,i} + λ_{2,i})⋅(x_{A,i} − (λ_{1,i}^2 − x_{A,i} − x_{P,i})) − 2y_{A,i}) = 0
let poly2 = {
let lambda_neg = lambda1_cur.clone() + lambda2_cur.clone();
let lambda1_expr =
lambda1_cur.clone() * lambda1_cur.clone() - x_a_cur.clone() - x_p_cur.clone();
lambda_neg * (x_a_cur.clone() - lambda1_expr)
- Expression::Constant(pallas::Base::from_u64(2)) * y_a_cur.clone()
// Closures for expressions that are derived multiple times
// x_{R,i} = λ_{1,i}^2 - x_{A,i} - x_{P,i}
let x_r = |meta: &mut VirtualCells<pallas::Base>, rotation| {
let x_a = meta.query_advice(self.x_a, rotation);
let x_p = meta.query_advice(self.x_p, rotation);
let lambda_1 = meta.query_advice(self.lambda1, rotation);
lambda_1.square() - x_a - x_p
};
// λ_{2,i}^2 − x_{A,i+1} −(λ_{1,i}^2 − x_{A,i} − x_{P,i}) − x_{A,i} = 0
let poly3 = lambda2_cur.clone() * lambda2_cur.clone()
- x_a_next.clone()
- (lambda1_cur.clone() * lambda1_cur)
+ x_p_cur;
// y_{A,i} = (λ_{1,i} + λ_{2,i}) * (x_{A,i} - x_{R,i}) / 2
let y_a = |meta: &mut VirtualCells<pallas::Base>, rotation: Rotation| {
let x_a = meta.query_advice(self.x_a, rotation);
let lambda_1 = meta.query_advice(self.lambda1, rotation);
let lambda_2 = meta.query_advice(self.lambda2, rotation);
// λ_{2,i}⋅(x_{A,i} − x_{A,i+1}) − y_{A,i} − y_{A,i+1} = 0
let poly4 = lambda2_cur * (x_a_cur - x_a_next) - y_a_cur - y_a_next;
(lambda_1 + lambda_2) * (x_a - x_r(meta, rotation)) * pallas::Base::TWO_INV
};
array::IntoIter::new([bool_check, x_p_check, y_p_check, poly1, poly2, poly3, poly4])
.map(move |poly| q_mul.clone() * poly)
let y_a_cur = y_a(meta, Rotation::cur());
let y_a_next = y_a(meta, Rotation::next());
// q_mul == 1
let q_mul_one_checks = {
let q_mul_is_one =
q_mul.clone() * (two.clone() - q_mul.clone()) * (three.clone() - q_mul.clone());
let y_a_witnessed = meta.query_advice(self.lambda1, Rotation::cur());
let y_a = y_a_next.clone();
Some(("init y_a", q_mul_is_one * (y_a - y_a_witnessed)))
};
// q_mul == 2
let q_mul_two_checks = {
let q_mul_is_two =
q_mul.clone() * (one.clone() - q_mul.clone()) * (three - q_mul.clone());
// z_i
let z_cur = meta.query_advice(self.z, Rotation::cur());
// z_{i+1}
let z_prev = meta.query_advice(self.z, Rotation::prev());
// x_{A,i}
let x_a_cur = meta.query_advice(self.x_a, Rotation::cur());
// x_{A,i-1}
let x_a_next = meta.query_advice(self.x_a, Rotation::next());
// x_{P,i}
let x_p_cur = meta.query_advice(self.x_p, Rotation::cur());
// x_{P,i-1}
let x_p_next = meta.query_advice(self.x_p, Rotation::next());
// y_{P,i}
let y_p_cur = meta.query_advice(self.y_p, Rotation::cur());
// y_{P,i-1}
let y_p_next = meta.query_advice(self.y_p, Rotation::next());
// λ_{1,i}
let lambda1_cur = meta.query_advice(self.lambda1, Rotation::cur());
// λ_{2,i}
let lambda2_cur = meta.query_advice(self.lambda2, Rotation::cur());
// The current bit in the scalar decomposition, k_i = z_i - 2⋅z_{i+1}.
// Recall that we assigned the cumulative variable `z_i` in descending order,
// i from n down to 0. So z_{i+1} corresponds to the `z_prev` query.
let k = z_cur - z_prev * pallas::Base::from_u64(2);
// Check booleanity of decomposition.
let bool_check = k.clone() * (one.clone() - k.clone());
// The base used in double-and-add remains constant. We check that its
// x- and y- coordinates are the same throughout.
let x_p_check = x_p_cur.clone() - x_p_next;
let y_p_check = y_p_cur.clone() - y_p_next;
// λ_{1,i}⋅(x_{A,i} − x_{P,i}) − y_{A,i} + (2k_i - 1) y_{P,i} = 0
let poly1 = lambda1_cur * (x_a_cur.clone() - x_p_cur) - y_a_cur.clone()
+ (k * pallas::Base::from_u64(2) - one.clone()) * y_p_cur;
// λ_{2,i}^2 − x_{A,i-1} − x_{R,i} − x_{A,i} = 0
let secant_line = lambda2_cur.clone().square()
- x_a_next.clone()
- x_r(meta, Rotation::cur())
- x_a_cur.clone();
// λ_{2,i}⋅(x_{A,i} − x_{A,i-1}) − y_{A,i} − y_{A,i-1} = 0
let poly3 = lambda2_cur * (x_a_cur - x_a_next) - y_a_cur - y_a_next;
std::iter::empty()
.chain(Some((
"bool_check when q_mul = 2",
q_mul_is_two.clone() * bool_check,
)))
.chain(Some(("x_p_check", q_mul_is_two.clone() * x_p_check)))
.chain(Some(("y_p_check", q_mul_is_two.clone() * y_p_check)))
.chain(Some(("poly1", q_mul_is_two.clone() * poly1)))
.chain(Some(("secant_line", q_mul_is_two.clone() * secant_line)))
.chain(Some(("poly3", q_mul_is_two * poly3)))
};
// q_mul == 3
let q_mul_three_checks = {
let q_mul_is_three = q_mul.clone() * (one - q_mul.clone()) * (two - q_mul);
let y_a_final = meta.query_advice(self.lambda1, Rotation::cur());
let x_a_final = meta.query_advice(self.x_a, Rotation::cur());
// λ_{2,prev}⋅(x_{A,prev} − x_{A,final}) − y_{A,prev} − y_{A,final} = 0
let poly3 = {
let lambda2_prev = meta.query_advice(self.lambda2, Rotation::prev());
let x_a_prev = meta.query_advice(self.x_a, Rotation::prev());
let y_a_prev = y_a(meta, Rotation::prev());
lambda2_prev * (x_a_prev - x_a_final) - y_a_prev - y_a_final
};
Some(("final y_a", q_mul_is_three * poly3))
};
std::iter::empty()
.chain(q_mul_one_checks)
.chain(q_mul_two_checks)
.chain(q_mul_three_checks)
});
}
@ -181,7 +237,7 @@ impl Config {
// Handle exceptional cases
let (x_p, y_p) = (base.x.value(), base.y.value());
let (x_a, y_a) = (acc.0.value(), acc.1 .0);
let (x_a, y_a) = (acc.0.value(), acc.1.value());
if let (Some(x_a), Some(y_a), Some(x_p), Some(y_p)) = (x_a, y_a, x_p, y_p) {
// A is point at infinity
@ -195,32 +251,64 @@ impl Config {
}
}
// Enable `q_mul` on all but the last row of the incomplete range.
for row in 1..(self.num_bits - 1) {
self.q_mul.enable(region, offset + row)?;
// Set q_mul values
{
// q_mul = 1 on offset 0
region.assign_fixed(
|| "q_mul = 1",
self.q_mul,
offset,
|| Ok(pallas::Base::one()),
)?;
// q_mul = 2 on all rows after offset 0, excluding the last row.
for idx in 1..(self.num_bits) {
region.assign_fixed(
|| "q_mul = 2",
self.q_mul,
offset + idx,
|| Ok(pallas::Base::from_u64(2)),
)?;
}
// q_mul = 3 on the last row.
region.assign_fixed(
|| "q_mul = 3",
self.q_mul,
offset + self.num_bits + 1,
|| Ok(pallas::Base::from_u64(3)),
)?;
}
// Initialise the running `z` sum for the scalar bits.
let mut z = copy(region, || "starting z", self.z, offset, &acc.2, &self.perm)?;
// Initialise double-and-add
let (mut x_a, mut y_a, mut z) = {
// Initialise the running `z` sum for the scalar bits.
let z = copy(region, || "starting z", self.z, offset, &acc.2, &self.perm)?;
// Initialise acc
let x_a = copy(
region,
|| "starting x_a",
self.x_a,
offset + 1,
&acc.0,
&self.perm,
)?;
let y_a = copy(
region,
|| "starting y_a",
self.lambda1,
offset,
&acc.1,
&self.perm,
)?;
(x_a, y_a.value(), z)
};
// Increase offset by 1; we used row 0 for initializing `z`.
let offset = offset + 1;
// Define `x_p`, `y_p`
let x_p = base.x.value();
let y_p = base.y.value();
// Initialise acc
let mut x_a = copy(
region,
|| "starting x_a",
self.x_a,
offset,
&acc.0,
&self.perm,
)?;
let mut y_a = *acc.1;
// Initialise vector to store all interstitial `z` running sum values.
let mut zs: Vec<Z<pallas::Base>> = Vec::new();
@ -297,7 +385,7 @@ impl Config {
let x_a_new = lambda2
.zip(x_a.value())
.zip(x_r)
.map(|((lambda2, x_a), x_r)| lambda2 * lambda2 - x_a - x_r);
.map(|((lambda2, x_a), x_r)| lambda2.square() - x_a - x_r);
y_a = lambda2
.zip(x_a.value())
.zip(x_a_new)
@ -313,6 +401,17 @@ impl Config {
x_a = CellValue::new(x_a_cell, x_a_val);
}
// Witness final y_a
let y_a = {
let cell = region.assign_advice(
|| "y_a",
self.lambda1,
offset + self.num_bits,
|| y_a.ok_or(Error::SynthesisError),
)?;
CellValue::new(cell, y_a)
};
Ok((X(x_a), Y(y_a), zs))
}
}

3
src/circuit/gadget/ecc/chip/mul/overflow.rs
View File

@ -16,8 +16,6 @@ use pasta_curves::{arithmetic::FieldExt, pallas};
use std::iter;
pub struct Config {
// Selector to check decomposition of lsb
q_mul_decompose_var: Selector,
// Selector to check z_0 = alpha + t_q (mod p)
q_mul_overflow: Selector,
// 10-bit lookup table
@ -31,7 +29,6 @@ pub struct Config {
impl From<&EccConfig> for Config {
fn from(ecc_config: &EccConfig) -> Self {
Self {
q_mul_decompose_var: ecc_config.q_mul_decompose_var,
q_mul_overflow: ecc_config.q_mul_overflow,
lookup_config: ecc_config.lookup_config.clone(),
advices: [