diff --git a/ecdsa/src/gadgets/biguint.rs b/ecdsa/src/gadgets/biguint.rs
index b98fcdc1..6dfd39a6 100644
--- a/ecdsa/src/gadgets/biguint.rs
+++ b/ecdsa/src/gadgets/biguint.rs
@@ -6,7 +6,7 @@ use plonky2::iop::generator::{GeneratedValues, SimpleGenerator};
 use plonky2::iop::target::{BoolTarget, Target};
 use plonky2::iop::witness::{PartitionWitness, Witness};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::PrimeField;
 use plonky2_u32::gadgets::arithmetic_u32::{CircuitBuilderU32, U32Target};
 use plonky2_u32::gadgets::multiple_comparison::list_le_u32_circuit;
diff --git a/ecdsa/src/gadgets/curve.rs b/ecdsa/src/gadgets/curve.rs
index e511973b..1959d54a 100644
--- a/ecdsa/src/gadgets/curve.rs
+++ b/ecdsa/src/gadgets/curve.rs
@@ -1,7 +1,7 @@
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::target::BoolTarget;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 
 use crate::curve::curve_types::{AffinePoint, Curve, CurveScalar};
diff --git a/ecdsa/src/gadgets/curve_fixed_base.rs b/ecdsa/src/gadgets/curve_fixed_base.rs
index e64ec134..02ed458a 100644
--- a/ecdsa/src/gadgets/curve_fixed_base.rs
+++ b/ecdsa/src/gadgets/curve_fixed_base.rs
@@ -3,7 +3,7 @@ use plonky2::hash::hash_types::RichField;
 use plonky2::hash::keccak::KeccakHash;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::config::{GenericHashOut, Hasher};
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 
 use crate::curve::curve_types::{AffinePoint, Curve, CurveScalar};
diff --git a/ecdsa/src/gadgets/curve_msm.rs b/ecdsa/src/gadgets/curve_msm.rs
index c57cecd2..fb768b6e 100644
--- a/ecdsa/src/gadgets/curve_msm.rs
+++ b/ecdsa/src/gadgets/curve_msm.rs
@@ -3,7 +3,7 @@ use plonky2::hash::hash_types::RichField;
 use plonky2::hash::keccak::KeccakHash;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::config::{GenericHashOut, Hasher};
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 
 use crate::curve::curve_types::{Curve, CurveScalar};
diff --git a/ecdsa/src/gadgets/curve_windowed_mul.rs b/ecdsa/src/gadgets/curve_windowed_mul.rs
index 62437f67..0113b5ee 100644
--- a/ecdsa/src/gadgets/curve_windowed_mul.rs
+++ b/ecdsa/src/gadgets/curve_windowed_mul.rs
@@ -6,7 +6,7 @@ use plonky2::hash::keccak::KeccakHash;
 use plonky2::iop::target::{BoolTarget, Target};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::config::{GenericHashOut, Hasher};
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_u32::gadgets::arithmetic_u32::{CircuitBuilderU32, U32Target};
 
diff --git a/ecdsa/src/gadgets/ecdsa.rs b/ecdsa/src/gadgets/ecdsa.rs
index afd79c61..c8fae72c 100644
--- a/ecdsa/src/gadgets/ecdsa.rs
+++ b/ecdsa/src/gadgets/ecdsa.rs
@@ -2,7 +2,7 @@ use std::marker::PhantomData;
 
 use plonky2::hash::hash_types::RichField;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::secp256k1_scalar::Secp256K1Scalar;
 
 use crate::curve::curve_types::Curve;
diff --git a/ecdsa/src/gadgets/glv.rs b/ecdsa/src/gadgets/glv.rs
index c567e5ab..fd1ce0e6 100644
--- a/ecdsa/src/gadgets/glv.rs
+++ b/ecdsa/src/gadgets/glv.rs
@@ -5,7 +5,7 @@ use plonky2::iop::generator::{GeneratedValues, SimpleGenerator};
 use plonky2::iop::target::{BoolTarget, Target};
 use plonky2::iop::witness::PartitionWitness;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::{Field, PrimeField};
 use plonky2_field::secp256k1_base::Secp256K1Base;
 use plonky2_field::secp256k1_scalar::Secp256K1Scalar;
diff --git a/ecdsa/src/gadgets/nonnative.rs b/ecdsa/src/gadgets/nonnative.rs
index 0ff3e1fa..46f0f335 100644
--- a/ecdsa/src/gadgets/nonnative.rs
+++ b/ecdsa/src/gadgets/nonnative.rs
@@ -7,7 +7,7 @@ use plonky2::iop::target::{BoolTarget, Target};
 use plonky2::iop::witness::PartitionWitness;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2_field::field_types::PrimeField;
-use plonky2_field::{extension_field::Extendable, field_types::Field};
+use plonky2_field::{extension::Extendable, field_types::Field};
 use plonky2_u32::gadgets::arithmetic_u32::{CircuitBuilderU32, U32Target};
 use plonky2_u32::gadgets::range_check::range_check_u32_circuit;
 use plonky2_u32::witness::generated_values_set_u32_target;
diff --git a/ecdsa/src/gadgets/split_nonnative.rs b/ecdsa/src/gadgets/split_nonnative.rs
index 60e765c1..bfcff487 100644
--- a/ecdsa/src/gadgets/split_nonnative.rs
+++ b/ecdsa/src/gadgets/split_nonnative.rs
@@ -4,7 +4,7 @@ use itertools::Itertools;
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::target::Target;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_u32::gadgets::arithmetic_u32::{CircuitBuilderU32, U32Target};
 
diff --git a/evm/src/all_stark.rs b/evm/src/all_stark.rs
index 6b33f9af..96785f1b 100644
--- a/evm/src/all_stark.rs
+++ b/evm/src/all_stark.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::hash::hash_types::RichField;
 
 use crate::config::StarkConfig;
diff --git a/evm/src/constraint_consumer.rs b/evm/src/constraint_consumer.rs
index fd21e366..07b5ba24 100644
--- a/evm/src/constraint_consumer.rs
+++ b/evm/src/constraint_consumer.rs
@@ -1,6 +1,6 @@
 use std::marker::PhantomData;
 
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::ext_target::ExtensionTarget;
diff --git a/evm/src/cpu/cpu_stark.rs b/evm/src/cpu/cpu_stark.rs
index 4b4d47d9..8277a2fe 100644
--- a/evm/src/cpu/cpu_stark.rs
+++ b/evm/src/cpu/cpu_stark.rs
@@ -1,7 +1,7 @@
 use std::marker::PhantomData;
 
 use itertools::Itertools;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/cpu/decode.rs b/evm/src/cpu/decode.rs
index 5cd132a0..0bbac969 100644
--- a/evm/src/cpu/decode.rs
+++ b/evm/src/cpu/decode.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/cpu/simple_logic/eq_iszero.rs b/evm/src/cpu/simple_logic/eq_iszero.rs
index 994eff91..5b10ce59 100644
--- a/evm/src/cpu/simple_logic/eq_iszero.rs
+++ b/evm/src/cpu/simple_logic/eq_iszero.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::ext_target::ExtensionTarget;
diff --git a/evm/src/cpu/simple_logic/mod.rs b/evm/src/cpu/simple_logic/mod.rs
index ee9491dc..aa95da53 100644
--- a/evm/src/cpu/simple_logic/mod.rs
+++ b/evm/src/cpu/simple_logic/mod.rs
@@ -1,7 +1,7 @@
 mod eq_iszero;
 mod not;
 
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::ext_target::ExtensionTarget;
diff --git a/evm/src/cpu/simple_logic/not.rs b/evm/src/cpu/simple_logic/not.rs
index 90b26ccd..f4c15e0f 100644
--- a/evm/src/cpu/simple_logic/not.rs
+++ b/evm/src/cpu/simple_logic/not.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/cross_table_lookup.rs b/evm/src/cross_table_lookup.rs
index e80e5b29..57c1a50a 100644
--- a/evm/src/cross_table_lookup.rs
+++ b/evm/src/cross_table_lookup.rs
@@ -2,7 +2,7 @@ use std::iter::repeat;
 
 use anyhow::{ensure, Result};
 use itertools::Itertools;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
diff --git a/evm/src/get_challenges.rs b/evm/src/get_challenges.rs
index 2e7d8dcb..88727ad3 100644
--- a/evm/src/get_challenges.rs
+++ b/evm/src/get_challenges.rs
@@ -1,5 +1,5 @@
 use itertools::izip;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::fri::proof::{FriProof, FriProofTarget};
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::challenger::{Challenger, RecursiveChallenger};
diff --git a/evm/src/keccak/keccak_stark.rs b/evm/src/keccak/keccak_stark.rs
index 59e9daac..efa578d5 100644
--- a/evm/src/keccak/keccak_stark.rs
+++ b/evm/src/keccak/keccak_stark.rs
@@ -2,7 +2,7 @@ use std::marker::PhantomData;
 
 use itertools::Itertools;
 use log::info;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
diff --git a/evm/src/keccak/logic.rs b/evm/src/keccak/logic.rs
index 7d248258..be84a699 100644
--- a/evm/src/keccak/logic.rs
+++ b/evm/src/keccak/logic.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::PrimeField64;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/keccak/round_flags.rs b/evm/src/keccak/round_flags.rs
index 41a0c0ec..6ccd5da4 100644
--- a/evm/src/keccak/round_flags.rs
+++ b/evm/src/keccak/round_flags.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/logic.rs b/evm/src/logic.rs
index 34a25c00..c79bf4d2 100644
--- a/evm/src/logic.rs
+++ b/evm/src/logic.rs
@@ -1,7 +1,7 @@
 use std::marker::PhantomData;
 
 use itertools::izip;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/lookup.rs b/evm/src/lookup.rs
index 70f1467b..b20deaac 100644
--- a/evm/src/lookup.rs
+++ b/evm/src/lookup.rs
@@ -1,7 +1,7 @@
 use std::cmp::Ordering;
 
 use itertools::Itertools;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/memory/memory_stark.rs b/evm/src/memory/memory_stark.rs
index db0a2b12..348a615e 100644
--- a/evm/src/memory/memory_stark.rs
+++ b/evm/src/memory/memory_stark.rs
@@ -2,7 +2,7 @@ use std::collections::{HashMap, HashSet};
 use std::marker::PhantomData;
 
 use itertools::{izip, multiunzip, Itertools};
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
diff --git a/evm/src/permutation.rs b/evm/src/permutation.rs
index cb690064..8823bac7 100644
--- a/evm/src/permutation.rs
+++ b/evm/src/permutation.rs
@@ -2,7 +2,7 @@
 
 use itertools::Itertools;
 use plonky2::field::batch_util::batch_multiply_inplace;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
diff --git a/evm/src/proof.rs b/evm/src/proof.rs
index 7329853b..b1275844 100644
--- a/evm/src/proof.rs
+++ b/evm/src/proof.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::fri::oracle::PolynomialBatch;
 use plonky2::fri::proof::{
     CompressedFriProof, FriChallenges, FriChallengesTarget, FriProof, FriProofTarget,
diff --git a/evm/src/prover.rs b/evm/src/prover.rs
index ba4fac52..3652cd54 100644
--- a/evm/src/prover.rs
+++ b/evm/src/prover.rs
@@ -1,5 +1,5 @@
 use anyhow::{ensure, Result};
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::field::packable::Packable;
 use plonky2::field::packed_field::PackedField;
diff --git a/evm/src/recursive_verifier.rs b/evm/src/recursive_verifier.rs
index 37e108cb..fcbeecea 100644
--- a/evm/src/recursive_verifier.rs
+++ b/evm/src/recursive_verifier.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::fri::witness_util::set_fri_proof_target;
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/stark.rs b/evm/src/stark.rs
index 42d775ab..a1c6ef0b 100644
--- a/evm/src/stark.rs
+++ b/evm/src/stark.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::fri::structure::{
diff --git a/evm/src/stark_testing.rs b/evm/src/stark_testing.rs
index 3fbcf83a..abff2e36 100644
--- a/evm/src/stark_testing.rs
+++ b/evm/src/stark_testing.rs
@@ -1,6 +1,6 @@
 use anyhow::{ensure, Result};
-use plonky2::field::extension_field::Extendable;
-use plonky2::field::extension_field::FieldExtension;
+use plonky2::field::extension::Extendable;
+use plonky2::field::extension::FieldExtension;
 use plonky2::field::field_types::Field;
 use plonky2::field::polynomial::{PolynomialCoeffs, PolynomialValues};
 use plonky2::hash::hash_types::RichField;
diff --git a/evm/src/util.rs b/evm/src/util.rs
index 5620d21d..a6bec5df 100644
--- a/evm/src/util.rs
+++ b/evm/src/util.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
diff --git a/evm/src/vanishing_poly.rs b/evm/src/vanishing_poly.rs
index 16417918..cd50fdba 100644
--- a/evm/src/vanishing_poly.rs
+++ b/evm/src/vanishing_poly.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
diff --git a/evm/src/verifier.rs b/evm/src/verifier.rs
index a26e1b16..89075328 100644
--- a/evm/src/verifier.rs
+++ b/evm/src/verifier.rs
@@ -1,5 +1,5 @@
 use anyhow::{ensure, Result};
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::fri::verifier::verify_fri_proof;
 use plonky2::hash::hash_types::RichField;
diff --git a/field/src/extension_field/algebra.rs b/field/src/extension/algebra.rs
similarity index 98%
rename from field/src/extension_field/algebra.rs
rename to field/src/extension/algebra.rs
index 58244726..b4d67f91 100644
--- a/field/src/extension_field/algebra.rs
+++ b/field/src/extension/algebra.rs
@@ -2,7 +2,7 @@ use std::fmt::{Debug, Display, Formatter};
 use std::iter::{Product, Sum};
 use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
-use crate::extension_field::OEF;
+use crate::extension::OEF;
 
 /// Let `F_D` be the optimal extension field `F[X]/(X^D-W)`. Then `ExtensionAlgebra<F_D>` is the quotient `F_D[X]/(X^D-W)`.
 /// It's a `D`-dimensional algebra over `F_D` useful to lift the multiplication over `F_D` to a multiplication over `(F_D)^D`.
@@ -192,8 +192,8 @@ impl<F: OEF<D>, const D: usize> PolynomialCoeffsAlgebra<F, D> {
 mod tests {
     use itertools::Itertools;
 
-    use crate::extension_field::algebra::ExtensionAlgebra;
-    use crate::extension_field::{Extendable, FieldExtension};
+    use crate::extension::algebra::ExtensionAlgebra;
+    use crate::extension::{Extendable, FieldExtension};
     use crate::field_types::Field;
     use crate::goldilocks_field::GoldilocksField;
 
diff --git a/field/src/extension_field/mod.rs b/field/src/extension/mod.rs
similarity index 100%
rename from field/src/extension_field/mod.rs
rename to field/src/extension/mod.rs
diff --git a/field/src/extension_field/quadratic.rs b/field/src/extension/quadratic.rs
similarity index 97%
rename from field/src/extension_field/quadratic.rs
rename to field/src/extension/quadratic.rs
index 9cdc01c3..01ea8b2e 100644
--- a/field/src/extension_field/quadratic.rs
+++ b/field/src/extension/quadratic.rs
@@ -7,7 +7,7 @@ use num::Integer;
 use rand::Rng;
 use serde::{Deserialize, Serialize};
 
-use crate::extension_field::{Extendable, FieldExtension, Frobenius, OEF};
+use crate::extension::{Extendable, FieldExtension, Frobenius, OEF};
 use crate::field_types::Field;
 use crate::ops::Square;
 
@@ -231,7 +231,7 @@ mod tests {
 
         test_field_extension!(crate::goldilocks_field::GoldilocksField, 2);
         test_field_arithmetic!(
-            crate::extension_field::quadratic::QuadraticExtension<
+            crate::extension::quadratic::QuadraticExtension<
                 crate::goldilocks_field::GoldilocksField,
             >
         );
diff --git a/field/src/extension_field/quartic.rs b/field/src/extension/quartic.rs
similarity index 98%
rename from field/src/extension_field/quartic.rs
rename to field/src/extension/quartic.rs
index 09e35a4f..0521a333 100644
--- a/field/src/extension_field/quartic.rs
+++ b/field/src/extension/quartic.rs
@@ -8,7 +8,7 @@ use num::Integer;
 use rand::Rng;
 use serde::{Deserialize, Serialize};
 
-use crate::extension_field::{Extendable, FieldExtension, Frobenius, OEF};
+use crate::extension::{Extendable, FieldExtension, Frobenius, OEF};
 use crate::field_types::Field;
 use crate::ops::Square;
 
@@ -264,7 +264,7 @@ mod tests {
 
         test_field_extension!(crate::goldilocks_field::GoldilocksField, 4);
         test_field_arithmetic!(
-            crate::extension_field::quartic::QuarticExtension<
+            crate::extension::quartic::QuarticExtension<
                 crate::goldilocks_field::GoldilocksField,
             >
         );
diff --git a/field/src/extension_field/quintic.rs b/field/src/extension/quintic.rs
similarity index 98%
rename from field/src/extension_field/quintic.rs
rename to field/src/extension/quintic.rs
index 1600107d..fd400986 100644
--- a/field/src/extension_field/quintic.rs
+++ b/field/src/extension/quintic.rs
@@ -7,7 +7,7 @@ use num::traits::Pow;
 use rand::Rng;
 use serde::{Deserialize, Serialize};
 
-use crate::extension_field::{Extendable, FieldExtension, Frobenius, OEF};
+use crate::extension::{Extendable, FieldExtension, Frobenius, OEF};
 use crate::field_types::Field;
 use crate::ops::Square;
 
@@ -270,7 +270,7 @@ mod tests {
 
         test_field_extension!(crate::goldilocks_field::GoldilocksField, 5);
         test_field_arithmetic!(
-            crate::extension_field::quintic::QuinticExtension<
+            crate::extension::quintic::QuinticExtension<
                 crate::goldilocks_field::GoldilocksField,
             >
         );
diff --git a/field/src/field_testing.rs b/field/src/field_testing.rs
index a57d99fd..cd54b08e 100644
--- a/field/src/field_testing.rs
+++ b/field/src/field_testing.rs
@@ -1,5 +1,5 @@
-use crate::extension_field::Extendable;
-use crate::extension_field::Frobenius;
+use crate::extension::Extendable;
+use crate::extension::Frobenius;
 use crate::field_types::Field;
 use crate::ops::Square;
 
diff --git a/field/src/field_types.rs b/field/src/field_types.rs
index 4adfdbf4..97c8776b 100644
--- a/field/src/field_types.rs
+++ b/field/src/field_types.rs
@@ -10,7 +10,7 @@ use rand::Rng;
 use serde::de::DeserializeOwned;
 use serde::Serialize;
 
-use crate::extension_field::Frobenius;
+use crate::extension::Frobenius;
 use crate::ops::Square;
 
 /// A finite field.
diff --git a/field/src/goldilocks_extensions.rs b/field/src/goldilocks_extensions.rs
index 95265fe3..5bbfd0ab 100644
--- a/field/src/goldilocks_extensions.rs
+++ b/field/src/goldilocks_extensions.rs
@@ -2,10 +2,10 @@ use std::ops::Mul;
 
 use static_assertions::const_assert;
 
-use crate::extension_field::quadratic::QuadraticExtension;
-use crate::extension_field::quartic::QuarticExtension;
-use crate::extension_field::quintic::QuinticExtension;
-use crate::extension_field::{Extendable, Frobenius};
+use crate::extension::quadratic::QuadraticExtension;
+use crate::extension::quartic::QuarticExtension;
+use crate::extension::quintic::QuinticExtension;
+use crate::extension::{Extendable, Frobenius};
 use crate::field_types::Field;
 use crate::goldilocks_field::{reduce160, GoldilocksField};
 
diff --git a/field/src/interpolation.rs b/field/src/interpolation.rs
index 1a2e37df..7d28303c 100644
--- a/field/src/interpolation.rs
+++ b/field/src/interpolation.rs
@@ -78,7 +78,7 @@ pub fn interpolate2<F: Field>(points: [(F, F); 2], x: F) -> F {
 #[cfg(test)]
 mod tests {
     use super::*;
-    use crate::extension_field::quartic::QuarticExtension;
+    use crate::extension::quartic::QuarticExtension;
     use crate::field_types::Field;
     use crate::goldilocks_field::GoldilocksField;
     use crate::polynomial::PolynomialCoeffs;
diff --git a/field/src/lib.rs b/field/src/lib.rs
index e54f2aa7..4cfdb65c 100644
--- a/field/src/lib.rs
+++ b/field/src/lib.rs
@@ -12,7 +12,7 @@
 pub(crate) mod arch;
 pub mod batch_util;
 pub mod cosets;
-pub mod extension_field;
+pub mod extension;
 pub mod fft;
 pub mod field_types;
 pub mod goldilocks_extensions;
diff --git a/field/src/polynomial/division.rs b/field/src/polynomial/division.rs
index c394b4b1..6ff5f818 100644
--- a/field/src/polynomial/division.rs
+++ b/field/src/polynomial/division.rs
@@ -133,7 +133,7 @@ impl<F: Field> PolynomialCoeffs<F> {
 mod tests {
     use rand::{thread_rng, Rng};
 
-    use crate::extension_field::quartic::QuarticExtension;
+    use crate::extension::quartic::QuarticExtension;
     use crate::field_types::Field;
     use crate::goldilocks_field::GoldilocksField;
     use crate::polynomial::PolynomialCoeffs;
diff --git a/field/src/polynomial/mod.rs b/field/src/polynomial/mod.rs
index 035ee724..c0aaadf1 100644
--- a/field/src/polynomial/mod.rs
+++ b/field/src/polynomial/mod.rs
@@ -9,7 +9,7 @@ use itertools::Itertools;
 use plonky2_util::log2_strict;
 use serde::{Deserialize, Serialize};
 
-use crate::extension_field::{Extendable, FieldExtension};
+use crate::extension::{Extendable, FieldExtension};
 use crate::fft::{fft, fft_with_options, ifft, FftRootTable};
 use crate::field_types::Field;
 
diff --git a/insertion/src/insert_gadget.rs b/insertion/src/insert_gadget.rs
index d4cbf0ec..aa0b30e3 100644
--- a/insertion/src/insert_gadget.rs
+++ b/insertion/src/insert_gadget.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::ext_target::ExtensionTarget;
 use plonky2::iop::target::Target;
diff --git a/insertion/src/insertion_gate.rs b/insertion/src/insertion_gate.rs
index e5991a19..db36f7e6 100644
--- a/insertion/src/insertion_gate.rs
+++ b/insertion/src/insertion_gate.rs
@@ -1,7 +1,7 @@
 use std::marker::PhantomData;
 use std::ops::Range;
 
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::gates::gate::Gate;
 use plonky2::gates::util::StridedConstraintConsumer;
diff --git a/plonky2/benches/field_arithmetic.rs b/plonky2/benches/field_arithmetic.rs
index 62d1c2c5..392d7b52 100644
--- a/plonky2/benches/field_arithmetic.rs
+++ b/plonky2/benches/field_arithmetic.rs
@@ -1,9 +1,9 @@
 mod allocator;
 
 use criterion::{criterion_group, criterion_main, BatchSize, Criterion};
-use plonky2::field::extension_field::quadratic::QuadraticExtension;
-use plonky2::field::extension_field::quartic::QuarticExtension;
-use plonky2::field::extension_field::quintic::QuinticExtension;
+use plonky2::field::extension::quadratic::QuadraticExtension;
+use plonky2::field::extension::quartic::QuarticExtension;
+use plonky2::field::extension::quintic::QuinticExtension;
 use plonky2::field::field_types::Field;
 use plonky2::field::goldilocks_field::GoldilocksField;
 use tynm::type_name;
diff --git a/plonky2/examples/bench_recursion.rs b/plonky2/examples/bench_recursion.rs
index 3ef89700..1f2d127f 100644
--- a/plonky2/examples/bench_recursion.rs
+++ b/plonky2/examples/bench_recursion.rs
@@ -25,7 +25,7 @@ use plonky2::{
     },
     util::timing::TimingTree,
 };
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use rand::{rngs::OsRng, RngCore, SeedableRng};
 use rand_chacha::ChaCha8Rng;
 use structopt::StructOpt;
diff --git a/plonky2/src/fri/challenges.rs b/plonky2/src/fri/challenges.rs
index 0655d31f..011a8897 100644
--- a/plonky2/src/fri/challenges.rs
+++ b/plonky2/src/fri/challenges.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::polynomial::PolynomialCoeffs;
 
 use crate::fri::proof::{FriChallenges, FriChallengesTarget};
diff --git a/plonky2/src/fri/oracle.rs b/plonky2/src/fri/oracle.rs
index 30058423..73fc2dfe 100644
--- a/plonky2/src/fri/oracle.rs
+++ b/plonky2/src/fri/oracle.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::fft::FftRootTable;
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
diff --git a/plonky2/src/fri/proof.rs b/plonky2/src/fri/proof.rs
index 9c6961a4..f7945b28 100644
--- a/plonky2/src/fri/proof.rs
+++ b/plonky2/src/fri/proof.rs
@@ -1,7 +1,7 @@
 use std::collections::HashMap;
 
 use itertools::izip;
-use plonky2_field::extension_field::{flatten, unflatten, Extendable};
+use plonky2_field::extension::{flatten, unflatten, Extendable};
 use plonky2_field::polynomial::PolynomialCoeffs;
 use serde::{Deserialize, Serialize};
 
diff --git a/plonky2/src/fri/prover.rs b/plonky2/src/fri/prover.rs
index 5a20ab9d..6136a9a1 100644
--- a/plonky2/src/fri/prover.rs
+++ b/plonky2/src/fri/prover.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2_field::extension_field::{flatten, unflatten, Extendable};
+use plonky2_field::extension::{flatten, unflatten, Extendable};
 use plonky2_field::polynomial::{PolynomialCoeffs, PolynomialValues};
 use plonky2_util::reverse_index_bits_in_place;
 use rayon::prelude::*;
diff --git a/plonky2/src/fri/recursive_verifier.rs b/plonky2/src/fri/recursive_verifier.rs
index f56e19ca..2da264c7 100644
--- a/plonky2/src/fri/recursive_verifier.rs
+++ b/plonky2/src/fri/recursive_verifier.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_util::{log2_strict, reverse_index_bits_in_place};
 
 use crate::fri::proof::{
diff --git a/plonky2/src/fri/structure.rs b/plonky2/src/fri/structure.rs
index 240abd5d..1a37a1b2 100644
--- a/plonky2/src/fri/structure.rs
+++ b/plonky2/src/fri/structure.rs
@@ -3,7 +3,7 @@
 
 use std::ops::Range;
 
-use crate::field::extension_field::Extendable;
+use crate::field::extension::Extendable;
 use crate::hash::hash_types::RichField;
 use crate::iop::ext_target::ExtensionTarget;
 
diff --git a/plonky2/src/fri/verifier.rs b/plonky2/src/fri/verifier.rs
index 2607ab0d..bf18e803 100644
--- a/plonky2/src/fri/verifier.rs
+++ b/plonky2/src/fri/verifier.rs
@@ -1,5 +1,5 @@
 use anyhow::{ensure, Result};
-use plonky2_field::extension_field::{flatten, Extendable, FieldExtension};
+use plonky2_field::extension::{flatten, Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 use plonky2_field::interpolation::{barycentric_weights, interpolate};
 use plonky2_util::{log2_strict, reverse_index_bits_in_place};
diff --git a/plonky2/src/fri/witness_util.rs b/plonky2/src/fri/witness_util.rs
index 741f839d..ddf3c401 100644
--- a/plonky2/src/fri/witness_util.rs
+++ b/plonky2/src/fri/witness_util.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::fri::proof::{FriProof, FriProofTarget};
 use crate::hash::hash_types::RichField;
diff --git a/plonky2/src/gadgets/arithmetic.rs b/plonky2/src/gadgets/arithmetic.rs
index fdfce6aa..bbf3b889 100644
--- a/plonky2/src/gadgets/arithmetic.rs
+++ b/plonky2/src/gadgets/arithmetic.rs
@@ -1,6 +1,6 @@
 use std::borrow::Borrow;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field64;
 
 use crate::gates::arithmetic_base::ArithmeticGate;
diff --git a/plonky2/src/gadgets/arithmetic_extension.rs b/plonky2/src/gadgets/arithmetic_extension.rs
index 83054a79..acca2096 100644
--- a/plonky2/src/gadgets/arithmetic_extension.rs
+++ b/plonky2/src/gadgets/arithmetic_extension.rs
@@ -1,7 +1,7 @@
 use std::borrow::Borrow;
 
-use plonky2_field::extension_field::FieldExtension;
-use plonky2_field::extension_field::{Extendable, OEF};
+use plonky2_field::extension::FieldExtension;
+use plonky2_field::extension::{Extendable, OEF};
 use plonky2_field::field_types::{Field, Field64};
 use plonky2_util::bits_u64;
 
@@ -569,7 +569,7 @@ pub(crate) struct ExtensionArithmeticOperation<F: Field64 + Extendable<D>, const
 #[cfg(test)]
 mod tests {
     use anyhow::Result;
-    use plonky2_field::extension_field::algebra::ExtensionAlgebra;
+    use plonky2_field::extension::algebra::ExtensionAlgebra;
     use plonky2_field::field_types::Field;
 
     use crate::iop::ext_target::ExtensionAlgebraTarget;
diff --git a/plonky2/src/gadgets/hash.rs b/plonky2/src/gadgets/hash.rs
index 90b77371..ec235340 100644
--- a/plonky2/src/gadgets/hash.rs
+++ b/plonky2/src/gadgets/hash.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::hash::hash_types::RichField;
 use crate::hash::hashing::SPONGE_WIDTH;
diff --git a/plonky2/src/gadgets/interpolation.rs b/plonky2/src/gadgets/interpolation.rs
index 3479e2a8..d7a6c311 100644
--- a/plonky2/src/gadgets/interpolation.rs
+++ b/plonky2/src/gadgets/interpolation.rs
@@ -1,6 +1,6 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::gates::gate::Gate;
 use crate::hash::hash_types::RichField;
@@ -105,7 +105,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 #[cfg(test)]
 mod tests {
     use anyhow::Result;
-    use plonky2_field::extension_field::FieldExtension;
+    use plonky2_field::extension::FieldExtension;
     use plonky2_field::field_types::Field;
     use plonky2_field::interpolation::interpolant;
 
diff --git a/plonky2/src/gadgets/polynomial.rs b/plonky2/src/gadgets/polynomial.rs
index 6e4a9bb4..60bfcca4 100644
--- a/plonky2/src/gadgets/polynomial.rs
+++ b/plonky2/src/gadgets/polynomial.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::hash::hash_types::RichField;
 use crate::iop::ext_target::{ExtensionAlgebraTarget, ExtensionTarget};
diff --git a/plonky2/src/gadgets/random_access.rs b/plonky2/src/gadgets/random_access.rs
index d6377451..686636cf 100644
--- a/plonky2/src/gadgets/random_access.rs
+++ b/plonky2/src/gadgets/random_access.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_util::log2_strict;
 
 use crate::gates::random_access::RandomAccessGate;
diff --git a/plonky2/src/gadgets/range_check.rs b/plonky2/src/gadgets/range_check.rs
index f00578e8..267b1040 100644
--- a/plonky2/src/gadgets/range_check.rs
+++ b/plonky2/src/gadgets/range_check.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::hash::hash_types::RichField;
 use crate::iop::generator::{GeneratedValues, SimpleGenerator};
diff --git a/plonky2/src/gadgets/select.rs b/plonky2/src/gadgets/select.rs
index 9312c4cc..c4634c56 100644
--- a/plonky2/src/gadgets/select.rs
+++ b/plonky2/src/gadgets/select.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::hash::hash_types::RichField;
 use crate::iop::ext_target::ExtensionTarget;
diff --git a/plonky2/src/gadgets/split_base.rs b/plonky2/src/gadgets/split_base.rs
index 5ceede66..5e29f322 100644
--- a/plonky2/src/gadgets/split_base.rs
+++ b/plonky2/src/gadgets/split_base.rs
@@ -1,7 +1,7 @@
 use std::borrow::Borrow;
 
 use itertools::Itertools;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 
 use crate::gates::base_sum::BaseSumGate;
diff --git a/plonky2/src/gadgets/split_join.rs b/plonky2/src/gadgets/split_join.rs
index 9c9e8d3d..dff91bf6 100644
--- a/plonky2/src/gadgets/split_join.rs
+++ b/plonky2/src/gadgets/split_join.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_util::ceil_div_usize;
 
 use crate::gates::base_sum::BaseSumGate;
diff --git a/plonky2/src/gates/arithmetic_base.rs b/plonky2/src/gates/arithmetic_base.rs
index 86338ecf..f91d2722 100644
--- a/plonky2/src/gates/arithmetic_base.rs
+++ b/plonky2/src/gates/arithmetic_base.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::packed_field::PackedField;
 
 use crate::gates::gate::Gate;
diff --git a/plonky2/src/gates/arithmetic_extension.rs b/plonky2/src/gates/arithmetic_extension.rs
index 66dcfdd2..e4e07f83 100644
--- a/plonky2/src/gates/arithmetic_extension.rs
+++ b/plonky2/src/gates/arithmetic_extension.rs
@@ -1,7 +1,7 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
-use plonky2_field::extension_field::FieldExtension;
+use plonky2_field::extension::Extendable;
+use plonky2_field::extension::FieldExtension;
 
 use crate::gates::gate::Gate;
 use crate::gates::util::StridedConstraintConsumer;
diff --git a/plonky2/src/gates/assert_le.rs b/plonky2/src/gates/assert_le.rs
index ac47b6f5..4aa6284f 100644
--- a/plonky2/src/gates/assert_le.rs
+++ b/plonky2/src/gates/assert_le.rs
@@ -1,6 +1,6 @@
 use std::marker::PhantomData;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::{Field, Field64};
 use plonky2_field::packed_field::PackedField;
 use plonky2_util::{bits_u64, ceil_div_usize};
@@ -450,7 +450,7 @@ mod tests {
     use std::marker::PhantomData;
 
     use anyhow::Result;
-    use plonky2_field::extension_field::quartic::QuarticExtension;
+    use plonky2_field::extension::quartic::QuarticExtension;
     use plonky2_field::field_types::Field;
     use plonky2_field::field_types::PrimeField64;
     use plonky2_field::goldilocks_field::GoldilocksField;
diff --git a/plonky2/src/gates/base_sum.rs b/plonky2/src/gates/base_sum.rs
index d26747de..83453058 100644
--- a/plonky2/src/gates/base_sum.rs
+++ b/plonky2/src/gates/base_sum.rs
@@ -1,6 +1,6 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::{Field, Field64};
 use plonky2_field::packed_field::PackedField;
 
diff --git a/plonky2/src/gates/constant.rs b/plonky2/src/gates/constant.rs
index e0ebd9a0..449193e7 100644
--- a/plonky2/src/gates/constant.rs
+++ b/plonky2/src/gates/constant.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::packed_field::PackedField;
 
 use crate::gates::gate::Gate;
diff --git a/plonky2/src/gates/exponentiation.rs b/plonky2/src/gates/exponentiation.rs
index 179395f3..4edbaccd 100644
--- a/plonky2/src/gates/exponentiation.rs
+++ b/plonky2/src/gates/exponentiation.rs
@@ -1,6 +1,6 @@
 use std::marker::PhantomData;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_field::ops::Square;
 use plonky2_field::packed_field::PackedField;
diff --git a/plonky2/src/gates/gate.rs b/plonky2/src/gates/gate.rs
index 56026103..81dde0bd 100644
--- a/plonky2/src/gates/gate.rs
+++ b/plonky2/src/gates/gate.rs
@@ -5,7 +5,7 @@ use std::ops::Range;
 use std::sync::Arc;
 
 use plonky2_field::batch_util::batch_multiply_inplace;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 
 use crate::gates::selectors::UNUSED_SELECTOR;
diff --git a/plonky2/src/gates/gate_testing.rs b/plonky2/src/gates/gate_testing.rs
index a6e37adc..afe0c657 100644
--- a/plonky2/src/gates/gate_testing.rs
+++ b/plonky2/src/gates/gate_testing.rs
@@ -1,5 +1,5 @@
 use anyhow::{ensure, Result};
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 use plonky2_field::polynomial::{PolynomialCoeffs, PolynomialValues};
 use plonky2_util::log2_ceil;
diff --git a/plonky2/src/gates/interpolation.rs b/plonky2/src/gates/interpolation.rs
index 3bec5d1e..ca7cdea3 100644
--- a/plonky2/src/gates/interpolation.rs
+++ b/plonky2/src/gates/interpolation.rs
@@ -1,8 +1,8 @@
 use std::marker::PhantomData;
 use std::ops::Range;
 
-use plonky2_field::extension_field::algebra::PolynomialCoeffsAlgebra;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::algebra::PolynomialCoeffsAlgebra;
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::interpolation::interpolant;
 use plonky2_field::polynomial::PolynomialCoeffs;
 
diff --git a/plonky2/src/gates/low_degree_interpolation.rs b/plonky2/src/gates/low_degree_interpolation.rs
index 47f02be0..eece05b3 100644
--- a/plonky2/src/gates/low_degree_interpolation.rs
+++ b/plonky2/src/gates/low_degree_interpolation.rs
@@ -1,8 +1,8 @@
 use std::marker::PhantomData;
 use std::ops::Range;
 
-use plonky2_field::extension_field::algebra::PolynomialCoeffsAlgebra;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::algebra::PolynomialCoeffsAlgebra;
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 use plonky2_field::interpolation::interpolant;
 use plonky2_field::polynomial::PolynomialCoeffs;
@@ -382,7 +382,7 @@ impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F>
 #[cfg(test)]
 mod tests {
     use anyhow::Result;
-    use plonky2_field::extension_field::quadratic::QuadraticExtension;
+    use plonky2_field::extension::quadratic::QuadraticExtension;
     use plonky2_field::field_types::Field;
     use plonky2_field::goldilocks_field::GoldilocksField;
     use plonky2_field::polynomial::PolynomialCoeffs;
diff --git a/plonky2/src/gates/multiplication_extension.rs b/plonky2/src/gates/multiplication_extension.rs
index c5bfaef2..ab29bba7 100644
--- a/plonky2/src/gates/multiplication_extension.rs
+++ b/plonky2/src/gates/multiplication_extension.rs
@@ -1,7 +1,7 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
-use plonky2_field::extension_field::FieldExtension;
+use plonky2_field::extension::Extendable;
+use plonky2_field::extension::FieldExtension;
 
 use crate::gates::gate::Gate;
 use crate::gates::util::StridedConstraintConsumer;
diff --git a/plonky2/src/gates/noop.rs b/plonky2/src/gates/noop.rs
index 85375f01..fb5326bd 100644
--- a/plonky2/src/gates/noop.rs
+++ b/plonky2/src/gates/noop.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::gates::gate::Gate;
 use crate::hash::hash_types::RichField;
diff --git a/plonky2/src/gates/packed_util.rs b/plonky2/src/gates/packed_util.rs
index 7b420343..2df33666 100644
--- a/plonky2/src/gates/packed_util.rs
+++ b/plonky2/src/gates/packed_util.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::packable::Packable;
 use plonky2_field::packed_field::PackedField;
 
diff --git a/plonky2/src/gates/poseidon.rs b/plonky2/src/gates/poseidon.rs
index 72b54b2d..6e6d20b5 100644
--- a/plonky2/src/gates/poseidon.rs
+++ b/plonky2/src/gates/poseidon.rs
@@ -1,6 +1,6 @@
 use std::marker::PhantomData;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 
 use crate::gates::gate::Gate;
diff --git a/plonky2/src/gates/poseidon_mds.rs b/plonky2/src/gates/poseidon_mds.rs
index 0d52cc5c..00d55fea 100644
--- a/plonky2/src/gates/poseidon_mds.rs
+++ b/plonky2/src/gates/poseidon_mds.rs
@@ -1,9 +1,9 @@
 use std::marker::PhantomData;
 use std::ops::Range;
 
-use plonky2_field::extension_field::algebra::ExtensionAlgebra;
-use plonky2_field::extension_field::Extendable;
-use plonky2_field::extension_field::FieldExtension;
+use plonky2_field::extension::algebra::ExtensionAlgebra;
+use plonky2_field::extension::Extendable;
+use plonky2_field::extension::FieldExtension;
 use plonky2_field::field_types::Field;
 
 use crate::gates::gate::Gate;
diff --git a/plonky2/src/gates/public_input.rs b/plonky2/src/gates/public_input.rs
index 3e3a4d4a..baff421e 100644
--- a/plonky2/src/gates/public_input.rs
+++ b/plonky2/src/gates/public_input.rs
@@ -1,6 +1,6 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::packed_field::PackedField;
 
 use crate::gates::gate::Gate;
diff --git a/plonky2/src/gates/random_access.rs b/plonky2/src/gates/random_access.rs
index d99a591f..a20aa1a4 100644
--- a/plonky2/src/gates/random_access.rs
+++ b/plonky2/src/gates/random_access.rs
@@ -1,7 +1,7 @@
 use std::marker::PhantomData;
 
 use itertools::Itertools;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
 
diff --git a/plonky2/src/gates/reducing.rs b/plonky2/src/gates/reducing.rs
index c29b9ff9..31960b64 100644
--- a/plonky2/src/gates/reducing.rs
+++ b/plonky2/src/gates/reducing.rs
@@ -1,7 +1,7 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
-use plonky2_field::extension_field::FieldExtension;
+use plonky2_field::extension::Extendable;
+use plonky2_field::extension::FieldExtension;
 
 use crate::gates::gate::Gate;
 use crate::gates::util::StridedConstraintConsumer;
diff --git a/plonky2/src/gates/reducing_extension.rs b/plonky2/src/gates/reducing_extension.rs
index dd454a4b..2ae25059 100644
--- a/plonky2/src/gates/reducing_extension.rs
+++ b/plonky2/src/gates/reducing_extension.rs
@@ -1,7 +1,7 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
-use plonky2_field::extension_field::FieldExtension;
+use plonky2_field::extension::Extendable;
+use plonky2_field::extension::FieldExtension;
 
 use crate::gates::gate::Gate;
 use crate::gates::util::StridedConstraintConsumer;
diff --git a/plonky2/src/gates/selectors.rs b/plonky2/src/gates/selectors.rs
index dffeb987..fff5d967 100644
--- a/plonky2/src/gates/selectors.rs
+++ b/plonky2/src/gates/selectors.rs
@@ -1,6 +1,6 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::polynomial::PolynomialValues;
 
 use crate::gates::gate::{GateInstance, GateRef};
diff --git a/plonky2/src/hash/hashing.rs b/plonky2/src/hash/hashing.rs
index 9d043ea3..c903201b 100644
--- a/plonky2/src/hash/hashing.rs
+++ b/plonky2/src/hash/hashing.rs
@@ -1,6 +1,6 @@
 //! Concrete instantiation of a hash function.
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::hash::hash_types::RichField;
 use crate::hash::hash_types::{HashOut, HashOutTarget};
diff --git a/plonky2/src/hash/merkle_proofs.rs b/plonky2/src/hash/merkle_proofs.rs
index c4188271..a46040f9 100644
--- a/plonky2/src/hash/merkle_proofs.rs
+++ b/plonky2/src/hash/merkle_proofs.rs
@@ -1,5 +1,5 @@
 use anyhow::{ensure, Result};
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use serde::{Deserialize, Serialize};
 
 use crate::hash::hash_types::RichField;
diff --git a/plonky2/src/hash/merkle_tree.rs b/plonky2/src/hash/merkle_tree.rs
index 5fbc441c..0c6b223c 100644
--- a/plonky2/src/hash/merkle_tree.rs
+++ b/plonky2/src/hash/merkle_tree.rs
@@ -206,7 +206,7 @@ impl<F: RichField, H: Hasher<F>> MerkleTree<F, H> {
 #[cfg(test)]
 mod tests {
     use anyhow::Result;
-    use plonky2_field::extension_field::Extendable;
+    use plonky2_field::extension::Extendable;
 
     use super::*;
     use crate::hash::merkle_proofs::verify_merkle_proof;
diff --git a/plonky2/src/hash/poseidon.rs b/plonky2/src/hash/poseidon.rs
index 7f168855..4f41622c 100644
--- a/plonky2/src/hash/poseidon.rs
+++ b/plonky2/src/hash/poseidon.rs
@@ -1,7 +1,7 @@
 //! Implementation of the Poseidon hash function, as described in
 //! https://eprint.iacr.org/2019/458.pdf
 
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::{Field, PrimeField64};
 use unroll::unroll_for_loops;
 
diff --git a/plonky2/src/iop/challenger.rs b/plonky2/src/iop/challenger.rs
index 5b374834..8670f216 100644
--- a/plonky2/src/iop/challenger.rs
+++ b/plonky2/src/iop/challenger.rs
@@ -1,7 +1,7 @@
 use std::convert::TryInto;
 use std::marker::PhantomData;
 
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 
 use crate::hash::hash_types::RichField;
 use crate::hash::hash_types::{HashOut, HashOutTarget, MerkleCapTarget};
diff --git a/plonky2/src/iop/ext_target.rs b/plonky2/src/iop/ext_target.rs
index 8af1c6f7..31ef2159 100644
--- a/plonky2/src/iop/ext_target.rs
+++ b/plonky2/src/iop/ext_target.rs
@@ -1,7 +1,7 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::algebra::ExtensionAlgebra;
-use plonky2_field::extension_field::{Extendable, FieldExtension, OEF};
+use plonky2_field::extension::algebra::ExtensionAlgebra;
+use plonky2_field::extension::{Extendable, FieldExtension, OEF};
 use plonky2_field::field_types::Field;
 
 use crate::hash::hash_types::RichField;
diff --git a/plonky2/src/iop/generator.rs b/plonky2/src/iop/generator.rs
index 265a04ec..30fac52b 100644
--- a/plonky2/src/iop/generator.rs
+++ b/plonky2/src/iop/generator.rs
@@ -1,7 +1,7 @@
 use std::fmt::Debug;
 use std::marker::PhantomData;
 
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 
 use crate::hash::hash_types::{HashOut, HashOutTarget, RichField};
diff --git a/plonky2/src/iop/witness.rs b/plonky2/src/iop/witness.rs
index 60bb730b..03c9d0f8 100644
--- a/plonky2/src/iop/witness.rs
+++ b/plonky2/src/iop/witness.rs
@@ -1,7 +1,7 @@
 use std::collections::HashMap;
 
 use itertools::Itertools;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 
 use crate::fri::structure::{FriOpenings, FriOpeningsTarget};
diff --git a/plonky2/src/plonk/circuit_builder.rs b/plonky2/src/plonk/circuit_builder.rs
index b01a8fbb..4249e1ef 100644
--- a/plonky2/src/plonk/circuit_builder.rs
+++ b/plonky2/src/plonk/circuit_builder.rs
@@ -4,7 +4,7 @@ use std::time::Instant;
 
 use log::{debug, info, Level};
 use plonky2_field::cosets::get_unique_coset_shifts;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::fft::fft_root_table;
 use plonky2_field::field_types::Field;
 use plonky2_field::polynomial::PolynomialValues;
diff --git a/plonky2/src/plonk/circuit_data.rs b/plonky2/src/plonk/circuit_data.rs
index ee04b58e..67bf89cf 100644
--- a/plonky2/src/plonk/circuit_data.rs
+++ b/plonky2/src/plonk/circuit_data.rs
@@ -2,7 +2,7 @@ use std::collections::BTreeMap;
 use std::ops::{Range, RangeFrom};
 
 use anyhow::Result;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::fft::FftRootTable;
 
 use crate::field::field_types::Field;
diff --git a/plonky2/src/plonk/config.rs b/plonky2/src/plonk/config.rs
index cb6d9a9b..f55bad1f 100644
--- a/plonky2/src/plonk/config.rs
+++ b/plonky2/src/plonk/config.rs
@@ -1,7 +1,7 @@
 use std::fmt::Debug;
 
-use plonky2_field::extension_field::quadratic::QuadraticExtension;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::quadratic::QuadraticExtension;
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::goldilocks_field::GoldilocksField;
 use serde::{de::DeserializeOwned, Serialize};
 
diff --git a/plonky2/src/plonk/get_challenges.rs b/plonky2/src/plonk/get_challenges.rs
index e8fd3933..a8ca52e5 100644
--- a/plonky2/src/plonk/get_challenges.rs
+++ b/plonky2/src/plonk/get_challenges.rs
@@ -1,6 +1,6 @@
 use std::collections::HashSet;
 
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::polynomial::PolynomialCoeffs;
 
 use crate::fri::proof::{CompressedFriProof, FriChallenges, FriProof, FriProofTarget};
diff --git a/plonky2/src/plonk/plonk_common.rs b/plonky2/src/plonk/plonk_common.rs
index 42b9f90a..ef73707a 100644
--- a/plonky2/src/plonk/plonk_common.rs
+++ b/plonky2/src/plonk/plonk_common.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
 
diff --git a/plonky2/src/plonk/proof.rs b/plonky2/src/plonk/proof.rs
index 3f05ad0c..357c6836 100644
--- a/plonky2/src/plonk/proof.rs
+++ b/plonky2/src/plonk/proof.rs
@@ -1,5 +1,5 @@
 use anyhow::ensure;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use rayon::prelude::*;
 use serde::{Deserialize, Serialize};
 
diff --git a/plonky2/src/plonk/prover.rs b/plonky2/src/plonk/prover.rs
index 3c235a0a..18e21085 100644
--- a/plonky2/src/plonk/prover.rs
+++ b/plonky2/src/plonk/prover.rs
@@ -2,7 +2,7 @@ use std::mem::swap;
 
 use anyhow::ensure;
 use anyhow::Result;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::polynomial::{PolynomialCoeffs, PolynomialValues};
 use plonky2_field::zero_poly_coset::ZeroPolyOnCoset;
 use plonky2_util::{ceil_div_usize, log2_ceil};
diff --git a/plonky2/src/plonk/recursive_verifier.rs b/plonky2/src/plonk/recursive_verifier.rs
index 8db3b679..ecce34e1 100644
--- a/plonky2/src/plonk/recursive_verifier.rs
+++ b/plonky2/src/plonk/recursive_verifier.rs
@@ -1,4 +1,4 @@
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::hash::hash_types::{HashOutTarget, RichField};
 use crate::plonk::circuit_builder::CircuitBuilder;
diff --git a/plonky2/src/plonk/vanishing_poly.rs b/plonky2/src/plonk/vanishing_poly.rs
index 29facac0..06f5078d 100644
--- a/plonky2/src/plonk/vanishing_poly.rs
+++ b/plonky2/src/plonk/vanishing_poly.rs
@@ -1,5 +1,5 @@
 use plonky2_field::batch_util::batch_add_inplace;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 use plonky2_field::zero_poly_coset::ZeroPolyOnCoset;
 
diff --git a/plonky2/src/plonk/vars.rs b/plonky2/src/plonk/vars.rs
index 8c7b71e3..4fe99cd0 100644
--- a/plonky2/src/plonk/vars.rs
+++ b/plonky2/src/plonk/vars.rs
@@ -1,7 +1,7 @@
 use std::ops::Range;
 
-use plonky2_field::extension_field::algebra::ExtensionAlgebra;
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::algebra::ExtensionAlgebra;
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
 
diff --git a/plonky2/src/plonk/verifier.rs b/plonky2/src/plonk/verifier.rs
index e4dd41e6..6c83c211 100644
--- a/plonky2/src/plonk/verifier.rs
+++ b/plonky2/src/plonk/verifier.rs
@@ -1,5 +1,5 @@
 use anyhow::{ensure, Result};
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 
 use crate::fri::verifier::verify_fri_proof;
diff --git a/plonky2/src/util/partial_products.rs b/plonky2/src/util/partial_products.rs
index 9f9ebed4..cc09bbef 100644
--- a/plonky2/src/util/partial_products.rs
+++ b/plonky2/src/util/partial_products.rs
@@ -1,7 +1,7 @@
 use std::iter;
 
 use itertools::Itertools;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_util::ceil_div_usize;
 
diff --git a/plonky2/src/util/reducing.rs b/plonky2/src/util/reducing.rs
index 5747e197..1590d8a3 100644
--- a/plonky2/src/util/reducing.rs
+++ b/plonky2/src/util/reducing.rs
@@ -1,6 +1,6 @@
 use std::borrow::Borrow;
 
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
 use plonky2_field::polynomial::PolynomialCoeffs;
diff --git a/plonky2/src/util/serialization.rs b/plonky2/src/util/serialization.rs
index c0566010..74f10ff1 100644
--- a/plonky2/src/util/serialization.rs
+++ b/plonky2/src/util/serialization.rs
@@ -2,7 +2,7 @@ use std::collections::HashMap;
 use std::io::Cursor;
 use std::io::{Read, Result, Write};
 
-use plonky2_field::extension_field::{Extendable, FieldExtension};
+use plonky2_field::extension::{Extendable, FieldExtension};
 use plonky2_field::field_types::{Field64, PrimeField64};
 use plonky2_field::polynomial::PolynomialCoeffs;
 
diff --git a/starky/src/constraint_consumer.rs b/starky/src/constraint_consumer.rs
index ada28730..574c7e70 100644
--- a/starky/src/constraint_consumer.rs
+++ b/starky/src/constraint_consumer.rs
@@ -1,6 +1,6 @@
 use std::marker::PhantomData;
 
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::ext_target::ExtensionTarget;
diff --git a/starky/src/fibonacci_stark.rs b/starky/src/fibonacci_stark.rs
index 85683d09..4e0171b6 100644
--- a/starky/src/fibonacci_stark.rs
+++ b/starky/src/fibonacci_stark.rs
@@ -1,6 +1,6 @@
 use std::marker::PhantomData;
 
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
 use plonky2::hash::hash_types::RichField;
@@ -122,7 +122,7 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for FibonacciStar
 #[cfg(test)]
 mod tests {
     use anyhow::Result;
-    use plonky2::field::extension_field::Extendable;
+    use plonky2::field::extension::Extendable;
     use plonky2::field::field_types::Field;
     use plonky2::hash::hash_types::RichField;
     use plonky2::iop::witness::PartialWitness;
diff --git a/starky/src/get_challenges.rs b/starky/src/get_challenges.rs
index ceafa297..e84f5599 100644
--- a/starky/src/get_challenges.rs
+++ b/starky/src/get_challenges.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::polynomial::PolynomialCoeffs;
 use plonky2::fri::proof::{FriProof, FriProofTarget};
 use plonky2::gadgets::polynomial::PolynomialCoeffsExtTarget;
diff --git a/starky/src/permutation.rs b/starky/src/permutation.rs
index 6ee9ccb4..c401664b 100644
--- a/starky/src/permutation.rs
+++ b/starky/src/permutation.rs
@@ -2,7 +2,7 @@
 
 use itertools::Itertools;
 use plonky2::field::batch_util::batch_multiply_inplace;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
diff --git a/starky/src/proof.rs b/starky/src/proof.rs
index 287df783..c321b484 100644
--- a/starky/src/proof.rs
+++ b/starky/src/proof.rs
@@ -1,5 +1,5 @@
 use itertools::Itertools;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::fri::oracle::PolynomialBatch;
 use plonky2::fri::proof::{
     CompressedFriProof, FriChallenges, FriChallengesTarget, FriProof, FriProofTarget,
diff --git a/starky/src/prover.rs b/starky/src/prover.rs
index 75e63ea5..e148b195 100644
--- a/starky/src/prover.rs
+++ b/starky/src/prover.rs
@@ -2,7 +2,7 @@ use std::iter::once;
 
 use anyhow::{ensure, Result};
 use itertools::Itertools;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::field::packable::Packable;
 use plonky2::field::packed_field::PackedField;
diff --git a/starky/src/recursive_verifier.rs b/starky/src/recursive_verifier.rs
index 982c313a..7078fdea 100644
--- a/starky/src/recursive_verifier.rs
+++ b/starky/src/recursive_verifier.rs
@@ -2,7 +2,7 @@ use std::iter::once;
 
 use anyhow::{ensure, Result};
 use itertools::Itertools;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::fri::witness_util::set_fri_proof_target;
 use plonky2::hash::hash_types::RichField;
diff --git a/starky/src/stark.rs b/starky/src/stark.rs
index aad71c57..b81c1d08 100644
--- a/starky/src/stark.rs
+++ b/starky/src/stark.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed_field::PackedField;
 use plonky2::fri::structure::{
     FriBatchInfo, FriBatchInfoTarget, FriInstanceInfo, FriInstanceInfoTarget, FriOracleInfo,
diff --git a/starky/src/stark_testing.rs b/starky/src/stark_testing.rs
index 65ae64b0..704912b7 100644
--- a/starky/src/stark_testing.rs
+++ b/starky/src/stark_testing.rs
@@ -1,5 +1,5 @@
 use anyhow::{ensure, Result};
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::polynomial::{PolynomialCoeffs, PolynomialValues};
 use plonky2::hash::hash_types::RichField;
diff --git a/starky/src/vanishing_poly.rs b/starky/src/vanishing_poly.rs
index 122f0191..01b71231 100644
--- a/starky/src/vanishing_poly.rs
+++ b/starky/src/vanishing_poly.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
diff --git a/starky/src/verifier.rs b/starky/src/verifier.rs
index 06a6b3cc..2dc2fb46 100644
--- a/starky/src/verifier.rs
+++ b/starky/src/verifier.rs
@@ -2,7 +2,7 @@ use std::iter::once;
 
 use anyhow::{ensure, Result};
 use itertools::Itertools;
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::fri::verifier::verify_fri_proof;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/addition.rs b/system_zero/src/alu/addition.rs
index 5ce6bfb3..f9454779 100644
--- a/system_zero/src/alu/addition.rs
+++ b/system_zero/src/alu/addition.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/bitops.rs b/system_zero/src/alu/bitops.rs
index fb5effcd..4bbb5db9 100644
--- a/system_zero/src/alu/bitops.rs
+++ b/system_zero/src/alu/bitops.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/canonical.rs b/system_zero/src/alu/canonical.rs
index fb90eb0d..f14d0aaf 100644
--- a/system_zero/src/alu/canonical.rs
+++ b/system_zero/src/alu/canonical.rs
@@ -2,7 +2,7 @@
 //!
 //! See https://hackmd.io/NC-yRmmtRQSvToTHb96e8Q#Checking-element-validity
 
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/division.rs b/system_zero/src/alu/division.rs
index 9d578ee9..4b3294a1 100644
--- a/system_zero/src/alu/division.rs
+++ b/system_zero/src/alu/division.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/mod.rs b/system_zero/src/alu/mod.rs
index c3f3b859..f7bfb09e 100644
--- a/system_zero/src/alu/mod.rs
+++ b/system_zero/src/alu/mod.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/mul_add.rs b/system_zero/src/alu/mul_add.rs
index 1fb881d7..9b77e0b2 100644
--- a/system_zero/src/alu/mul_add.rs
+++ b/system_zero/src/alu/mul_add.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/rotate_shift.rs b/system_zero/src/alu/rotate_shift.rs
index e23f3f92..b4d3f591 100644
--- a/system_zero/src/alu/rotate_shift.rs
+++ b/system_zero/src/alu/rotate_shift.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/alu/subtraction.rs b/system_zero/src/alu/subtraction.rs
index 2f15da1c..d1b9c049 100644
--- a/system_zero/src/alu/subtraction.rs
+++ b/system_zero/src/alu/subtraction.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/core_registers.rs b/system_zero/src/core_registers.rs
index 7f32c0b7..44a9fc3c 100644
--- a/system_zero/src/core_registers.rs
+++ b/system_zero/src/core_registers.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/lookup.rs b/system_zero/src/lookup.rs
index 65175a31..e5850d1b 100644
--- a/system_zero/src/lookup.rs
+++ b/system_zero/src/lookup.rs
@@ -7,7 +7,7 @@
 use std::cmp::Ordering;
 
 use itertools::Itertools;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::{Field, PrimeField64};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
diff --git a/system_zero/src/permutation_unit.rs b/system_zero/src/permutation_unit.rs
index 430481da..52f85322 100644
--- a/system_zero/src/permutation_unit.rs
+++ b/system_zero/src/permutation_unit.rs
@@ -1,4 +1,4 @@
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 use plonky2::hash::hashing::SPONGE_WIDTH;
diff --git a/system_zero/src/system_zero.rs b/system_zero/src/system_zero.rs
index 85b9a7cf..4b3bce95 100644
--- a/system_zero/src/system_zero.rs
+++ b/system_zero/src/system_zero.rs
@@ -1,6 +1,6 @@
 use std::marker::PhantomData;
 
-use plonky2::field::extension_field::{Extendable, FieldExtension};
+use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed_field::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
 use plonky2::hash::hash_types::RichField;
diff --git a/u32/src/gadgets/arithmetic_u32.rs b/u32/src/gadgets/arithmetic_u32.rs
index 9ec0c29f..7a7731b1 100644
--- a/u32/src/gadgets/arithmetic_u32.rs
+++ b/u32/src/gadgets/arithmetic_u32.rs
@@ -5,7 +5,7 @@ use plonky2::iop::generator::{GeneratedValues, SimpleGenerator};
 use plonky2::iop::target::Target;
 use plonky2::iop::witness::{PartitionWitness, Witness};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::gates::add_many_u32::U32AddManyGate;
 use crate::gates::arithmetic_u32::U32ArithmeticGate;
diff --git a/u32/src/gadgets/multiple_comparison.rs b/u32/src/gadgets/multiple_comparison.rs
index 9e39f997..7a0b67a2 100644
--- a/u32/src/gadgets/multiple_comparison.rs
+++ b/u32/src/gadgets/multiple_comparison.rs
@@ -1,7 +1,7 @@
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::target::{BoolTarget, Target};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_util::ceil_div_usize;
 
 use super::arithmetic_u32::U32Target;
diff --git a/u32/src/gadgets/range_check.rs b/u32/src/gadgets/range_check.rs
index cfbcef57..fb6a9b1e 100644
--- a/u32/src/gadgets/range_check.rs
+++ b/u32/src/gadgets/range_check.rs
@@ -1,7 +1,7 @@
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::target::Target;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 
 use crate::gadgets::arithmetic_u32::U32Target;
 use crate::gates::range_check_u32::U32RangeCheckGate;
diff --git a/u32/src/gates/add_many_u32.rs b/u32/src/gates/add_many_u32.rs
index ef79a95f..839094ad 100644
--- a/u32/src/gates/add_many_u32.rs
+++ b/u32/src/gates/add_many_u32.rs
@@ -12,7 +12,7 @@ use plonky2::iop::witness::{PartitionWitness, Witness};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::circuit_data::CircuitConfig;
 use plonky2::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBase};
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_util::ceil_div_usize;
 
@@ -349,7 +349,7 @@ mod tests {
     use plonky2::hash::hash_types::HashOut;
     use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
     use plonky2::plonk::vars::EvaluationVars;
-    use plonky2_field::extension_field::quartic::QuarticExtension;
+    use plonky2_field::extension::quartic::QuarticExtension;
     use plonky2_field::field_types::Field;
     use plonky2_field::goldilocks_field::GoldilocksField;
     use rand::Rng;
diff --git a/u32/src/gates/arithmetic_u32.rs b/u32/src/gates/arithmetic_u32.rs
index 42604bd7..cf699488 100644
--- a/u32/src/gates/arithmetic_u32.rs
+++ b/u32/src/gates/arithmetic_u32.rs
@@ -16,7 +16,7 @@ use plonky2::plonk::vars::{
     EvaluationTargets, EvaluationVars, EvaluationVarsBase, EvaluationVarsBaseBatch,
     EvaluationVarsBasePacked,
 };
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
 
diff --git a/u32/src/gates/comparison.rs b/u32/src/gates/comparison.rs
index a731d91f..19f74010 100644
--- a/u32/src/gates/comparison.rs
+++ b/u32/src/gates/comparison.rs
@@ -15,7 +15,7 @@ use plonky2::plonk::vars::{
     EvaluationTargets, EvaluationVars, EvaluationVarsBase, EvaluationVarsBaseBatch,
     EvaluationVarsBasePacked,
 };
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::{Field, Field64};
 use plonky2_field::packed_field::PackedField;
 use plonky2_util::{bits_u64, ceil_div_usize};
diff --git a/u32/src/gates/range_check_u32.rs b/u32/src/gates/range_check_u32.rs
index bcc760cd..260cbb1b 100644
--- a/u32/src/gates/range_check_u32.rs
+++ b/u32/src/gates/range_check_u32.rs
@@ -10,7 +10,7 @@ use plonky2::iop::witness::{PartitionWitness, Witness};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::plonk_common::{reduce_with_powers, reduce_with_powers_ext_circuit};
 use plonky2::plonk::vars::{EvaluationTargets, EvaluationVars, EvaluationVarsBase};
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_util::ceil_div_usize;
 
@@ -210,7 +210,7 @@ mod tests {
     use plonky2::hash::hash_types::HashOut;
     use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
     use plonky2::plonk::vars::EvaluationVars;
-    use plonky2_field::extension_field::quartic::QuarticExtension;
+    use plonky2_field::extension::quartic::QuarticExtension;
     use plonky2_field::field_types::Field;
     use plonky2_field::goldilocks_field::GoldilocksField;
     use plonky2_util::ceil_div_usize;
diff --git a/u32/src/gates/subtraction_u32.rs b/u32/src/gates/subtraction_u32.rs
index ee06a164..5cd7866e 100644
--- a/u32/src/gates/subtraction_u32.rs
+++ b/u32/src/gates/subtraction_u32.rs
@@ -15,7 +15,7 @@ use plonky2::plonk::vars::{
     EvaluationTargets, EvaluationVars, EvaluationVarsBase, EvaluationVarsBaseBatch,
     EvaluationVarsBasePacked,
 };
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
 
@@ -337,7 +337,7 @@ mod tests {
     use plonky2::hash::hash_types::HashOut;
     use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
     use plonky2::plonk::vars::EvaluationVars;
-    use plonky2_field::extension_field::quartic::QuarticExtension;
+    use plonky2_field::extension::quartic::QuarticExtension;
     use plonky2_field::field_types::Field;
     use plonky2_field::field_types::PrimeField64;
     use plonky2_field::goldilocks_field::GoldilocksField;
diff --git a/waksman/src/gates/switch.rs b/waksman/src/gates/switch.rs
index ce9815d5..a0d4c6ce 100644
--- a/waksman/src/gates/switch.rs
+++ b/waksman/src/gates/switch.rs
@@ -16,7 +16,7 @@ use plonky2::plonk::vars::{
     EvaluationTargets, EvaluationVars, EvaluationVarsBase, EvaluationVarsBaseBatch,
     EvaluationVarsBasePacked,
 };
-use plonky2_field::extension_field::Extendable;
+use plonky2_field::extension::Extendable;
 use plonky2_field::field_types::Field;
 use plonky2_field::packed_field::PackedField;
 
diff --git a/waksman/src/permutation.rs b/waksman/src/permutation.rs
index 907c153f..a3842591 100644
--- a/waksman/src/permutation.rs
+++ b/waksman/src/permutation.rs
@@ -1,7 +1,7 @@
 use std::collections::BTreeMap;
 use std::marker::PhantomData;
 
-use plonky2::field::{extension_field::Extendable, field_types::Field};
+use plonky2::field::{extension::Extendable, field_types::Field};
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::generator::{GeneratedValues, SimpleGenerator};
 use plonky2::iop::target::Target;
diff --git a/waksman/src/sorting.rs b/waksman/src/sorting.rs
index 5f44f66d..53e3dcbf 100644
--- a/waksman/src/sorting.rs
+++ b/waksman/src/sorting.rs
@@ -1,7 +1,7 @@
 use std::marker::PhantomData;
 
 use itertools::izip;
-use plonky2::field::extension_field::Extendable;
+use plonky2::field::extension::Extendable;
 use plonky2::field::field_types::Field;
 use plonky2::gates::assert_le::AssertLessThanGate;
 use plonky2::hash::hash_types::RichField;