Implement pedersen hashes inside and outside of the circuit.
This commit is contained in:
Sean Bowe
parent
07f2e553a7
commit
e9c9618ef4
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@ -5,7 +5,8 @@ pub mod boolean;
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pub mod uint32;
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pub mod blake2s;
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pub mod num;
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pub mod mont;
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pub mod mont; // TODO: rename
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pub mod pedersen_hash;
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use bellman::SynthesisError;
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@ -27,8 +27,9 @@ use ::jubjub::{
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};
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pub struct EdwardsPoint<E: Engine, Var> {
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x: AllocatedNum<E, Var>,
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y: AllocatedNum<E, Var>
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// TODO: make these not pub
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pub x: AllocatedNum<E, Var>,
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pub y: AllocatedNum<E, Var>
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}
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impl<E: JubjubEngine, Var: Copy> EdwardsPoint<E, Var> {
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@ -0,0 +1,310 @@
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use pairing::{Engine, Field};
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use super::*;
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use super::mont::{
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MontgomeryPoint,
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EdwardsPoint
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};
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use super::num::AllocatedNum;
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use super::boolean::Boolean;
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use ::jubjub::*;
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use bellman::{
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ConstraintSystem,
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LinearCombination
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};
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// Synthesize the constants for each base pattern.
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fn synth<'a, E: Engine, I>(
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window_size: usize,
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constants: I,
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assignment: &mut [E::Fr]
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)
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where I: IntoIterator<Item=&'a E::Fr>
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{
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assert_eq!(assignment.len(), 1 << window_size);
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for (i, constant) in constants.into_iter().enumerate() {
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let mut cur = assignment[i];
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cur.negate();
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cur.add_assign(constant);
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assignment[i] = cur;
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for (j, eval) in assignment.iter_mut().enumerate().skip(i + 1) {
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if j & i == i {
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eval.add_assign(&cur);
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}
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}
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}
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}
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pub fn pedersen_hash<E: JubjubEngine, CS, Var: Copy>(
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mut cs: CS,
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bits: &[Boolean<Var>],
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params: &E::Params
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) -> Result<EdwardsPoint<E, Var>, SynthesisError>
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where CS: ConstraintSystem<E, Variable=Var>
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{
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let mut edwards_result = None;
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let mut bits = bits.iter();
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let mut segment_generators = params.pedersen_circuit_generators().iter();
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let boolean_false = Boolean::constant(false);
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let mut segment_i = 0;
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loop {
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let mut segment_result = None;
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let mut segment_windows = &segment_generators.next()
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.expect("enough segments")[..];
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let mut window_i = 0;
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while let Some(a) = bits.next() {
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let b = bits.next().unwrap_or(&boolean_false);
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let c = bits.next().unwrap_or(&boolean_false);
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let tmp = lookup3_xy_with_conditional_negation(
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cs.namespace(|| format!("segment {}, window {}", segment_i, window_i)),
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&[a.clone(), b.clone(), c.clone()],
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&segment_windows[0]
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)?;
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let tmp = MontgomeryPoint::interpret_unchecked(tmp.0, tmp.1);
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match segment_result {
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None => {
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segment_result = Some(tmp);
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},
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Some(ref mut segment_result) => {
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*segment_result = tmp.add(
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cs.namespace(|| format!("addition of segment {}, window {}", segment_i, window_i)),
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segment_result,
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params
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)?;
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}
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}
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segment_windows = &segment_windows[1..];
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if segment_windows.len() == 0 {
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break;
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}
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window_i += 1;
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}
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match segment_result {
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Some(segment_result) => {
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// Convert this segment into twisted Edwards form.
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let segment_result = segment_result.into_edwards(
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cs.namespace(|| format!("conversion of segment {} into edwards", segment_i)),
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params
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)?;
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match edwards_result {
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Some(ref mut edwards_result) => {
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*edwards_result = segment_result.add(
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cs.namespace(|| format!("addition of segment {} to accumulator", segment_i)),
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edwards_result,
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params
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)?;
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},
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None => {
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edwards_result = Some(segment_result);
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}
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}
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},
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None => {
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// We didn't process any new bits.
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break;
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}
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}
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segment_i += 1;
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}
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// TODO: maybe assert bits.len() > 0
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Ok(edwards_result.unwrap())
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}
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/// Performs a 3-bit window table lookup, where
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/// one of the bits is a sign bit.
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fn lookup3_xy_with_conditional_negation<E: Engine, CS, Var: Copy>(
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mut cs: CS,
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bits: &[Boolean<Var>],
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coords: &[(E::Fr, E::Fr)]
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) -> Result<(AllocatedNum<E, Var>, AllocatedNum<E, Var>), SynthesisError>
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where CS: ConstraintSystem<E, Variable=Var>
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{
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assert_eq!(bits.len(), 3);
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assert_eq!(coords.len(), 4);
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// Calculate the index into `coords`
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let i =
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match (bits[0].get_value(), bits[1].get_value()) {
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(Some(a_value), Some(b_value)) => {
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let mut tmp = 0;
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if a_value {
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tmp += 1;
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}
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if b_value {
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tmp += 2;
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}
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Some(tmp)
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},
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_ => None
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};
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// Allocate the x-coordinate resulting from the lookup
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let res_x = AllocatedNum::alloc(
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cs.namespace(|| "x"),
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|| {
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Ok(coords[*i.get()?].0)
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}
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)?;
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// Allocate the y-coordinate resulting from the lookup
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let res_y = AllocatedNum::alloc(
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cs.namespace(|| "y"),
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|| {
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Ok(coords[*i.get()?].1)
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}
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)?;
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let one = cs.one();
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// Compute the coefficients for the lookup constraints
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let mut x_coeffs = [E::Fr::zero(); 4];
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let mut y_coeffs = [E::Fr::zero(); 4];
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synth::<E, _>(2, coords.iter().map(|c| &c.0), &mut x_coeffs);
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synth::<E, _>(2, coords.iter().map(|c| &c.1), &mut y_coeffs);
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cs.enforce(
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|| "x-coordinate lookup",
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LinearCombination::<Var, E>::zero() + (x_coeffs[0b01], one)
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+ &bits[1].lc::<E>(one, x_coeffs[0b11]),
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LinearCombination::<Var, E>::zero() + &bits[0].lc::<E>(one, E::Fr::one()),
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LinearCombination::<Var, E>::zero() + res_x.get_variable()
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- (x_coeffs[0b00], one)
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- &bits[1].lc::<E>(one, x_coeffs[0b10])
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);
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cs.enforce(
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|| "y-coordinate lookup",
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LinearCombination::<Var, E>::zero() + (y_coeffs[0b01], one)
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+ &bits[1].lc::<E>(one, y_coeffs[0b11]),
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LinearCombination::<Var, E>::zero() + &bits[0].lc::<E>(one, E::Fr::one()),
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LinearCombination::<Var, E>::zero() + res_y.get_variable()
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- (y_coeffs[0b00], one)
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- &bits[1].lc::<E>(one, y_coeffs[0b10])
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);
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let final_y = res_y.conditionally_negate(&mut cs, &bits[2])?;
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Ok((res_x, final_y))
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}
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#[cfg(test)]
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mod test {
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use rand::{SeedableRng, Rand, Rng, XorShiftRng};
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use super::*;
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use ::circuit::test::*;
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use ::circuit::boolean::{Boolean, AllocatedBit};
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use pairing::bls12_381::{Bls12, Fr};
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#[test]
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fn test_pedersen_hash() {
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let mut rng = XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
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let params = &JubjubBls12::new();
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for length in 1..1000 {
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for _ in 0..5 {
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let mut input: Vec<bool> = (0..length).map(|_| rng.gen()).collect();
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let mut cs = TestConstraintSystem::<Bls12>::new();
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let input_bools: Vec<Boolean<_>> = input.iter().enumerate().map(|(i, b)| {
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Boolean::from(
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AllocatedBit::alloc(cs.namespace(|| format!("input {}", i)), Some(*b)).unwrap()
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)
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}).collect();
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let res = pedersen_hash(
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cs.namespace(|| "pedersen hash"),
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&input_bools,
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params
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).unwrap();
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assert!(cs.is_satisfied());
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let expected = ::pedersen_hash::pedersen_hash::<Bls12, _>(
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input.into_iter(),
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params
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).into_xy();
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assert_eq!(res.x.get_value().unwrap(), expected.0);
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assert_eq!(res.y.get_value().unwrap(), expected.1);
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}
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}
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}
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#[test]
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fn test_lookup3_xy_with_conditional_negation() {
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let mut rng = XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
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for _ in 0..100 {
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let mut cs = TestConstraintSystem::<Bls12>::new();
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let a_val = rng.gen();
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let a = Boolean::from(
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AllocatedBit::alloc(cs.namespace(|| "a"), Some(a_val)).unwrap()
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);
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let b_val = rng.gen();
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let b = Boolean::from(
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AllocatedBit::alloc(cs.namespace(|| "b"), Some(b_val)).unwrap()
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);
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let c_val = rng.gen();
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let c = Boolean::from(
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AllocatedBit::alloc(cs.namespace(|| "c"), Some(c_val)).unwrap()
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);
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let bits = vec![a, b, c];
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let points: Vec<(Fr, Fr)> = (0..4).map(|_| (rng.gen(), rng.gen())).collect();
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let res = lookup3_xy_with_conditional_negation(&mut cs, &bits, &points).unwrap();
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assert!(cs.is_satisfied());
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let mut index = 0;
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if a_val { index += 1 }
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if b_val { index += 2 }
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assert_eq!(res.0.get_value().unwrap(), points[index].0);
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let mut tmp = points[index].1;
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if c_val { tmp.negate() }
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assert_eq!(res.1.get_value().unwrap(), tmp);
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}
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}
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#[test]
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fn test_synth() {
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let mut rng = XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
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let window_size = 4;
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let mut assignment = vec![Fr::zero(); (1 << window_size)];
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let constants: Vec<_> = (0..(1 << window_size)).map(|_| Fr::rand(&mut rng)).collect();
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synth::<Bls12, _>(window_size, &constants, &mut assignment);
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for b in 0..(1 << window_size) {
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let mut acc = Fr::zero();
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for j in 0..(1 << window_size) {
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if j & b == j {
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acc.add_assign(&assignment[j]);
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}
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}
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assert_eq!(acc, constants[b]);
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}
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}
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}
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@ -21,6 +21,8 @@ use pairing::{
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SqrtField
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};
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use super::group_hash::group_hash;
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use pairing::bls12_381::{
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Bls12,
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Fr
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@ -42,6 +44,9 @@ pub trait JubjubParams<E: JubjubEngine>: Sized {
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fn montgomery_a(&self) -> &E::Fr;
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fn montgomery_2a(&self) -> &E::Fr;
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fn scale(&self) -> &E::Fr;
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fn pedersen_hash_generators(&self) -> &[edwards::Point<E, PrimeOrder>];
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fn pedersen_hash_chunks_per_generator(&self) -> usize;
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fn pedersen_circuit_generators(&self) -> &[Vec<Vec<(E::Fr, E::Fr)>>];
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}
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pub enum Unknown { }
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@ -58,7 +63,9 @@ pub struct JubjubBls12 {
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edwards_d: Fr,
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montgomery_a: Fr,
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montgomery_2a: Fr,
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scale: Fr
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scale: Fr,
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pedersen_hash_generators: Vec<edwards::Point<Bls12, PrimeOrder>>,
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pedersen_circuit_generators: Vec<Vec<Vec<(Fr, Fr)>>>
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}
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impl JubjubParams<Bls12> for JubjubBls12 {
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@ -66,6 +73,15 @@ impl JubjubParams<Bls12> for JubjubBls12 {
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fn montgomery_a(&self) -> &Fr { &self.montgomery_a }
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fn montgomery_2a(&self) -> &Fr { &self.montgomery_2a }
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fn scale(&self) -> &Fr { &self.scale }
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fn pedersen_hash_generators(&self) -> &[edwards::Point<Bls12, PrimeOrder>] {
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&self.pedersen_hash_generators
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}
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fn pedersen_hash_chunks_per_generator(&self) -> usize {
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62
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}
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fn pedersen_circuit_generators(&self) -> &[Vec<Vec<(Fr, Fr)>>] {
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&self.pedersen_circuit_generators
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}
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}
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impl JubjubBls12 {
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@ -74,7 +90,7 @@ impl JubjubBls12 {
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let mut montgomery_2a = montgomery_a;
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montgomery_2a.double();
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JubjubBls12 {
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let mut tmp = JubjubBls12 {
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// d = -(10240/10241)
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edwards_d: Fr::from_str("19257038036680949359750312669786877991949435402254120286184196891950884077233").unwrap(),
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// A = 40962
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@ -82,8 +98,55 @@ impl JubjubBls12 {
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// 2A = 2.A
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montgomery_2a: montgomery_2a,
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// scaling factor = sqrt(4 / (a - d))
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scale: Fr::from_str("17814886934372412843466061268024708274627479829237077604635722030778476050649").unwrap()
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scale: Fr::from_str("17814886934372412843466061268024708274627479829237077604635722030778476050649").unwrap(),
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pedersen_hash_generators: vec![],
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pedersen_circuit_generators: vec![]
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};
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{
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let mut cur = 0;
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let mut pedersen_hash_generators = vec![];
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// TODO: pre-generate the right amount
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while pedersen_hash_generators.len() < 10 {
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let gh = group_hash(&[cur], &tmp);
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cur += 1;
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if let Some(gh) = gh {
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pedersen_hash_generators.push(edwards::Point::from_montgomery(&gh, &tmp));
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}
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}
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tmp.pedersen_hash_generators = pedersen_hash_generators;
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}
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{
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let mut pedersen_circuit_generators = vec![];
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for mut gen in tmp.pedersen_hash_generators.iter().cloned() {
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let mut gen = montgomery::Point::from_edwards(&gen, &tmp);
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let mut windows = vec![];
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for _ in 0..tmp.pedersen_hash_chunks_per_generator() {
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let mut coeffs = vec![];
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let mut g = gen.clone();
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for _ in 0..4 {
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coeffs.push(g.into_xy().expect("cannot produce O"));
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g = g.add(&gen, &tmp);
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}
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windows.push(coeffs);
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for _ in 0..4 {
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gen = gen.double(&tmp);
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}
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}
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pedersen_circuit_generators.push(windows);
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}
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tmp.pedersen_circuit_generators = pedersen_circuit_generators;
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}
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tmp
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}
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}
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@ -9,6 +9,7 @@ use super::{
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use pairing::{
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Field,
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PrimeField,
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PrimeFieldRepr,
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SqrtField,
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LegendreSymbol
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};
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@ -311,4 +312,33 @@ fn test_jubjub_params<E: JubjubEngine>(params: &E::Params) {
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tmp = tmp.sqrt().unwrap();
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assert_eq!(&tmp, params.scale());
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}
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{
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// Check that the number of windows per generator
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// in the Pedersen hash does not allow for collisions
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let mut cur = E::Fr::one().into_repr();
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let mut pacc = E::Fr::zero().into_repr();
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let mut nacc = E::Fr::char();
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for _ in 0..params.pedersen_hash_chunks_per_generator()
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||||
{
|
||||
// tmp = cur * 4
|
||||
let mut tmp = cur;
|
||||
tmp.mul2();
|
||||
tmp.mul2();
|
||||
|
||||
assert_eq!(pacc.add_nocarry(&tmp), false);
|
||||
assert_eq!(nacc.sub_noborrow(&tmp), false);
|
||||
|
||||
assert!(pacc < E::Fr::char());
|
||||
assert!(pacc < nacc);
|
||||
|
||||
// cur = cur * 16
|
||||
for _ in 0..4 {
|
||||
cur.mul2();
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
|
|||
|
|
@ -7,3 +7,4 @@ extern crate rand;
|
|||
pub mod jubjub;
|
||||
pub mod circuit;
|
||||
pub mod group_hash;
|
||||
pub mod pedersen_hash;
|
||||
|
|
|
|||
|
|
@ -0,0 +1,68 @@
|
|||
use jubjub::*;
|
||||
use pairing::*;
|
||||
|
||||
pub fn pedersen_hash<E, I>(
|
||||
bits: I,
|
||||
params: &E::Params
|
||||
) -> edwards::Point<E, PrimeOrder>
|
||||
where I: IntoIterator<Item=bool>,
|
||||
E: JubjubEngine
|
||||
{
|
||||
let mut bits = bits.into_iter();
|
||||
|
||||
let mut result = edwards::Point::zero();
|
||||
let mut generators = params.pedersen_hash_generators().iter();
|
||||
|
||||
loop {
|
||||
let mut acc = E::Fs::zero();
|
||||
let mut cur = E::Fs::one();
|
||||
let mut chunks_remaining = params.pedersen_hash_chunks_per_generator();
|
||||
let mut encountered_bits = false;
|
||||
|
||||
// Grab three bits from the input
|
||||
while let Some(a) = bits.next() {
|
||||
encountered_bits = true;
|
||||
|
||||
let b = bits.next().unwrap_or(false);
|
||||
let c = bits.next().unwrap_or(false);
|
||||
|
||||
// Start computing this portion of the scalar
|
||||
let mut tmp = cur;
|
||||
if a {
|
||||
tmp.add_assign(&cur);
|
||||
}
|
||||
cur.double(); // 2^1 * cur
|
||||
if b {
|
||||
tmp.add_assign(&cur);
|
||||
}
|
||||
|
||||
// conditionally negate
|
||||
if c {
|
||||
tmp.negate();
|
||||
}
|
||||
|
||||
acc.add_assign(&tmp);
|
||||
|
||||
chunks_remaining -= 1;
|
||||
|
||||
if chunks_remaining == 0 {
|
||||
break;
|
||||
} else {
|
||||
cur.double(); // 2^2 * cur
|
||||
cur.double(); // 2^3 * cur
|
||||
cur.double(); // 2^4 * cur
|
||||
}
|
||||
}
|
||||
|
||||
if !encountered_bits {
|
||||
break;
|
||||
}
|
||||
|
||||
// TODO: use wNAF or something
|
||||
let mut tmp = generators.next().expect("we don't have enough generators").clone();
|
||||
tmp = tmp.mul(acc, params);
|
||||
result = result.add(&tmp, params);
|
||||
}
|
||||
|
||||
result
|
||||
}
|
||||
Loading…
Reference in New Issue