Implement pedersen hashes inside and outside of the circuit.

src/circuit/mod.rs

@@ -5,7 +5,8 @@ pub mod boolean;
 pub mod uint32;
 pub mod blake2s;
 pub mod num;
-pub mod mont;
+pub mod mont; // TODO: rename
+pub mod pedersen_hash;
 
 use bellman::SynthesisError;
 

src/circuit/mont.rs

@@ -27,8 +27,9 @@ use ::jubjub::{
 };
 
 pub struct EdwardsPoint<E: Engine, Var> {
-    x: AllocatedNum<E, Var>,
+    // TODO: make these not pub
-    y: AllocatedNum<E, Var>
+    pub x: AllocatedNum<E, Var>,
+    pub y: AllocatedNum<E, Var>
 }
 
 impl<E: JubjubEngine, Var: Copy> EdwardsPoint<E, Var> {

src/circuit/pedersen_hash.rs

@@ -0,0 +1,310 @@
+use pairing::{Engine, Field};
+use super::*;
+use super::mont::{
+    MontgomeryPoint,
+    EdwardsPoint
+};
+use super::num::AllocatedNum;
+use super::boolean::Boolean;
+use ::jubjub::*;
+use bellman::{
+    ConstraintSystem,
+    LinearCombination
+};
+
+// 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);
+            }
+        }
+    }
+}
+
+pub fn pedersen_hash<E: JubjubEngine, CS, Var: Copy>(
+    mut cs: CS,
+    bits: &[Boolean<Var>],
+    params: &E::Params
+) -> Result<EdwardsPoint<E, Var>, SynthesisError>
+    where CS: ConstraintSystem<E, Variable=Var>
+{
+    let mut edwards_result = None;
+    let mut bits = bits.iter();
+    let mut segment_generators = params.pedersen_circuit_generators().iter();
+    let boolean_false = Boolean::constant(false);
+
+    let mut segment_i = 0;
+    loop {
+        let mut segment_result = None;
+        let mut segment_windows = &segment_generators.next()
+                                                     .expect("enough segments")[..];
+
+        let mut window_i = 0;
+        while let Some(a) = bits.next() {
+            let b = bits.next().unwrap_or(&boolean_false);
+            let c = bits.next().unwrap_or(&boolean_false);
+
+            let tmp = lookup3_xy_with_conditional_negation(
+                cs.namespace(|| format!("segment {}, window {}", segment_i, window_i)),
+                &[a.clone(), b.clone(), c.clone()],
+                &segment_windows[0]
+            )?;
+
+            let tmp = MontgomeryPoint::interpret_unchecked(tmp.0, tmp.1);
+
+            match segment_result {
+                None => {
+                    segment_result = Some(tmp);
+                },
+                Some(ref mut segment_result) => {
+                    *segment_result = tmp.add(
+                        cs.namespace(|| format!("addition of segment {}, window {}", segment_i, window_i)),
+                        segment_result,
+                        params
+                    )?;
+                }
+            }
+
+            segment_windows = &segment_windows[1..];
+
+            if segment_windows.len() == 0 {
+                break;
+            }
+
+            window_i += 1;
+        }
+
+        match segment_result {
+            Some(segment_result) => {
+                // Convert this segment into twisted Edwards form.
+                let segment_result = segment_result.into_edwards(
+                    cs.namespace(|| format!("conversion of segment {} into edwards", segment_i)),
+                    params
+                )?;
+
+                match edwards_result {
+                    Some(ref mut edwards_result) => {
+                        *edwards_result = segment_result.add(
+                            cs.namespace(|| format!("addition of segment {} to accumulator", segment_i)),
+                            edwards_result,
+                            params
+                        )?;
+                    },
+                    None => {
+                        edwards_result = Some(segment_result);
+                    }
+                }
+            },
+            None => {
+                // We didn't process any new bits.
+                break;
+            }
+        }
+
+        segment_i += 1;
+    }
+
+    // TODO: maybe assert bits.len() > 0
+    Ok(edwards_result.unwrap())
+}
+
+/// Performs a 3-bit window table lookup, where
+/// one of the bits is a sign bit.
+fn lookup3_xy_with_conditional_negation<E: Engine, CS, Var: Copy>(
+    mut cs: CS,
+    bits: &[Boolean<Var>],
+    coords: &[(E::Fr, E::Fr)]
+) -> Result<(AllocatedNum<E, Var>, AllocatedNum<E, Var>), SynthesisError>
+    where CS: ConstraintSystem<E, Variable=Var>
+{
+    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 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)
+        }
+    )?;
+
+    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);
+
+    cs.enforce(
+        || "x-coordinate lookup",
+        LinearCombination::<Var, E>::zero() + (x_coeffs[0b01], one)
+                                            + &bits[1].lc::<E>(one, x_coeffs[0b11]),
+        LinearCombination::<Var, E>::zero() + &bits[0].lc::<E>(one, E::Fr::one()),
+        LinearCombination::<Var, E>::zero() + res_x.get_variable()
+                                            - (x_coeffs[0b00], one)
+                                            - &bits[1].lc::<E>(one, x_coeffs[0b10])
+    );
+
+    cs.enforce(
+        || "y-coordinate lookup",
+        LinearCombination::<Var, E>::zero() + (y_coeffs[0b01], one)
+                                            + &bits[1].lc::<E>(one, y_coeffs[0b11]),
+        LinearCombination::<Var, E>::zero() + &bits[0].lc::<E>(one, E::Fr::one()),
+        LinearCombination::<Var, E>::zero() + res_y.get_variable()
+                                            - (y_coeffs[0b00], one)
+                                            - &bits[1].lc::<E>(one, y_coeffs[0b10])
+    );
+
+    let final_y = res_y.conditionally_negate(&mut cs, &bits[2])?;
+
+    Ok((res_x, final_y))
+}
+
+#[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_pedersen_hash() {
+        let mut rng = XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
+        let params = &JubjubBls12::new();
+
+        for length in 1..1000 {
+            for _ in 0..5 {
+                let mut input: Vec<bool> = (0..length).map(|_| rng.gen()).collect();
+
+                let mut cs = TestConstraintSystem::<Bls12>::new();
+
+                let input_bools: Vec<Boolean<_>> = input.iter().enumerate().map(|(i, b)| {
+                    Boolean::from(
+                        AllocatedBit::alloc(cs.namespace(|| format!("input {}", i)), Some(*b)).unwrap()
+                    )
+                }).collect();
+
+                let res = pedersen_hash(
+                    cs.namespace(|| "pedersen hash"),
+                    &input_bools,
+                    params
+                ).unwrap();
+
+                assert!(cs.is_satisfied());
+
+                let expected = ::pedersen_hash::pedersen_hash::<Bls12, _>(
+                    input.into_iter(),
+                    params
+                ).into_xy();
+
+                assert_eq!(res.x.get_value().unwrap(), expected.0);
+                assert_eq!(res.y.get_value().unwrap(), expected.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]);
+        }
+    }
+}

src/jubjub/mod.rs

@@ -21,6 +21,8 @@ use pairing::{
     SqrtField
 };
 
+use super::group_hash::group_hash;
+
 use pairing::bls12_381::{
     Bls12,
     Fr
@@ -42,6 +44,9 @@ pub trait JubjubParams<E: JubjubEngine>: Sized {
     fn montgomery_a(&self) -> &E::Fr;
     fn montgomery_2a(&self) -> &E::Fr;
     fn scale(&self) -> &E::Fr;
+    fn pedersen_hash_generators(&self) -> &[edwards::Point<E, PrimeOrder>];
+    fn pedersen_hash_chunks_per_generator(&self) -> usize;
+    fn pedersen_circuit_generators(&self) -> &[Vec<Vec<(E::Fr, E::Fr)>>];
 }
 
 pub enum Unknown { }
@@ -58,7 +63,9 @@ pub struct JubjubBls12 {
     edwards_d: Fr,
     montgomery_a: Fr,
     montgomery_2a: Fr,
-    scale: Fr
+    scale: Fr,
+    pedersen_hash_generators: Vec<edwards::Point<Bls12, PrimeOrder>>,
+    pedersen_circuit_generators: Vec<Vec<Vec<(Fr, Fr)>>>
 }
 
 impl JubjubParams<Bls12> for JubjubBls12 {
@@ -66,6 +73,15 @@ impl JubjubParams<Bls12> for JubjubBls12 {
     fn montgomery_a(&self) -> &Fr { &self.montgomery_a }
     fn montgomery_2a(&self) -> &Fr { &self.montgomery_2a }
     fn scale(&self) -> &Fr { &self.scale }
+    fn pedersen_hash_generators(&self) -> &[edwards::Point<Bls12, PrimeOrder>] {
+        &self.pedersen_hash_generators
+    }
+    fn pedersen_hash_chunks_per_generator(&self) -> usize {
+        62
+    }
+    fn pedersen_circuit_generators(&self) -> &[Vec<Vec<(Fr, Fr)>>] {
+        &self.pedersen_circuit_generators
+    }
 }
 
 impl JubjubBls12 {
@@ -74,7 +90,7 @@ impl JubjubBls12 {
         let mut montgomery_2a = montgomery_a;
         montgomery_2a.double();
 
-        JubjubBls12 {
+        let mut tmp = JubjubBls12 {
             // d = -(10240/10241)
             edwards_d: Fr::from_str("19257038036680949359750312669786877991949435402254120286184196891950884077233").unwrap(),
             // A = 40962
@@ -82,8 +98,55 @@ impl JubjubBls12 {
             // 2A = 2.A
             montgomery_2a: montgomery_2a,
             // scaling factor = sqrt(4 / (a - d))
-            scale: Fr::from_str("17814886934372412843466061268024708274627479829237077604635722030778476050649").unwrap()
+            scale: Fr::from_str("17814886934372412843466061268024708274627479829237077604635722030778476050649").unwrap(),
+
+            pedersen_hash_generators: vec![],
+            pedersen_circuit_generators: vec![]
+        };
+
+        {
+            let mut cur = 0;
+            let mut pedersen_hash_generators = vec![];
+
+            // TODO: pre-generate the right amount
+            while pedersen_hash_generators.len() < 10 {
+                let gh = group_hash(&[cur], &tmp);
+                cur += 1;
+
+                if let Some(gh) = gh {
+                    pedersen_hash_generators.push(edwards::Point::from_montgomery(&gh, &tmp));
+                }
+            }
+
+            tmp.pedersen_hash_generators = pedersen_hash_generators;
         }
+
+        {
+            let mut pedersen_circuit_generators = vec![];
+
+            for mut gen in tmp.pedersen_hash_generators.iter().cloned() {
+                let mut gen = montgomery::Point::from_edwards(&gen, &tmp);
+                let mut windows = vec![];
+                for _ in 0..tmp.pedersen_hash_chunks_per_generator() {
+                    let mut coeffs = vec![];
+                    let mut g = gen.clone();
+                    for _ in 0..4 {
+                        coeffs.push(g.into_xy().expect("cannot produce O"));
+                        g = g.add(&gen, &tmp);
+                    }
+                    windows.push(coeffs);
+
+                    for _ in 0..4 {
+                        gen = gen.double(&tmp);
+                    }
+                }
+                pedersen_circuit_generators.push(windows);
+            }
+
+            tmp.pedersen_circuit_generators = pedersen_circuit_generators;
+        }
+
+        tmp
     }
 }
 

src/jubjub/tests.rs

@@ -9,6 +9,7 @@ use super::{
 use pairing::{
     Field,
     PrimeField,
+    PrimeFieldRepr,
     SqrtField,
     LegendreSymbol
 };
@@ -311,4 +312,33 @@ fn test_jubjub_params<E: JubjubEngine>(params: &E::Params) {
         tmp = tmp.sqrt().unwrap();
         assert_eq!(&tmp, params.scale());
     }
+
+    {
+        // Check that the number of windows per generator
+        // in the Pedersen hash does not allow for collisions
+
+        let mut cur = E::Fr::one().into_repr();
+
+        let mut pacc = E::Fr::zero().into_repr();
+        let mut nacc = E::Fr::char();
+
+        for _ in 0..params.pedersen_hash_chunks_per_generator()
+        {
+            // 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();
+            }
+        }
+    }
 }

src/lib.rs

@@ -7,3 +7,4 @@ extern crate rand;
 pub mod jubjub;
 pub mod circuit;
 pub mod group_hash;
+pub mod pedersen_hash;

src/pedersen_hash.rs

@@ -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
+}