Add support for periodic columns in LogUp-GKR

air/src/air/logup_gkr/mod.rs

@@ -145,6 +145,27 @@ pub trait LogUpGkrEvaluator: Clone + Sync {
     ) -> SColumnConstraint<E> {
         SColumnConstraint::new(gkr_data, composition_coefficient)
     }
+
+    /// Returns the periodic values used in the LogUp-GKR statement, either as base field element
+    /// during circuit evaluation or as extension field element during the run of sum-check for
+    /// the input layer.
+    fn build_periodic_values<F, E>(&self) -> PeriodicTable<F>
+    where
+        F: FieldElement<BaseField = Self::BaseField>,
+        E: FieldElement<BaseField = Self::BaseField> + ExtensionOf<F>,
+    {
+        let mut table = Vec::new();
+
+        let oracles = self.get_oracles();
+
+        for oracle in oracles {
+            if let LogUpGkrOracle::PeriodicValue(values) = oracle {
+                let values = embed_in_extension(values.to_vec());
+                table.push(values)
+            }
+        }
+        PeriodicTable { table }
+    }
 }
 
 #[derive(Clone, Default)]
@@ -229,3 +250,72 @@ pub enum LogUpGkrOracle<B: StarkField> {
     /// must be a power of 2.
     PeriodicValue(Vec<B>),
 }
+
+// PERIODIC COLUMNS FOR LOGUP
+// =================================================================================================
+
+/// Stores the periodic columns used in a LogUp-GKR statement.
+///
+/// Each stored periodic column is interpreted as a multi-linear extension polynomial of the column
+/// with the given periodic values. Due to the periodic nature of the values, storing, binding of
+/// an argument and evaluating the said multi-linear extension can be all done linearly in the size
+/// of the smallest cycle defining the periodic values. Hence we only store the values of this
+/// smallest cycle. The cycle is assumed throughout to be a power of 2.
+#[derive(Clone, Debug, Default, PartialEq, PartialOrd, Eq, Ord)]
+pub struct PeriodicTable<E: FieldElement> {
+    pub table: Vec<Vec<E>>,
+}
+
+impl<E> PeriodicTable<E>
+where
+    E: FieldElement,
+{
+    pub fn new(table: Vec<Vec<E::BaseField>>) -> Self {
+        let mut result = vec![];
+        for col in table.iter() {
+            let res = embed_in_extension(col.to_vec());
+            result.push(res)
+        }
+
+        Self { table: result }
+    }
+
+    pub fn num_columns(&self) -> usize {
+        self.table.len()
+    }
+
+    pub fn table(&self) -> &[Vec<E>] {
+        &self.table
+    }
+
+    pub fn get_periodic_values_at(&self, row: usize, values: &mut [E]) {
+        self.table
+            .iter()
+            .zip(values.iter_mut())
+            .for_each(|(col, value)| *value = col[row % col.len()])
+    }
+
+    pub fn bind_least_significant_variable(&mut self, round_challenge: E) {
+        for col in self.table.iter_mut() {
+            if col.len() > 1 {
+                let num_evals = col.len() >> 1;
+                for i in 0..num_evals {
+                    col[i] = col[i << 1] + round_challenge * (col[(i << 1) + 1] - col[i << 1]);
+                }
+                col.truncate(num_evals)
+            }
+        }
+    }
+}
+
+// HELPER
+// =================================================================================================
+
+fn embed_in_extension<E: FieldElement>(values: Vec<E::BaseField>) -> Vec<E> {
+    let mut res = vec![];
+    for v in values {
+        res.push(E::from(v))
+    }
+
+    res
+}

air/src/air/mod.rs

@@ -33,7 +33,7 @@ use logup_gkr::PhantomLogUpGkrEval;
 pub use logup_gkr::{
     LagrangeKernelBoundaryConstraint, LagrangeKernelConstraints, LagrangeKernelEvaluationFrame,
     LagrangeKernelRandElements, LagrangeKernelTransitionConstraints, LogUpGkrEvaluator,
-    LogUpGkrOracle,
+    LogUpGkrOracle, PeriodicTable,
 };
 
 mod coefficients;

air/src/lib.rs

@@ -47,6 +47,6 @@ pub use air::{
     DeepCompositionCoefficients, EvaluationFrame, GkrData,
     LagrangeConstraintsCompositionCoefficients, LagrangeKernelBoundaryConstraint,
     LagrangeKernelConstraints, LagrangeKernelEvaluationFrame, LagrangeKernelRandElements,
-    LagrangeKernelTransitionConstraints, LogUpGkrEvaluator, LogUpGkrOracle, TraceInfo,
-    TransitionConstraintDegree, TransitionConstraints,
+    LagrangeKernelTransitionConstraints, LogUpGkrEvaluator, LogUpGkrOracle, PeriodicTable,
+    TraceInfo, TransitionConstraintDegree, TransitionConstraints,
 };

prover/src/logup_gkr/mod.rs

@@ -109,16 +109,21 @@ impl<E: FieldElement> EvaluatedCircuit<E> {
         log_up_randomness: &[E],
     ) -> CircuitLayer<E> {
         let num_fractions = evaluator.get_num_fractions();
+        let periodic_values = evaluator.build_periodic_values::<E::BaseField, E>();
+
         let mut input_layer_wires =
             Vec::with_capacity(main_trace.main_segment().num_rows() * num_fractions);
         let mut main_frame = EvaluationFrame::new(main_trace.main_segment().num_cols());
 
         let mut query = vec![E::BaseField::ZERO; evaluator.get_oracles().len()];
+        let mut periodic_values_row = vec![E::BaseField::ZERO; periodic_values.num_columns()];
         let mut numerators = vec![E::ZERO; num_fractions];
         let mut denominators = vec![E::ZERO; num_fractions];
         for i in 0..main_trace.main_segment().num_rows() {
             let wires_from_trace_row = {
                 main_trace.read_main_frame(i, &mut main_frame);
+                periodic_values.get_periodic_values_at(i, &mut periodic_values_row);
+                evaluator.build_query(&main_frame, &periodic_values_row, &mut query);
 
                 evaluator.build_query(&main_frame, &[], &mut query);
 

prover/src/logup_gkr/prover.rs

@@ -1,6 +1,6 @@
 use alloc::vec::Vec;
 
-use air::{LogUpGkrEvaluator, LogUpGkrOracle};
+use air::{LogUpGkrEvaluator, LogUpGkrOracle, PeriodicTable};
 use crypto::{ElementHasher, RandomCoin};
 use math::FieldElement;
 use sumcheck::{
@@ -75,11 +75,18 @@ pub fn prove_gkr<E: FieldElement>(
     let (before_final_layer_proofs, gkr_claim) = prove_intermediate_layers(circuit, public_coin)?;
 
     // build the MLEs of the relevant main trace columns
-    let main_trace_mls =
+    let (main_trace_mls, mut periodic_table) =
         build_mls_from_main_trace_segment(evaluator.get_oracles(), main_trace.main_segment())?;
 
-    let final_layer_proof =
-        prove_input_layer(evaluator, logup_randomness, main_trace_mls, gkr_claim, public_coin)?;
+    // run the GKR prover for the input layer
+    let final_layer_proof = prove_input_layer(
+        evaluator,
+        logup_randomness,
+        main_trace_mls,
+        &mut periodic_table,
+        gkr_claim,
+        public_coin,
+    )?;
 
     Ok(GkrCircuitProof {
         circuit_outputs: CircuitOutput { numerators, denominators },
@@ -97,6 +104,7 @@ fn prove_input_layer<
     evaluator: &impl LogUpGkrEvaluator<BaseField = E::BaseField>,
     log_up_randomness: Vec<E>,
     multi_linear_ext_polys: Vec<MultiLinearPoly<E>>,
+    periodic_table: &mut PeriodicTable<E>,
     claim: GkrClaim<E>,
     transcript: &mut C,
 ) -> Result<FinalLayerProof<E>, GkrProverError> {
@@ -114,6 +122,7 @@ fn prove_input_layer<
         r_batch,
         log_up_randomness,
         multi_linear_ext_polys,
+        periodic_table,
         transcript,
     )?;
 
@@ -125,8 +134,9 @@ fn prove_input_layer<
 fn build_mls_from_main_trace_segment<E: FieldElement>(
     oracles: &[LogUpGkrOracle<E::BaseField>],
     main_trace: &ColMatrix<<E as FieldElement>::BaseField>,
-) -> Result<Vec<MultiLinearPoly<E>>, GkrProverError> {
+) -> Result<(Vec<MultiLinearPoly<E>>, PeriodicTable<E>), GkrProverError> {
     let mut mls = vec![];
+    let mut periodic_values = vec![];
 
     for oracle in oracles {
         match oracle {
@@ -146,10 +156,10 @@ fn build_mls_from_main_trace_segment<E: FieldElement>(
                 let ml = MultiLinearPoly::from_evaluations(values);
                 mls.push(ml)
             },
-            LogUpGkrOracle::PeriodicValue(_) => unimplemented!(),
+            LogUpGkrOracle::PeriodicValue(values) => periodic_values.push(values.to_vec()),
         };
     }
-    Ok(mls)
+    Ok((mls, PeriodicTable::new(periodic_values)))
 }
 
 /// Proves all GKR layers except for input layer.

sumcheck/Cargo.toml

@@ -43,7 +43,6 @@ utils = { version = "0.9", path = "../utils/core", package = "winter-utils", def
 rayon = { version = "1.8", optional = true }
 smallvec = { version = "1.13", default-features = false }
 thiserror = { version = "1.0", git = "https://github.com/bitwalker/thiserror", branch = "no-std", default-features = false }
-
 [dev-dependencies]
 criterion = "0.5"
 rand-utils = { version = "0.9", path = "../utils/rand", package = "winter-rand-utils" }

sumcheck/benches/sum_check_high_degree.rs

@@ -5,7 +5,7 @@
 
 use std::{marker::PhantomData, time::Duration};
 
-use air::{EvaluationFrame, LogUpGkrEvaluator, LogUpGkrOracle};
+use air::{EvaluationFrame, LogUpGkrEvaluator, LogUpGkrOracle, PeriodicTable};
 use criterion::{criterion_group, criterion_main, BatchSize, BenchmarkId, Criterion};
 use crypto::{hashers::Blake3_192, DefaultRandomCoin, RandomCoin};
 use math::{fields::f64::BaseElement, ExtensionOf, FieldElement, StarkField};
@@ -37,13 +37,14 @@ fn sum_check_high_degree(c: &mut Criterion) {
                     )
                 },
                 |(
-                    (claim, r_batch, rand_pt, (ml0, ml1, ml2, ml3, ml4)),
+                    (claim, r_batch, rand_pt, (ml0, ml1, ml2, ml3, ml4), periodic_table),
                     evaluator,
                     logup_randomness,
                     transcript,
                 )| {
                     let mls = vec![ml0, ml1, ml2, ml3, ml4];
                     let mut transcript = transcript;
+                    let mut periodic_table = periodic_table;
 
                     sum_check_prove_higher_degree(
                         &evaluator,
@@ -52,6 +53,7 @@ fn sum_check_high_degree(c: &mut Criterion) {
                         r_batch,
                         logup_randomness,
                         mls,
+                        &mut periodic_table,
                         &mut transcript,
                     )
                 },
@@ -76,21 +78,29 @@ fn setup_sum_check<E: FieldElement>(
         MultiLinearPoly<E>,
         MultiLinearPoly<E>,
     ),
+    PeriodicTable<E>,
 ) {
     let n = 1 << log_size;
     let table = MultiLinearPoly::from_evaluations(rand_vector(n));
     let multiplicity = MultiLinearPoly::from_evaluations(rand_vector(n));
     let values_0 = MultiLinearPoly::from_evaluations(rand_vector(n));
     let values_1 = MultiLinearPoly::from_evaluations(rand_vector(n));
     let values_2 = MultiLinearPoly::from_evaluations(rand_vector(n));
+    let periodic_table = PeriodicTable::default();
 
     // this will not generate the correct claim with overwhelming probability but should be fine
     // for benchmarking
     let rand_pt: Vec<E> = rand_vector(log_size + 2);
     let r_batch: E = rand_value();
     let claim: E = rand_value();
 
-    (claim, r_batch, rand_pt, (table, multiplicity, values_0, values_1, values_2))
+    (
+        claim,
+        r_batch,
+        rand_pt,
+        (table, multiplicity, values_0, values_1, values_2),
+        periodic_table,
+    )
 }
 
 #[derive(Clone, Default)]