diff --git a/Cargo.toml b/Cargo.toml
index 6297a23..00342b8 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -1,7 +1,8 @@
 [workspace]
 members = [
     "polynomial",
-    "univariate-polynomial-iop-zerotest"
+    "univariate-polynomial-iop-zerotest",
+    "zk-plonky2-permutation-circuit"
 ]
 resolver = "2"
 
diff --git a/zk-plonky2-permutation-circuit/Cargo.toml b/zk-plonky2-permutation-circuit/Cargo.toml
new file mode 100644
index 0000000..3f30d95
--- /dev/null
+++ b/zk-plonky2-permutation-circuit/Cargo.toml
@@ -0,0 +1,10 @@
+[package]
+edition = "2021"
+name = "zk-plonky2-permutation-circuit"
+version = "0.1.0"
+
+[dependencies]
+anyhow = "1.0.81"
+plonky2 = "0.2.0"
+plonky2_field = "0.2.0"
+array_tool = "1.0.3"
diff --git a/zk-plonky2-permutation-circuit/src/custom_gates/mod.rs b/zk-plonky2-permutation-circuit/src/custom_gates/mod.rs
new file mode 100644
index 0000000..5a2a8f4
--- /dev/null
+++ b/zk-plonky2-permutation-circuit/src/custom_gates/mod.rs
@@ -0,0 +1 @@
+pub mod switch;
diff --git a/zk-plonky2-permutation-circuit/src/custom_gates/switch.rs b/zk-plonky2-permutation-circuit/src/custom_gates/switch.rs
new file mode 100644
index 0000000..08a538f
--- /dev/null
+++ b/zk-plonky2-permutation-circuit/src/custom_gates/switch.rs
@@ -0,0 +1,266 @@
+use array_tool::vec::Union;
+use std::marker::PhantomData;
+
+use plonky2::{
+    gates::gate::Gate,
+    hash::hash_types::RichField,
+    iop::{generator::{GeneratedValues, WitnessGenerator, WitnessGeneratorRef}, target::Target, wire::Wire, witness::{Witness, WitnessWrite, PartitionWitness}},
+    plonk::circuit_data::CommonCircuitData,
+    util::serialization::{Buffer, IoResult, Read, Write},
+};
+use plonky2_field::types::Field;
+use plonky2_field::extension::Extendable;
+
+/// A gate for conditionally swapping input values based on a boolean.
+#[derive(Copy, Clone, Debug)]
+pub struct SwitchGate<F: RichField + Extendable<D, Extension = F>, const D: usize> {
+    _phantom: PhantomData<F>,
+}
+
+impl<F: RichField + Extendable<D, Extension = F>, const D: usize> SwitchGate<F, D> {
+    pub fn new() -> Self {
+        Self{_phantom: PhantomData}
+    }
+
+    pub fn wire_switch_bool() -> usize {
+        0
+    }
+
+    pub fn wire_input_1() -> usize {
+        1
+    }
+
+    pub fn wire_input_2() -> usize {
+        2
+    }
+
+    pub fn wire_output_1() -> usize {
+        3
+    }
+
+    pub fn wire_output_2() -> usize {
+        4
+    }
+}
+
+impl<F: RichField + Extendable<D, Extension = F>, const D: usize> Gate<F, D> for SwitchGate<F, D> {
+    fn id(&self) -> String {
+        format!("{self:?}<D={D}>")
+    }
+
+    fn serialize(&self, dst: &mut Vec<u8>, common_data: &CommonCircuitData<F, D>) -> IoResult<()> {
+        dst.write_bool(false) // TODO: remove
+    }
+
+    fn deserialize(src: &mut Buffer, common_data: &CommonCircuitData<F, D>) -> IoResult<Self>
+    where
+        Self: Sized,
+    {
+        Ok(Self{_phantom: PhantomData})
+    }
+
+    fn eval_unfiltered(
+        &self,
+        vars: plonky2::plonk::vars::EvaluationVars<F, D>,
+    ) -> Vec<<F as Extendable<D>>::Extension> {
+        let mut constraints = Vec::with_capacity(4);
+        let switch_bool = vars.local_wires[Self::wire_switch_bool()];
+        let not_switch = F::Extension::ONE - switch_bool;
+
+        let input_1 = vars.local_wires[Self::wire_input_1()];
+        let input_2 = vars.local_wires[Self::wire_input_2()];
+        let output_1 = vars.local_wires[Self::wire_output_1()];
+        let output_2 = vars.local_wires[Self::wire_output_2()];
+
+        constraints.push(not_switch * (output_1 - input_1));
+        constraints.push(not_switch * (output_2 - input_2));
+
+        constraints.push(switch_bool * (output_2 - input_1));
+        constraints.push(switch_bool * (output_1 - input_2));
+        constraints
+    }
+
+    fn eval_unfiltered_circuit(
+        &self,
+        builder: &mut plonky2::plonk::circuit_builder::CircuitBuilder<F, D>,
+        vars: plonky2::plonk::vars::EvaluationTargets<D>,
+    ) -> Vec<plonky2::iop::ext_target::ExtensionTarget<D>> {
+        let mut constraints = Vec::with_capacity(4);
+
+        let one = builder.one_extension();
+
+        let switch_bool = vars.local_wires[Self::wire_switch_bool()];
+        let not_switch = builder.sub_extension(one, switch_bool);
+
+        let input_1 = vars.local_wires[Self::wire_input_1()];
+        let input_2 = vars.local_wires[Self::wire_input_2()];
+        let output_1 = vars.local_wires[Self::wire_output_1()];
+        let output_2 = vars.local_wires[Self::wire_output_2()];
+
+        constraints
+            .push(builder.mul_extension(not_switch, builder.sub_extension(input_1, output_1)));
+        constraints
+            .push(builder.mul_extension(not_switch, builder.sub_extension(input_2, output_2)));
+
+        constraints
+            .push(builder.mul_extension(switch_bool, builder.sub_extension(input_1, output_2)));
+        constraints
+            .push(builder.mul_extension(switch_bool, builder.sub_extension(input_2, output_1)));
+
+        constraints
+    }
+
+    fn generators(&self, row: usize, local_constants: &[F]) -> Vec<WitnessGeneratorRef<F, D>> {
+        // unimplemented!()
+        let g = Box::new(SwitchGenerator::<F, D> {
+            row,
+            gate: *self,
+        });
+        vec![g]
+    }
+
+    fn num_wires(&self) -> usize {
+        5
+    }
+
+    fn num_constants(&self) -> usize {
+        0
+    }
+
+    fn degree(&self) -> usize {
+        2
+    }
+
+    fn num_constraints(&self) -> usize {
+        4
+    }
+}
+
+#[derive(Debug)]
+struct SwitchGenerator<F: RichField + Extendable<D, Extension = F>, const D: usize> {
+    row: usize,
+    gate: SwitchGate<F, D>,
+}
+
+impl<F: RichField + Extendable<D, Extension = F>, const D: usize> SwitchGenerator<F, D> {
+    /// List of wire targets for inputs and outputs
+    fn dependencies_inputs_outputs(&self) -> Vec<Target> {
+        let local_target = |column| Target::wire(self.row, column);
+
+        let mut deps = Vec::new();
+
+        deps.push(local_target(SwitchGate::wire_first_input()));
+        deps.push(local_target(SwitchGate::wire_second_input()));
+        deps.push(local_target(SwitchGate::wire_first_output()));
+        deps.push(local_target(SwitchGate::wire_second_output()));
+
+        deps
+    }
+
+    /// List of wire targets for inputs and switching boolean
+    fn dependencies_switch_inputs(&self) -> Vec<Target> {
+        let local_target = |column| Target::wire(self.row, column);
+
+        let mut deps = Vec::new();
+
+        deps.push(local_target(SwitchGate::wire_first_input()));
+        deps.push(local_target(SwitchGate::wire_second_input()));
+        deps.push(local_target(SwitchGate::wire_switch_bool()));
+
+        deps
+    }
+
+    /// Run when all input and output wires are present
+    fn set_switch_wire(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
+        let get_local_wire = |column| {
+            witness.get_wire(Wire {
+                row: self.row,
+                column,
+            })
+        };
+        let switch_bool_wire = Wire {
+            row: self.row,
+            column: SwitchGate::wire_switch_bool(),
+        };
+
+        let mut input_1 = get_local_wire(SwitchGate::wire_input_1());
+        let mut input_2 = get_local_wire(SwitchGate::wire_input_2());
+        let mut output_1 = get_local_wire(SwitchGate::wire_output_1());
+        let mut output_2 = get_local_wire(SwitchGate::wire_output_2());
+
+        if input_1 == output_1 && input_2 == output_2 {
+            out_buffer.set_wire(switch_bool_wire, F::ZERO);
+        } else if input_1 == output_2 && input_2 == output_1 {
+            out_buffer.set_wire(switch_bool_wire, F::ONE);
+        } else {
+            panic!("No permutation from given inputs to given outputs");
+        }
+    }
+
+    /// Run when only inputs and switching boolean is available
+    fn set_output_wires(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
+        let get_local_wire = |column| {
+            witness.get_wire(Wire {
+                row: self.row,
+                column,
+            })
+        };
+        let switch_bool_wire = Wire {
+            row: self.row,
+            column: SwitchGate::wire_switch_bool(),
+        };
+
+        let mut input_1 = get_local_wire(SwitchGate::wire_input_1());
+        let mut input_2 = get_local_wire(SwitchGate::wire_input_2());
+        let mut output_1 = get_local_wire(SwitchGate::wire_output_1());
+        let mut output_2 = get_local_wire(SwitchGate::wire_output_2());
+
+        let (expected_output_1, expected_output_2) = if switch_bool_wire == F::ZERO {
+            (input_1, input_2)
+        } else if switch_bool_wire == F::ONE {
+            (input_2, input_1)
+        } else {
+            panic!("Invalid switch bool value");
+        };
+
+        out_buffer.set_wire(output_1, expected_output_1);
+        out_buffer.set_wire(output_2, expected_output_2);
+    }
+}
+
+impl<F: RichField + Extendable<D>, const D: usize> WitnessGenerator<F, D> for SwitchGenerator<F, D> {
+    fn id(&self) -> String {
+        format!("{self:?}<D={D}>")
+    }
+
+    fn serialize(&self, dst: &mut Vec<u8>, common_data: &CommonCircuitData<F, D>) -> IoResult<()> {
+        dst.write_usize(self.row)
+    }
+
+    fn deserialize(src: &mut Buffer, common_data: &CommonCircuitData<F, D>) -> IoResult<Self>
+        where
+            Self: Sized {
+        Ok(Self{row: src.read_bool().unwrap(), gate: SwitchGate::new()})
+    }
+    /// Register the different columns to watch
+    fn watch_list(&self) -> Vec<Target> {
+        self.dependencies_inputs_outputs()
+            .union(self.dependencies_switch_inputs())
+    }
+
+    /// Figure out which columns change and set the remaining
+    /// Can work in two modes:
+    /// 1. If input and switch wires are pre-populated
+    /// 2. If input and output wires are pre-populated
+    fn run(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) -> bool {
+        if witness.contains_all(&self.dependencies_switch_inputs()) {
+            self.set_output_wires(witness, out_buffer);
+            true
+        } else if witness.contains_all(&self.dependencies_inputs_outputs()) {
+            self.set_switch_wire(witness, out_buffer);
+            true
+        } else {
+            false
+        }
+    }
+}
diff --git a/zk-plonky2-permutation-circuit/src/lib.rs b/zk-plonky2-permutation-circuit/src/lib.rs
new file mode 100644
index 0000000..bacdca9
--- /dev/null
+++ b/zk-plonky2-permutation-circuit/src/lib.rs
@@ -0,0 +1,68 @@
+mod custom_gates;
+
+use custom_gates::switch::SwitchGate;
+use plonky2::hash::hash_types::RichField;
+use plonky2::iop::target::Target;
+use plonky2::plonk::circuit_builder::CircuitBuilder;
+use plonky2_field::extension::Extendable;
+
+// Inspired by https://github.com/0xPolygonZero/plonky2-waksman/blob/main/src/permutation.rs
+
+/// Assert that two set of targets are permutation of each other
+pub fn assert_permutation_circuit<F: RichField + Extendable<D>, const D: usize>(
+    builder: &mut CircuitBuilder<F, D>,
+    a: Vec<Target>,
+    b: Vec<Target>,
+) {
+    assert_eq!(
+        a.len(),
+        b.len(),
+        "Permutation must have same number of inputs and outputs"
+    );
+
+    match a.len() {
+        // Two empty lists are permutations of one another, trivially.
+        0 => (),
+        // Two singleton lists are permutations of one another as long as their items are equal.
+        1 => {
+            builder.connect(a[0], b[0]);
+        }
+        2 => assert_permutation_2x2_circuit(builder, a[0], a[1], b[0], b[1]),
+        // For larger lists, we recursively use two smaller permutation networks.
+        _ => unimplemented!(), // assert_permutation_helper_circuit(builder, a, b),
+    }
+}
+
+/// Assert that [a1, a2] is a permutation of [b1, b2].
+fn assert_permutation_2x2_circuit<F: RichField + Extendable<D>, const D: usize>(
+    builder: &mut CircuitBuilder<F, D>,
+    a1: Target,
+    a2: Target,
+    b1: Target,
+    b2: Target,
+) {
+    let (_switch, out_1, out_2) = create_switch_circuit(builder, a1, a2);
+    // Add constraints
+    builder.connect(b1, out_1);
+    builder.connect(b2, out_2);
+}
+
+/// Given two input wire chunks, add a new switch to the circuit (by adding one copy to a switch
+/// gate). Returns the wire for the switch boolean, and the two output wire chunks.
+fn create_switch_circuit<F: RichField + Extendable<D>, const D: usize>(
+    builder: &mut CircuitBuilder<F, D>,
+    a1: Target,
+    a2: Target,
+) -> (Target, Target, Target) {
+    let gate = SwitchGate::new();
+    let (row, _next_copy) = builder.find_slot(gate, &vec![], &[]);
+
+    builder.connect(a1, Target::wire(row, SwitchGate::wire_input_1()));
+    builder.connect(a2, Target::wire(row, SwitchGate::wire_input_2()));
+
+    (
+        Target::wire(row, SwitchGate::wire_switch_bool()),
+        Target::wire(row, SwitchGate::wire_output_1()),
+        Target::wire(row, SwitchGate::wire_output_2()),
+    )
+}