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moved sqrt to PrimeField

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This commit is contained in:
Nicholas Ward 2022-09-26 11:31:11 -07:00
parent a053372176
commit 33d97eff1c
3 changed files with 58 additions and 65 deletions
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55
field/src/goldilocks_field.rs
View File

@ -280,61 +280,6 @@ impl DivAssign for GoldilocksField {
}
}
impl GoldilocksField {
pub fn is_quadratic_residue(&self) -> bool {
if self.is_zero() {
return true;
}
// This is based on Euler's criterion.
let power = Self::NEG_ONE.to_canonical_biguint() / 2u8;
let exp = self.exp_biguint(&power);
if exp == Self::ONE {
return true;
}
if exp == Self::NEG_ONE {
return false;
}
panic!("Unreachable")
}
pub fn sqrt(&self) -> Option<Self> {
if self.is_zero() {
Some(*self)
} else if self.is_quadratic_residue() {
let t = (Self::order() - BigUint::from(1u32))
/ (BigUint::from(2u32).pow(Self::TWO_ADICITY as u32));
let mut z = Self::POWER_OF_TWO_GENERATOR;
let mut w = self.exp_biguint(&((t - BigUint::from(1u32)) / BigUint::from(2u32)));
let mut x = w * *self;
let mut b = x * w;
let mut v = Self::TWO_ADICITY as usize;
while !b.is_one() {
let mut k = 0usize;
let mut b2k = b;
while !b2k.is_one() {
b2k = b2k * b2k;
k += 1;
}
let j = v - k - 1;
w = z;
for _ in 0..j {
w = w * w;
}
z = w * w;
b *= z;
x *= w;
v = k;
}
Some(x)
} else {
None
}
}
}
/// Fast addition modulo ORDER for x86-64.
/// This function is marked unsafe for the following reasons:
/// - It is only correct if x + y < 2**64 + ORDER = 0x1ffffffff00000001.

53
field/src/types.rs
View File

@ -427,6 +427,59 @@ pub trait Field:
pub trait PrimeField: Field {
fn to_canonical_biguint(&self) -> BigUint;
fn is_quadratic_residue(&self) -> bool {
if self.is_zero() {
return true;
}
// This is based on Euler's criterion.
let power = Self::NEG_ONE.to_canonical_biguint() / 2u8;
let exp = self.exp_biguint(&power);
if exp == Self::ONE {
return true;
}
if exp == Self::NEG_ONE {
return false;
}
panic!("Unreachable")
}
fn sqrt(&self) -> Option<Self> {
if self.is_zero() {
Some(*self)
} else if self.is_quadratic_residue() {
let t = (Self::order() - BigUint::from(1u32))
/ (BigUint::from(2u32).pow(Self::TWO_ADICITY as u32));
let mut z = Self::POWER_OF_TWO_GENERATOR;
let mut w = self.exp_biguint(&((t - BigUint::from(1u32)) / BigUint::from(2u32)));
let mut x = w * *self;
let mut b = x * w;
let mut v = Self::TWO_ADICITY as usize;
while !b.is_one() {
let mut k = 0usize;
let mut b2k = b;
while !b2k.is_one() {
b2k = b2k * b2k;
k += 1;
}
let j = v - k - 1;
w = z;
for _ in 0..j {
w = w * w;
}
z = w * w;
b *= z;
x *= w;
v = k;
}
Some(x)
} else {
None
}
}
}
/// A finite field of order less than 2^64.

15
plonky2/examples/square_root.rs
View File

@ -1,7 +1,7 @@
use std::marker::PhantomData;
use anyhow::Result;
use plonky2::field::types::Field;
use plonky2::field::types::{Field, PrimeField};
use plonky2::hash::hash_types::RichField;
use plonky2::iop::generator::{GeneratedValues, SimpleGenerator};
use plonky2::iop::target::Target;
@ -10,7 +10,6 @@ use plonky2::plonk::circuit_builder::CircuitBuilder;
use plonky2::plonk::circuit_data::CircuitConfig;
use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
use plonky2_field::extension::Extendable;
use plonky2_field::goldilocks_field::GoldilocksField;
#[derive(Debug)]
struct SquareRootGenerator<F: RichField + Extendable<D>, const D: usize> {
@ -19,18 +18,14 @@ struct SquareRootGenerator<F: RichField + Extendable<D>, const D: usize> {
_phantom: PhantomData<F>,
}
// We implement specifically for the Goldilocks field because it's currently the only field with
// the sqrt() function written.
impl SimpleGenerator<GoldilocksField> for SquareRootGenerator<GoldilocksField, 2> {
impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
for SquareRootGenerator<F, D>
{
fn dependencies(&self) -> Vec<Target> {
vec![self.x_squared]
}
fn run_once(
&self,
witness: &PartitionWitness<GoldilocksField>,
out_buffer: &mut GeneratedValues<GoldilocksField>,
) {
fn run_once(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
let x_squared = witness.get_target(self.x_squared);
let x = x_squared.sqrt().unwrap();