sapling-crypto/src/circuit/lookup.rs

308 lines
9.0 KiB
Rust

use pairing::{Engine, Field};
use super::*;
use super::num::{
AllocatedNum,
Num
};
use super::boolean::Boolean;
use bellman::{
ConstraintSystem
};
// Synthesize the constants for each base pattern.
fn synth<'a, E: Engine, I>(
window_size: usize,
constants: I,
assignment: &mut [E::Fr]
)
where I: IntoIterator<Item=&'a E::Fr>
{
assert_eq!(assignment.len(), 1 << window_size);
for (i, constant) in constants.into_iter().enumerate() {
let mut cur = assignment[i];
cur.negate();
cur.add_assign(constant);
assignment[i] = cur;
for (j, eval) in assignment.iter_mut().enumerate().skip(i + 1) {
if j & i == i {
eval.add_assign(&cur);
}
}
}
}
/// Performs a 3-bit window table lookup. `bits` is in
/// little-endian order.
pub fn lookup3_xy<E: Engine, CS>(
mut cs: CS,
bits: &[Boolean],
coords: &[(E::Fr, E::Fr)]
) -> Result<(AllocatedNum<E>, AllocatedNum<E>), SynthesisError>
where CS: ConstraintSystem<E>
{
assert_eq!(bits.len(), 3);
assert_eq!(coords.len(), 8);
// Calculate the index into `coords`
let i =
match (bits[0].get_value(), bits[1].get_value(), bits[2].get_value()) {
(Some(a_value), Some(b_value), Some(c_value)) => {
let mut tmp = 0;
if a_value {
tmp += 1;
}
if b_value {
tmp += 2;
}
if c_value {
tmp += 4;
}
Some(tmp)
},
_ => None
};
// Allocate the x-coordinate resulting from the lookup
let res_x = AllocatedNum::alloc(
cs.namespace(|| "x"),
|| {
Ok(coords[*i.get()?].0)
}
)?;
// Allocate the y-coordinate resulting from the lookup
let res_y = AllocatedNum::alloc(
cs.namespace(|| "y"),
|| {
Ok(coords[*i.get()?].1)
}
)?;
// Compute the coefficients for the lookup constraints
let mut x_coeffs = [E::Fr::zero(); 8];
let mut y_coeffs = [E::Fr::zero(); 8];
synth::<E, _>(3, coords.iter().map(|c| &c.0), &mut x_coeffs);
synth::<E, _>(3, coords.iter().map(|c| &c.1), &mut y_coeffs);
let precomp = Boolean::and(cs.namespace(|| "precomp"), &bits[1], &bits[2])?;
let one = CS::one();
cs.enforce(
|| "x-coordinate lookup",
|lc| lc + (x_coeffs[0b001], one)
+ &bits[1].lc::<E>(one, x_coeffs[0b011])
+ &bits[2].lc::<E>(one, x_coeffs[0b101])
+ &precomp.lc::<E>(one, x_coeffs[0b111]),
|lc| lc + &bits[0].lc::<E>(one, E::Fr::one()),
|lc| lc + res_x.get_variable()
- (x_coeffs[0b000], one)
- &bits[1].lc::<E>(one, x_coeffs[0b010])
- &bits[2].lc::<E>(one, x_coeffs[0b100])
- &precomp.lc::<E>(one, x_coeffs[0b110]),
);
cs.enforce(
|| "y-coordinate lookup",
|lc| lc + (y_coeffs[0b001], one)
+ &bits[1].lc::<E>(one, y_coeffs[0b011])
+ &bits[2].lc::<E>(one, y_coeffs[0b101])
+ &precomp.lc::<E>(one, y_coeffs[0b111]),
|lc| lc + &bits[0].lc::<E>(one, E::Fr::one()),
|lc| lc + res_y.get_variable()
- (y_coeffs[0b000], one)
- &bits[1].lc::<E>(one, y_coeffs[0b010])
- &bits[2].lc::<E>(one, y_coeffs[0b100])
- &precomp.lc::<E>(one, y_coeffs[0b110]),
);
Ok((res_x, res_y))
}
/// Performs a 3-bit window table lookup, where
/// one of the bits is a sign bit.
pub fn lookup3_xy_with_conditional_negation<E: Engine, CS>(
mut cs: CS,
bits: &[Boolean],
coords: &[(E::Fr, E::Fr)]
) -> Result<(Num<E>, Num<E>), SynthesisError>
where CS: ConstraintSystem<E>
{
assert_eq!(bits.len(), 3);
assert_eq!(coords.len(), 4);
// Calculate the index into `coords`
let i =
match (bits[0].get_value(), bits[1].get_value()) {
(Some(a_value), Some(b_value)) => {
let mut tmp = 0;
if a_value {
tmp += 1;
}
if b_value {
tmp += 2;
}
Some(tmp)
},
_ => None
};
// Allocate the y-coordinate resulting from the lookup
// and conditional negation
let y = AllocatedNum::alloc(
cs.namespace(|| "y"),
|| {
let mut tmp = coords[*i.get()?].1;
if *bits[2].get_value().get()? {
tmp.negate();
}
Ok(tmp)
}
)?;
let one = CS::one();
// Compute the coefficients for the lookup constraints
let mut x_coeffs = [E::Fr::zero(); 4];
let mut y_coeffs = [E::Fr::zero(); 4];
synth::<E, _>(2, coords.iter().map(|c| &c.0), &mut x_coeffs);
synth::<E, _>(2, coords.iter().map(|c| &c.1), &mut y_coeffs);
let precomp = Boolean::and(cs.namespace(|| "precomp"), &bits[0], &bits[1])?;
let x = Num::zero()
.add_bool_with_coeff(one, &Boolean::constant(true), x_coeffs[0b00])
.add_bool_with_coeff(one, &bits[0], x_coeffs[0b01])
.add_bool_with_coeff(one, &bits[1], x_coeffs[0b10])
.add_bool_with_coeff(one, &precomp, x_coeffs[0b11]);
let y_lc = precomp.lc::<E>(one, y_coeffs[0b11]) +
&bits[1].lc::<E>(one, y_coeffs[0b10]) +
&bits[0].lc::<E>(one, y_coeffs[0b01]) +
(y_coeffs[0b00], one);
cs.enforce(
|| "y-coordinate lookup",
|lc| lc + &y_lc + &y_lc,
|lc| lc + &bits[2].lc::<E>(one, E::Fr::one()),
|lc| lc + &y_lc - y.get_variable()
);
Ok((x, y.into()))
}
#[cfg(test)]
mod test {
use rand::{SeedableRng, Rand, Rng, XorShiftRng};
use super::*;
use ::circuit::test::*;
use ::circuit::boolean::{Boolean, AllocatedBit};
use pairing::bls12_381::{Bls12, Fr};
#[test]
fn test_lookup3_xy() {
let mut rng = XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0656]);
for _ in 0..100 {
let mut cs = TestConstraintSystem::<Bls12>::new();
let a_val = rng.gen();
let a = Boolean::from(
AllocatedBit::alloc(cs.namespace(|| "a"), Some(a_val)).unwrap()
);
let b_val = rng.gen();
let b = Boolean::from(
AllocatedBit::alloc(cs.namespace(|| "b"), Some(b_val)).unwrap()
);
let c_val = rng.gen();
let c = Boolean::from(
AllocatedBit::alloc(cs.namespace(|| "c"), Some(c_val)).unwrap()
);
let bits = vec![a, b, c];
let points: Vec<(Fr, Fr)> = (0..8).map(|_| (rng.gen(), rng.gen())).collect();
let res = lookup3_xy(&mut cs, &bits, &points).unwrap();
assert!(cs.is_satisfied());
let mut index = 0;
if a_val { index += 1 }
if b_val { index += 2 }
if c_val { index += 4 }
assert_eq!(res.0.get_value().unwrap(), points[index].0);
assert_eq!(res.1.get_value().unwrap(), points[index].1);
}
}
#[test]
fn test_lookup3_xy_with_conditional_negation() {
let mut rng = XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
for _ in 0..100 {
let mut cs = TestConstraintSystem::<Bls12>::new();
let a_val = rng.gen();
let a = Boolean::from(
AllocatedBit::alloc(cs.namespace(|| "a"), Some(a_val)).unwrap()
);
let b_val = rng.gen();
let b = Boolean::from(
AllocatedBit::alloc(cs.namespace(|| "b"), Some(b_val)).unwrap()
);
let c_val = rng.gen();
let c = Boolean::from(
AllocatedBit::alloc(cs.namespace(|| "c"), Some(c_val)).unwrap()
);
let bits = vec![a, b, c];
let points: Vec<(Fr, Fr)> = (0..4).map(|_| (rng.gen(), rng.gen())).collect();
let res = lookup3_xy_with_conditional_negation(&mut cs, &bits, &points).unwrap();
assert!(cs.is_satisfied());
let mut index = 0;
if a_val { index += 1 }
if b_val { index += 2 }
assert_eq!(res.0.get_value().unwrap(), points[index].0);
let mut tmp = points[index].1;
if c_val { tmp.negate() }
assert_eq!(res.1.get_value().unwrap(), tmp);
}
}
#[test]
fn test_synth() {
let mut rng = XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
let window_size = 4;
let mut assignment = vec![Fr::zero(); 1 << window_size];
let constants: Vec<_> = (0..(1 << window_size)).map(|_| Fr::rand(&mut rng)).collect();
synth::<Bls12, _>(window_size, &constants, &mut assignment);
for b in 0..(1 << window_size) {
let mut acc = Fr::zero();
for j in 0..(1 << window_size) {
if j & b == j {
acc.add_assign(&assignment[j]);
}
}
assert_eq!(acc, constants[b]);
}
}
}