Add support periodic columns to uni-stark prover

air/src/air.rs

@@ -1,3 +1,5 @@
+use alloc::vec;
+use alloc::vec::Vec;
 use core::ops::{Add, Mul, Sub};
 
 use p3_field::{Algebra, ExtensionField, Field, PrimeCharacteristicRing};
@@ -8,10 +10,22 @@ use p3_matrix::dense::RowMajorMatrix;
 pub trait BaseAir<F>: Sync {
     /// The number of columns (a.k.a. registers) in this AIR.
     fn width(&self) -> usize;
+
     /// Return an optional preprocessed trace matrix to be included in the prover's trace.
     fn preprocessed_trace(&self) -> Option<RowMajorMatrix<F>> {
         None
     }
+
+    /// Return the periodic table data.
+    ///
+    /// Periodic columns are columns whose values repeat with a period that divides the trace
+    /// length. Each inner `Vec<F>` represents one periodic column. The length of the inner
+    /// vector is the period of that column (must be a power of 2 that divides the trace length).
+    ///
+    /// By default returns an empty table (no periodic columns).
+    fn periodic_table(&self) -> Vec<Vec<F>> {
+        vec![]
+    }
 }
 
 /// An extension of `BaseAir` that includes support for public values.
@@ -232,6 +246,20 @@ pub trait PermutationAirBuilder: ExtensionBuilder {
     fn permutation_randomness(&self) -> &[Self::RandomVar];
 }
 
+/// Trait for builders supporting periodic columns.
+///
+/// Periodic columns are columns whose values repeat with a period dividing the trace length.
+/// They are never committed to the proof - instead, both prover and verifier compute them
+/// from the periodic table data provided by the AIR.
+pub trait PeriodicAirBuilder: AirBuilder {
+    /// Variable type for periodic column values.
+    /// For the prover, this is base field; for the verifier, this is extension field.
+    type PeriodicVar: Into<Self::Expr> + Copy;
+
+    /// Return the evaluations of periodic columns at the current row.
+    fn periodic_values(&self) -> &[Self::PeriodicVar];
+}
+
 /// A wrapper around an [`AirBuilder`] that enforces constraints only when a specified condition is met.
 ///
 /// This struct allows selectively applying constraints to certain rows or under certain conditions in the AIR,
@@ -287,6 +315,14 @@ impl<AB: PairBuilder> PairBuilder for FilteredAirBuilder<'_, AB> {
     }
 }
 
+impl<AB: AirBuilderWithPublicValues> AirBuilderWithPublicValues for FilteredAirBuilder<'_, AB> {
+    type PublicVar = AB::PublicVar;
+
+    fn public_values(&self) -> &[Self::PublicVar] {
+        self.inner.public_values()
+    }
+}
+
 impl<AB: ExtensionBuilder> ExtensionBuilder for FilteredAirBuilder<'_, AB> {
     type EF = AB::EF;
     type ExprEF = AB::ExprEF;
@@ -316,3 +352,11 @@ impl<AB: PermutationAirBuilder> PermutationAirBuilder for FilteredAirBuilder<'_,
         self.inner.permutation_randomness()
     }
 }
+
+impl<AB: PeriodicAirBuilder> PeriodicAirBuilder for FilteredAirBuilder<'_, AB> {
+    type PeriodicVar = AB::PeriodicVar;
+
+    fn periodic_values(&self) -> &[Self::PeriodicVar] {
+        self.inner.periodic_values()
+    }
+}

batch-stark/src/prover.rs

@@ -646,6 +646,7 @@ where
                 decomposed_alpha_powers: &decomposed_alpha_powers,
                 accumulator,
                 constraint_index: 0,
+                periodic_values: vec![], // batch-stark doesn't support periodic columns yet
             };
             let packed_perm_challenges = permutation_challenges
                 .iter()

batch-stark/src/verifier.rs

@@ -540,6 +540,7 @@ where
         is_transition: sels.is_transition,
         alpha: *alpha,
         accumulator: SC::Challenge::ZERO,
+        periodic_values: vec![], // batch-stark doesn't support periodic columns yet
     };
     let mut folder = VerifierConstraintFolderWithLookups {
         inner: inner_folder,

circle/Cargo.toml

@@ -10,6 +10,7 @@ keywords.workspace = true
 categories.workspace = true
 
 [dependencies]
+p3-air.workspace = true
 p3-challenger.workspace = true
 p3-commit.workspace = true
 p3-dft.workspace = true

circle/src/lib.rs

@@ -11,6 +11,7 @@ mod domain;
 mod folding;
 mod ordering;
 mod pcs;
+mod periodic;
 mod point;
 mod proof;
 mod prover;
@@ -20,4 +21,5 @@ pub use cfft::*;
 pub use domain::*;
 pub use ordering::*;
 pub use pcs::*;
+pub use periodic::*;
 pub use proof::*;