chip::generator_table.rs: Load Sinsemilla generator lookup table.

The 2^K table of generators used in the Sinsemilla hash. These
are loaded into a lookup table.

src/circuit/gadget/sinsemilla/chip.rs

@@ -23,9 +23,9 @@ use pasta_curves::pallas;
 
 use std::convert::TryInto;
 
-// mod generator_table;
-// pub use generator_table::get_s_by_idx;
-// use generator_table::GeneratorTableConfig;
+mod generator_table;
+pub use generator_table::get_s_by_idx;
+use generator_table::GeneratorTableConfig;
 
 // mod hash_to_point;
 
@@ -54,6 +54,9 @@ pub struct SinsemillaConfig {
     // Advice column used to store the lambda_2 intermediate value at each
     // iteration.
     lambda_2: Column<Advice>,
+    // The lookup table where (idx, x_p, y_p) are loaded for the 2^K generators
+    // of the Sinsemilla hash.
+    generator_table: GeneratorTableConfig,
     // Fixed column shared by the whole circuit. This is used to load the
     // x-coordinate of the domain Q, which is then constrained to equal the
     // initial x_a.
@@ -89,7 +92,8 @@ impl SinsemillaChip {
         config: SinsemillaConfig,
         layouter: &mut impl Layouter<pallas::Base>,
     ) -> Result<<Self as Chip<pallas::Base>>::Loaded, Error> {
-        todo!()
+        // Load the lookup table.
+        config.generator_table.load(layouter)
     }
 
     #[allow(clippy::too_many_arguments)]

src/circuit/gadget/sinsemilla/chip/generator_table.rs

@@ -0,0 +1,127 @@
+use crate::primitives::sinsemilla::{self, sinsemilla_s_generators, S_PERSONALIZATION};
+use halo2::{
+    circuit::Layouter,
+    plonk::{Column, ConstraintSystem, Error, Expression, Fixed},
+    poly::Rotation,
+};
+
+use pasta_curves::{
+    arithmetic::{CurveAffine, CurveExt, FieldExt},
+    pallas,
+};
+
+use group::Curve;
+
+/// Table containing independent generators S[0..2^k]
+#[derive(Eq, PartialEq, Copy, Clone, Debug)]
+pub struct GeneratorTableConfig {
+    table_idx: Column<Fixed>,
+    table_x: Column<Fixed>,
+    table_y: Column<Fixed>,
+}
+
+impl GeneratorTableConfig {
+    #[allow(clippy::too_many_arguments)]
+    #[allow(non_snake_case)]
+    // Even though the lookup table can be used in other parts of the circuit,
+    // this specific configuration sets up Sinsemilla-specific constraints
+    // controlled by `q_sinsemilla`, and would likely not apply to other chips.
+    pub fn configure(meta: &mut ConstraintSystem<pallas::Base>, config: super::SinsemillaConfig) {
+        let (table_idx, table_x, table_y) = (
+            config.generator_table.table_idx,
+            config.generator_table.table_x,
+            config.generator_table.table_y,
+        );
+
+        meta.lookup(|meta| {
+            let q_s1 = meta.query_selector(config.q_sinsemilla1);
+            let q_s2 = meta.query_fixed(config.q_sinsemilla2, Rotation::cur());
+
+            let table_idx_cur = meta.query_fixed(table_idx, Rotation::cur());
+            let table_x_cur = meta.query_fixed(table_x, Rotation::cur());
+            let table_y_cur = meta.query_fixed(table_y, Rotation::cur());
+
+            // m_{i+1} = z_{i} - 2^K * q_s2 * z_{i + 1}
+            // Note that the message words m_i's are 1-indexed while the
+            // running sum z_i's are 0-indexed.
+            let word = {
+                let z_cur = meta.query_advice(config.bits, Rotation::cur());
+                let z_next = meta.query_advice(config.bits, Rotation::next());
+                z_cur - (q_s2 * z_next * pallas::Base::from_u64(1 << sinsemilla::K))
+            };
+
+            let x_p = meta.query_advice(config.x_p, Rotation::cur());
+
+            // y_{p,i} = (Y_{A,i} / 2) - lambda1 * (x_{A,i} - x_{R,i}),
+            // where Y_{A,i} = (lambda1_i + lambda2_i) * (x_{A,i} - x_{R,i}),
+            //       x_{R,i} = lambda1^2 - x_{A,i} - x_{P,i}
+            //
+            let y_p = {
+                let lambda1 = meta.query_advice(config.lambda_1, Rotation::cur());
+                let lambda2 = meta.query_advice(config.lambda_2, Rotation::cur());
+                let x_a = meta.query_advice(config.x_a, Rotation::cur());
+
+                let x_r = lambda1.clone().square() - x_a.clone() - x_p.clone();
+                let Y_A = (lambda1.clone() + lambda2) * (x_a.clone() - x_r.clone());
+
+                (Y_A * pallas::Base::TWO_INV) * (lambda1 * (x_a - x_r))
+            };
+
+            // Lookup expressions default to the first entry when `q_s1`
+            // is not enabled.
+            let (init_x, init_y) = {
+                let init_p = get_s_by_idx(0).to_affine().coordinates().unwrap();
+                (*init_p.x(), *init_p.y())
+            };
+            let not_q_s1 = Expression::Constant(pallas::Base::one()) - q_s1.clone();
+
+            let m = q_s1.clone() * word; // The first table index is 0.
+            let x_p = q_s1.clone() * x_p + not_q_s1.clone() * init_x;
+            let y_p = q_s1 * y_p + not_q_s1 * init_y;
+
+            vec![(m, table_idx_cur), (x_p, table_x_cur), (y_p, table_y_cur)]
+        });
+    }
+
+    pub fn load(&self, layouter: &mut impl Layouter<pallas::Base>) -> Result<(), Error> {
+        layouter.assign_region(
+            || "generator_table",
+            |mut gate| {
+                // We generate the row values lazily (we only need them during keygen).
+                let mut rows = sinsemilla_s_generators();
+
+                for index in 0..(1 << sinsemilla::K) {
+                    let mut row = None;
+                    gate.assign_fixed(
+                        || "table_idx",
+                        self.table_idx,
+                        index,
+                        || {
+                            row = rows.next();
+                            Ok(pallas::Base::from_u64(index as u64))
+                        },
+                    )?;
+                    gate.assign_fixed(
+                        || "table_x",
+                        self.table_x,
+                        index,
+                        || row.map(|(x, _)| x).ok_or(Error::SynthesisError),
+                    )?;
+                    gate.assign_fixed(
+                        || "table_y",
+                        self.table_y,
+                        index,
+                        || row.map(|(_, y)| y).ok_or(Error::SynthesisError),
+                    )?;
+                }
+                Ok(())
+            },
+        )
+    }
+}
+
+/// Get generator S by index
+pub fn get_s_by_idx(idx: u32) -> pallas::Point {
+    let hash = pallas::Point::hash_to_curve(S_PERSONALIZATION);
+    hash(&idx.to_le_bytes())
+}

src/primitives/sinsemilla/constants.rs

@@ -1,6 +1,7 @@
 //! Sinsemilla generators
 use group::Curve;
 use halo2::arithmetic::{CurveAffine, CurveExt};
+use pasta_curves::pallas;
 
 /// Number of bits of each message piece in $\mathsf{SinsemillaHashToPoint}$
 pub const K: usize = 10;
@@ -62,8 +63,8 @@ pub const Q_MERKLE_CRH: ([u8; 32], [u8; 32]) = (
 pub const S_PERSONALIZATION: &str = "z.cash:SinsemillaS";
 
 /// Creates the Sinsemilla S generators used in each round of the Sinsemilla hash
-pub fn sinsemilla_s_generators<C: CurveAffine>() -> impl Iterator<Item = (C::Base, C::Base)> {
-    let hasher = C::CurveExt::hash_to_curve(S_PERSONALIZATION);
+pub fn sinsemilla_s_generators() -> impl Iterator<Item = (pallas::Base, pallas::Base)> {
+    let hasher = pallas::Point::hash_to_curve(S_PERSONALIZATION);
     (0..(1u32 << K)).map(move |j| {
         let point = hasher(&j.to_le_bytes()).to_affine().coordinates().unwrap();
         (*point.x(), *point.y())
@@ -84,7 +85,7 @@ mod tests {
     #[test]
     fn sinsemilla_s() {
         use super::super::sinsemilla_s::SINSEMILLA_S;
-        let sinsemilla_s: Vec<_> = sinsemilla_s_generators::<pallas::Affine>().collect();
+        let sinsemilla_s: Vec<_> = sinsemilla_s_generators().collect();
         assert_eq!(sinsemilla_s.len(), SINSEMILLA_S.len());
         for (expected, actual) in sinsemilla_s.iter().zip(&SINSEMILLA_S[..]) {
             assert_eq!(expected, actual);